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Professor Igor Shparlinski

Professor Igor Shparlinski

Professor
Science
School of Mathematics & Statistics

More information is available from http://web.maths.unsw.edu.au/~igorshparlinski/
E-mail
igor.shparlinski@unsw.edu.au
  • Books | 2006
    Abe M; Aoki K; Ateniese G; Avanzi R; Beerliov谩 Z; Billet O; Biryukov A; Blake I; Boyd C; Brier E; Castiglione A; Cha J; Chan A; Chen L; Cho K; Contini S; D'Arco P; Ding J; Doche C; Dunkelman O; Fitzi M; Fouque PA; Fournier JJA; Fujisaki K; Fujisaki E; Furukawa J; Galindo D; Halevi S; Handschuh H; Heneghan C; Holenstein T; Hoshino F; Hwang YH; Isshiki T; Jochemsz E; Joux A; Juels A; Jutla C; Kiayias A; Kikuchi H; Kobayashi T; Kohno T; Krawczyk H; Kumar S; Lange T; Lee JW; Masucci B; May A; Mihaljevic M; Minematsu K; Monrose F; Montague P; Myers S; Naccache D; Nicolosi A; Obana S; Okazaki S; Okeya K; Olivier F; Oyono R; Page D; Park JH; Peng K; Pietrzak K; Raub D; Sakai Y; Sakurai K; Schindler W; Seo JW; Shin JH; Shparlinski I; Steinfeld R; Szydlo M; Kalai YT; Teranishi I; Tokita T; Tunstall M; Vercauteren F; Villegas K; Walfish S; Wang H; Wang X; Warinschi B; De Weger B; Wolf C; Yampolskiy A; Yang YH; Yin YL; Yoon J; Pointcheval D, 2006, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface
    Books | 2003
    Everest G; van der Poorten A; Shparlinski I; Ward T, 2003, Recurrence Sequences, American Mathematical Society,
    Books | 2001
    Bozta艧 S; Shparlinski IE, 2001, Preface
    Books | 1999
    Konyagin S; Shparlinski I, 1999, Character Sums with Exponential Functions and their Applications, Cambridge University Press,
    Books | 1999
    Shparlinski I, 1999, Number Theoretic Methods in Cryptography, Birkh盲user Basel,
    Books | 1999
    Shparlinski IE, 1999, Finite Fields: Theory and Computation, Springer Netherlands,
    Books | 1992
    Shparlinski IE, 1992, Computational and Algorithmic Problems in Finite Fields, Springer Netherlands,
  • Book Chapters | 2025
    Shparlinski I, 2025, 'Computational Diffie-Hellman Problem', in Encyclopedia of Cryptography Security and Privacy Third Edition, pp. 403 - 407,
    Book Chapters | 2022
    Konyagin SV; Shparlinski IE; Vyugin IV, 2022, 'Polynomial equations in subgroups and applications', in Analysis at Large Dedicated to the Life and Work of Jean Bourgain, pp. 273 - 297,
    Book Chapters | 2020
    Cools R; Kuo FY; Sloan IH; Nuyens D, 2020, 'Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters', in Brenner SC; Shparlinski I; Shu C-W; Szyld D (ed.), 75 Years of Mathematics of Computation, American Mathematical Society, pp. 93 - 113,
    Book Chapters | 2018
    Kaszian J; Moree P; Shparlinski I, 2018, 'Periodic structure of the exponential pseudorandom number generator', in Applied Algebra and Number Theory, Cambridge University Press, pp. 190 - 203
    Book Chapters | 2017
    Ostafe A; Shparlinski IE, 2017, 'Orbits of algebraic dynamical systems in subgroups and subfields', in Elsholtz C; Grabner P (ed.), Number Theory - Diophantine Problems, Uniform Distribution and Applications: Festschrift in Honour of Robert F. Tichy's 60th Birthday, Springer, pp. 347 - 368,
    Book Chapters | 2014
    Kaszi谩n J; Moree P; Shparlinski IE, 2014, 'Periodic structure of the exponential pseudorandom number generator', in Applied Algebra and Number Theory, Cambridge University Press, pp. 190 - 203,
    Book Chapters | 2013
    Shparlinski IE, 2013, 'Additive Combinatorics over Finite Fields: New Results and Applications', in Finite Fields and Their Applications, DE GRUYTER, pp. 233 - 272,
    Book Chapters | 2011
    Cillerueloa J; Lucab F; Shparlinskic IE, 2011, 'Power values of palindromes', in Frontiers of Combinatorics and Number Theory, pp. 103 - 110
    Book Chapters | 2011
    Shparlinski I, 2011, 'Computational Diffie-Hellman Problem', in Encyclopedia of Cryptography and Security, Springer US, pp. 240 - 244,
    Book Chapters | 2007
    Murty R; Shparlinski I, 2007, 'GROUP STRUCTURE OF ELLIPTIC CURVES OVER FINITE FIELDS AND APPLICATIONS', in Garcia A; Stichtenoth H (ed.), TOPICS IN GEOMETRY, CODING THEORY AND CRYPTOGRAPHY, SPRINGER, pp. 167 - 198,
    Book Chapters | 2003
    Shparlinski I, 2003, '1/M Generator', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 279 - 282,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Approximation of the Discrete Logarithm Modulo p 鈥 1', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 123 - 128,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Approximation of the Discrete Logarithm Modulo p', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 109 - 122,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Approximation of the Discrete Logarithm by Boolean Functions', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 129 - 141,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Approximation of the Discrete Logarithm by Real Polynomials', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 143 - 156,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Arithmetic Functions', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 67 - 81,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Basic Notation and Definitions', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 17 - 26,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Bit Security of NTRU', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 223 - 229,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Bit Security of the Diffie鈥擧ellman Secret Key', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 189 - 194,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Bit Security of the RSA Encryption and the Shamir Message Passing Scheme', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 211 - 215,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Bit Security of the XTR and LUC Secret Keys', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 217 - 221,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Boolean Complexity of the Diffie-Hellman Secret Key', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 179 - 188,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Complexity Theory', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 103 - 106,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Concluding Remarks and Open Questions', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 341 - 365,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Distribution and Discrepancy', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 61 - 65,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Distribution of the ElGamal Signature', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 207 - 210,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Distribution of the RSA and Exponential Pairs', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 231 - 237,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Exponential Sums', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 37 - 60,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Exponentiation and Inversion with Precomputation', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 239 - 245,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Introduction', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 1 - 14,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Inversive, Polynomial and Quadratic Exponential Generators', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 283 - 294,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Lattices and the Hidden Number Problem', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 83 - 102,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Naor鈥擱eingold Function', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 271 - 277,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Polynomial Approximation and Arithmetic Complexity of the Diffie-Hellman Secret Key', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 159 - 177,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Polynomial Approximation, Permanents and Noisy Exponentiation in Finite Fields', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 325 - 332,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Polynomials and Recurrence Sequences', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 27 - 36,
    Book Chapters | 2003
    Shparlinski I, 2003, 'RSA and Blum鈥擝lum鈥擲hub Generators', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 249 - 270,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Security Against the Cycling Attack on the RSA and Timed-release Crypto', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 197 - 200,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Special Polynomials and Boolean Functions', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 333 - 339,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Square-Freeness Testing and Other Number-Theoretic Problems', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 303 - 308,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Subset Sum Generators', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 295 - 299,
    Book Chapters | 2003
    Shparlinski I, 2003, 'The Insecurity of the Digital Signature Algorithm with Partially Known Nonces', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 201 - 206,
    Book Chapters | 2003
    Shparlinski I, 2003, 'Trade-off Between the Boolean and Arithmetic Depths of Modulo p Functions', in Cryptographic Applications of Analytic Number Theory, Birkh盲user Basel, pp. 309 - 323,
    Book Chapters | 2002
    Shparlinski IE, 2002, 'EXPONENTIAL SUMS IN CODING THEORY, CRYPTOLOGY AND ALGORITHMS', in Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, CO-PUBLISHED WITH SINGAPORE UNIVERSITY PRESS, pp. 323 - 383,
    Book Chapters | 2001
    von zur Gathen J; Shparlinski I, 2001, 'Gau脽 Periods in Finite Fields', in Finite Fields and Applications, Springer Berlin Heidelberg, pp. 162 - 177,
    Book Chapters | 1999
    Friedlander JB; Lieman D; Shparlinski IE, 1999, 'On the Distribution of the RSA Generator', in Sequences and their Applications, Springer London, pp. 205 - 212,
    Book Chapters | 1996
    Mullen GL; Shparlinski I, 1996, 'Open problems and conjectures in finite fields', in Finite Fields and Applications, Cambridge University Press, pp. 243 - 268,
    Book Chapters | 1996
    Shparlinski I, 1996, 'Approximate constructions in finite fields', in Finite Fields and Applications, Cambridge University Press, pp. 313 - 332,
    Book Chapters | 1995
    Shparlinski IE, 1995, 'On Some Characteristics of Uniformity of Distribution and Their Applications', in Computational Algebra and Number Theory, Springer Netherlands, pp. 227 - 241,
    Book Chapters |
    Shparlinski IE, 'Diffie鈥揌ellman Problem', in Encyclopedia of Cryptography and Security, Springer US, pp. 154 - 158,
  • Edited Books | 2020
    Shparlinski I; Brenner SC; Shu C-W; Szyld DB, (eds.), 2020, 75 Years of Mathematics of Computation, American Mathematical Society,
  • Journal articles | 2026
    Koh D; Shparlinski IE, 2026, 'Mean value theorems for short rational exponential sums', Finite Fields and their Applications, 110,
    Journal articles | 2025
    Afifurrahman M; Kuperberg V; Ostafe A; Shparlinski IE, 2025, 'Statistics of ranks, determinants and characteristic polynomials of rational matrices', Forum Mathematicum, 37, pp. 1259 - 1289,
    Journal articles | 2025
    Banks W; Shparlinski IE, 2025, 'On the Greatest Common Divisor of Integer Parts of Polynomials', Michigan Mathematical Journal, 75, pp. 451 - 469,
    Journal articles | 2025
    Blomer V; Risager MS; Shparlinski IE, 2025, 'Triple sums of Kloosterman sums and the discrepancy of modular inverses', Journal of the London Mathematical Society, 112,
    Journal articles | 2025
    B茅rczes A; Hajdu L; Ostafe A; Shparlinski IE, 2025, 'Multiplicative dependence in linear recurrence sequences', Canadian Mathematical Bulletin,
    Journal articles | 2025
    Fouvry 脡; Shparlinski IE; Xi P, 2025, 'Estimates for trilinear and quadrilinear character sums', Revista Matematica Iberoamericana, 41, pp. 1925 - 1956,
    Journal articles | 2025
    Garaev MZ; Pardo JC; Shparlinski IE, 2025, 'BINARY and TERNARY CONGRUENCES INVOLVING INTERVALS and SETS MODULO A PRIME', Bulletin of the Australian Mathematical Society,
    Journal articles | 2025
    Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2025, 'ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS', Journal of the Institute of Mathematics of Jussieu, 24, pp. 1765 - 1806,
    Journal articles | 2025
    Klurman O; Shparlinski IE; Ter盲v盲inen J, 2025, 'On Artin's conjecture on average and short character sums', Bulletin of the London Mathematical Society, 57, pp. 2429 - 2443,
    Journal articles | 2025
    Kurlberg P; Ostafe A; Rudnick Z; Shparlinski IE, 2025, 'On Quantum Ergodicity for Higher Dimensional Cat Maps', Communications in Mathematical Physics, 406,
    Journal articles | 2025
    M茅rai L; Shparlinski IE, 2025, 'Number of characteristic polynomials of matrices with bounded height', Linear Algebra and Its Applications, 712, pp. 1 - 8,
    Journal articles | 2025
    Perucca A; Shparlinski IE, 2025, 'Uniform bounds for the density in Artin's conjecture on primitive roots', Bulletin of the London Mathematical Society, 57, pp. 978 - 991,
    Journal articles | 2025
    Shkredov ID; Shparlinski IE, 2025, 'On the determinants of matrices with elements from arbitrary sets', Mathematika, 71,
    Journal articles | 2025
    Shparlinski IE; Voloch JF, 2025, 'ON THE WARING PROBLEM WITH DICKSON POLYNOMIALS MODULO A PRIME', New Zealand Journal of Mathematics, 56, pp. 1 - 13,
    Journal articles | 2025
    Shparlinski IE; Wijaya LP, 2025, 'On nonzero coefficients of binary cyclotomic polynomials', Journal of Number Theory, 271, pp. 246 - 258,
    Journal articles | 2025
    Shparlinski IE, 2025, 'Sums of multidimensional Kloosterman sums', Periodica Mathematica Hungarica, 90, pp. 1 - 6,
    Journal articles | 2024
    Baker RC; Chen C; Shparlinski IE, 2024, 'Bounds on the norms of maximal operators on Weyl sums', Journal of Number Theory, 256, pp. 329 - 353,
    Journal articles | 2024
    Borda B; Munsch M; Shparlinski IE, 2024, 'Pointwise and correlation bounds on Dedekind sums over small subgroups', Research in Number Theory, 10, pp. 28 - 28,
    Journal articles | 2024
    Brandes J; Chen C; Shparlinski I, 2024, 'Local mean value estimates for Weyl sums', Revista Matematica Iberoamericana, 40, pp. 2095 - 2134,
    Journal articles | 2024
    Browning TD; Shparlinski IE, 2024, 'Square-free values of random polynomials', Journal of Number Theory, 261, pp. 220 - 240,
    Journal articles | 2024
    Bulinski K; Ostafe A; Shparlinski I, 2024, 'Counting embeddings of free groups into $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups', ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, pp. 12,
    Journal articles | 2024
    Bulinski K; Shparlinski IE, 2024, 'Counting elements of the congruence subgroup', Canadian Mathematical Bulletin, 67, pp. 955 - 969,
    Journal articles | 2024
    Dartyge C; Martin B; Rivat J; Shparlinski IE; Swaenepoel C, 2024, 'Reversible primes', Journal of the London Mathematical Society, 109, pp. 1 - 38,
    Journal articles | 2024
    Dartyge C; Martin B; Rivat J; Shparlinski IE; Swaenepoel C, 2024, 'Reversible primes', Journal of the London Mathematical Society, 109,
    Journal articles | 2024
    Dietmann R; Ostafe A; Shparlinski IE, 2024, 'Discriminants of fields generated by polynomials of given height', Israel Journal of Mathematics, 260, pp. 73 - 103,
    Journal articles | 2024
    Dubickas A; Sha M; Shparlinski IE, 2024, 'Euclidean minima of algebraic number fields', Archiv Der Mathematik, 122, pp. 405 - 414,
    Journal articles | 2024
    El Abdalaoui H; Shparlinski IE; Steiner RS, 2024, 'Chowla and Sarnak conjectures for Kloosterman sums', Mathematische Nachrichten, 297, pp. 209 - 228,
    Journal articles | 2024
    Garaev MZ; Rudnick Z; Shparlinski IE, 2024, 'On a family of sparse exponential sums', Mathematische Nachrichten, 297, pp. 4214 - 4231,
    Journal articles | 2024
    Garaev MZ; Shparlinski IE, 2024, 'On some congruences and exponential sums', Finite Fields and their Applications, 98,
    Journal articles | 2024
    Hauck M; Shparlinski IE, 2024, 'Smooth numbers with few nonzero binary digits', Canadian Mathematical Bulletin, 67, pp. 74 - 89,
    Journal articles | 2024
    Iyer S; Shparlinski I, 2024, 'Character sums over elements of extensions of finite fields with restricted coordinates', Finite Fields and Their Applications, 93, pp. 1 - 10,
    Journal articles | 2024
    Iyer S; Shparlinski IE, 2024, 'Character sums over elements of extensions of finite fields with restricted coordinates', Finite Fields and Their Applications, 93, pp. 102335 - 102335,
    Journal articles | 2024
    Kerr B; Mello J; Shparlinski IE, 2024, 'An effective local-global principle and additive combinatorics in finite fields', Journal D Analyse Mathematique, 152, pp. 109 - 135,
    Journal articles | 2024
    Kerr B; Mohammad A; Shparlinski IE, 2024, 'ADDITIVE ENERGY OF POLYNOMIAL IMAGES', SIAM Journal on Discrete Mathematics, 38, pp. 2163 - 2180,
    Journal articles | 2024
    Mohammadi A; Ostafe A; Shparlinski IE, 2024, 'On some matrix counting problems', Journal of the London Mathematical Society, 110,
    Journal articles | 2024
    M茅rai L; Shparlinski IE; Winterhof A, 2024, 'Character sums over sparse elements of finite fields', Bulletin of the London Mathematical Society, 56, pp. 1488 - 1510,
    Journal articles | 2024
    Ostafe A; Shparlinski IE; Voloch JF, 2024, 'Weil Sums over Small Subgroups', Mathematical Proceedings of the Cambridge Philosophical Society, 176, pp. 39 - 53,
    Journal articles | 2024
    Shkredov ID; Shparlinski IE; Zaharescu A, 2024, 'On the distribution of modular square roots of primes', Mathematische Zeitschrift, 306,
    Journal articles | 2024
    Shparlinski IE; Thuswaldner JM, 2024, 'Weyl Sums over Integers with Digital Restrictions', Michigan Mathematical Journal, 74, pp. 189 - 214,
    Journal articles | 2024
    Shparlinski IE, 2024, 'ON QUADRATIC FIELDS GENERATED BY POLYNOMIALS', Bulletin of the Australian Mathematical Society, 109, pp. 476 - 485,
    Journal articles | 2024
    Shparlinski IE, 2024, 'Rational numbers with small denominators in short intervals', Archiv Der Mathematik, 122, pp. 629 - 637,
    Journal articles | 2023
    Bag N; Shparlinski IE, 2023, 'Bounds on bilinear sums of Kloosterman sums', Journal of Number Theory, 242, pp. 102 - 111,
    Journal articles | 2023
    Brandes J; Shparlinski IE, 2023, 'Two-dimensional Weyl sums failing square-root cancellation along lines', Arkiv for Matematik, 61, pp. 267 - 276,
    Journal articles | 2023
    Chen C; Kerr B; Maynard J; Shparlinski IE, 2023, 'Metric theory of Weyl sums', Mathematische Annalen, 385, pp. 309 - 355,
    Journal articles | 2023
    Chen C; Shparlinski IE, 2023, 'Hybrid Bounds on Two-Parametric Families of Weyl Sums Along Smooth Curves', Michigan Mathematical Journal, 73, pp. 123 - 139,
    Journal articles | 2023
    D膮browski A; Pomyka艂a J; Shparlinski IE, 2023, 'On oracle factoring of integers', Journal of Complexity, 76,
    Journal articles | 2023
    Fouvry 脡; Shparlinski IE, 2023, 'On character sums with determinants', Science China Mathematics, 66, pp. 2693 - 2714,
    Journal articles | 2023
    Garaev MZ; Shparlinski IE, 2023, 'On the distribution of modular inverses from short intervals', Mathematika, 69, pp. 1183 - 1194,
    Journal articles | 2023
    Kaminski M; Shparlinski IE; Waldschmidt M, 2023, 'On sets of linear forms of maximal complexity', Computational Complexity, 32,
    Journal articles | 2023
    Kerr B; Shparlinski IE; Wu X; Xi P, 2023, 'Bounds on bilinear forms with Kloosterman sums', Journal of the London Mathematical Society, 108, pp. 578 - 621,
    Journal articles | 2023
    Konyagin SV; Sha M; Shparlinski IE; Stewart CL, 2023, 'On the distribution of multiplicatively dependent vectors', Mathematical Research Letters, 30, pp. 509 - 540,
    Journal articles | 2023
    Mans B; Sha M; Shparlinski IE; Sutantyo D, 2023, 'FUNCTIONAL GRAPHS OF FAMILIES OF QUADRATIC POLYNOMIALS', Mathematics of Computation, 92, pp. 2307 - 2331,
    Journal articles | 2023
    M茅rai L; Shparlinski IE, 2023, 'DISTRIBUTION OF RECURSIVE MATRIX PSEUDORANDOM NUMBER GENERATOR MODULO PRIME POWERS', Mathematics of Computation, 93, pp. 1355 - 1370,
    Journal articles | 2023
    Ostafe A; Shparlinski IE; Voloch JF, 2023, 'Equations and Character Sums with Matrix Powers, Kloosterman Sums over Small Subgroups, and Quantum Ergodicity', International Mathematics Research Notices, 2023, pp. 14196 - 14238,
    Journal articles | 2023
    Shparlinski IE, 2023, 'Fixed points of the subset sum pseudorandom number generators', Designs Codes and Cryptography, 91, pp. 2473 - 2479,
    Journal articles | 2023
    Shparlinski IE, 2023, 'On the Glasner property for matrices with polynomial entries', Journal of Number Theory, 242, pp. 522 - 531,
    Journal articles | 2023
    Shparlinski IE, 2023, 'On the number of Diophantine m-tuples in finite fields', Finite Fields and their Applications, 90, pp. 102241,
    Journal articles | 2022
    Bagshaw C; Shparlinski IE, 2022, 'Energy bounds, bilinear forms and their applications in function fields', Finite Fields and their Applications, 82,
    Journal articles | 2022
    Baker RC; Chen C; Shparlinski IE, 2022, 'Large Weyl sums and Hausdorff dimension', Journal of Mathematical Analysis and Applications, 510, pp. 1 - 46,
    Journal articles | 2022
    Baker RC; Chen C; Shparlinski IE, 2022, 'Large Weyl sums and Hausdorff dimension', Journal of Mathematical Analysis and Applications, 510, pp. 126030 - 126030,
    Journal articles | 2022
    Baker RC; Munsch M; Shparlinski IE, 2022, 'Additive energy and a large sieve inequality for sparse sequences', Mathematika, 68, pp. 362 - 399,
    Journal articles | 2022
    Banks W; Shparlinski I, 2022, 'On a conjecture of Soundararajan', Bulletin of the London Mathematical Society, 54, pp. 301 - 317,
    Journal articles | 2022
    Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2022, 'On sparsity of representations of polynomials as linear combinations of exponential functions', Journal of the London Mathematical Society, 105, pp. 2076 - 2103,
    Journal articles | 2022
    Ghioca D; Shparlinski IE, 2022, 'Order of torsion for reduction of linearly independent points for a family of Drinfeld modules', Journal of Number Theory, 233, pp. 112 - 125,
    Journal articles | 2022
    Kerr B; M茅rai L; Shparlinski IE, 2022, 'On digits of Mersenne numbers', Revista Matematica Iberoamericana, 38, pp. 1901 - 1925,
    Journal articles | 2022
    Ostafe A; Shparlinski IE; Pottmeyer L, 2022, 'Perfect powers in value sets and orbits of polynomials', The New York Journal of Mathematics
    Journal articles | 2022
    Ostafe A; Shparlinski IE; Pottmeyer L, 2022, 'Perfect powers in value sets and orbits of polynomials', The New York Journal of Mathematics, 27, pp. 903 - 917
    Journal articles | 2022
    Ostafe A; Shparlinski IE, 2022, 'On the Skolem problem and some related questions for parametric families of linear recurrence sequences', Canadian Journal of Mathematics, 74, pp. 773 - 792,
    Journal articles | 2022
    Shkredov ID; Shparlinski IE; Zaharescu A, 2022, 'Bilinear Forms with Modular Square Roots and Twisted Second Moments of Half Integral Weight Dirichlet Series', International Mathematics Research Notices, 2022, pp. 17431 - 17474,
    Journal articles | 2022
    Shparlinski IE, 2022, 'Bilinear sums of Gauss sums', Acta Arithmetica, 202, pp. 379 - 388,
    Journal articles | 2022
    Shparlinski IE, 2022, 'MULTIPLICATIVE PROPERTIES of HILBERT CUBES', SIAM Journal on Discrete Mathematics, 36, pp. 1064 - 1070,
    Journal articles | 2021
    Bag N; Shparlinski IE, 2021, 'Bounds of some double exponential sums', Journal of Number Theory, 219, pp. 228 - 236,
    Journal articles | 2021
    Baker RC; Chen C; Shparlinski IE, 2021, 'Bounds on the Norms of Maximal Operators on Weyl Sums', ,
    Journal articles | 2021
    Baker RC; Munsch M; Shparlinski IE, 2021, 'Additive energy and a large sieve inequality for sparse sequences', ,
    Journal articles | 2021
    Chen C; Shparlinski IE, 2021, 'Small values of Weyl sums', Journal of Mathematical Analysis and Applications, 495,
    Journal articles | 2021
    Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, 'A SPARSITY RESULT for the DYNAMICAL MORDELL-LANG CONJECTURE in POSITIVE CHARACTERISTIC', Bulletin of the Australian Mathematical Society, 104, pp. 381 - 390,
    Journal articles | 2021
    Karpinski M; Shparlinski IE, 2021, 'Noisy polynomial interpolation modulo prime powers', Journal of Complexity, 64,
    Journal articles | 2021
    Kerr B; Mello J; Shparlinski IE, 2021, 'On elements of large order on elliptic curves and multiplicative dependent images of rational functions over finite fields', Illinois Journal of Mathematics, 65, pp. 499 - 514,
    Journal articles | 2021
    Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2021, 'Energy bounds for modular roots and their applications', ,
    Journal articles | 2021
    M茅rai L; Ostafe A; Shparlinski IE, 2021, 'Dynamical irreducibility of polynomials modulo primes', Mathematische Zeitschrift, 298, pp. 1187 - 1199,
    Journal articles | 2021
    M茅rai L; Shparlinski IE, 2021, 'On the dynamical system generated by the M枚bius transformation at prime times', Research in Mathematical Sciences, 8, pp. 10,
    Journal articles | 2021
    Ostafe A; Pottmeyer L; Shparlinski IE, 2021, 'Perfect powers in value sets and orbits of polynomials', New York Journal of Mathematics, 27, pp. 903 - 917
    Journal articles | 2021
    Ostafe A; Shparlinski IE, 2021, 'Additive energy of cyclic matrix groups and character sums with matrix exponential functions', ,
    Journal articles | 2021
    Sha M; Shparlinski IE, 2021, 'M枚bius Randomness Law for Frobenius Traces of Ordinary Curves', Canadian Mathematical Bulletin, 64, pp. 192 - 203,
    Journal articles | 2021
    Shparlinski IE; Stewart CL, 2021, 'Counting solvable s-unit equations', Proceedings of the American Mathematical Society, 149, pp. 5119 - 5129,
    Journal articles | 2021
    Shparlinski IE; Thuswaldner JM, 2021, 'Weyl sums over integers with digital restrictions', ,
    Journal articles | 2021
    Shparlinski IE; Wang Q, 2021, 'Exponential sums with sparse polynomials over finite fields', SIAM Journal on Discrete Mathematics, 35, pp. 976 - 987,
    Journal articles | 2021
    Shparlinski IE, 2021, 'Bounds of trilinear sums with Kloosterman fractions', Archiv Der Mathematik, 117, pp. 261 - 266,
    Journal articles | 2021
    Shparlinski IE, 2021, 'On the arithmetic structure of rational numbers in the cantor set', Bulletin of the Australian Mathematical Society, 103, pp. 22 - 27,
    Journal articles | 2020
    , 2020, 'Corrections to 芒鈧揤alue sets of sparse polynomials芒鈧', Canadian Mathematical Bulletin, 65, pp. 1071 - 1073,
    Journal articles | 2020
    Brandes J; Shparlinski IE, 2020, 'Two-dimensional Weyl sums failing square-root cancellation along lines', ,
    Journal articles | 2020
    Chen C; Kerr B; Maynard J; Shparlinski I, 2020, 'Metric theory of Weyl sums', ,
    Journal articles | 2020
    Chen C; Kerr B; Shparlinski I, 2020, 'Metric theory of lower bounds on Weyl sums', ,
    Journal articles | 2020
    Chen C; Shparlinski IE, 2020, 'Hausdorff dimension of the large values of Weyl sums', Journal of Number Theory, 214, pp. 27 - 37,
    Journal articles | 2020
    Chen C; Shparlinski IE, 2020, 'Hybrid bounds on two-parametric family Weyl sums along smooth curves', ,
    Journal articles | 2020
    Di Benedetto D; Garaev MZ; Garcia VC; Gonzalez-Sanchez D; Shparlinski IE; Trujillo CA, 2020, 'New estimates for exponential sums over multiplicative subgroups and intervals in prime fields', Journal of Number Theory, 215, pp. 261 - 274,
    Journal articles | 2020
    Kerr B; Mello J; Shparlinski I, 2020, 'An effective local-global principle for algebraic varieties and the sum product problem in finite fields', ,
    Journal articles | 2020
    Kerr B; M茅rai L; Shparlinski IE, 2020, 'On digits of Mersenne numbers', ,
    Journal articles | 2020
    Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2020, 'On the Structure of Graphs of Markoff Triples', Quarterly Journal of Mathematics, 71, pp. 637 - 648,
    Journal articles | 2020
    Konyagin SV; Shparlinski IE; Vyugin IV, 2020, 'Polynomial Equations in Subgroups and Applications', ,
    Journal articles | 2020
    Li R; Shparlinski IE, 2020, 'Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers', ,
    Journal articles | 2020
    Liu K; Shparlinski IE; Zhang T, 2020, 'Average distribution of k-free numbers in arithmetic progressions', Mathematische Nachrichten, 293, pp. 1505 - 1514,
    Journal articles | 2020
    Macourt S; Petridis G; Shkredov ID; Shparlinski IE, 2020, 'BOUNDS of TRILINEAR and TRINOMIAL EXPONENTIAL SUMS', SIAM Journal on Discrete Mathematics, 34, pp. 2124 - 2136,
    Journal articles | 2020
    Munsch M; Shparlinski IE; Yau KH, 2020, 'SMOOTH SQUAREFREE AND SQUAREFULL INTEGERS IN ARITHMETIC PROGRESSIONS', MATHEMATIKA, 66, pp. 56 - 70,
    Journal articles | 2020
    Munsch M; Shparlinski IE, 2020, 'On smooth square-free numbers in arithmetic progressions', Journal of the London Mathematical Society, 101, pp. 1941 - 1067,
    Journal articles | 2020
    M茅rai L; Shparlinski IE, 2020, 'Distribution of short subsequences of inversive congruential pseudorandom numbers modulo $2^t$', Mathematics of Computation, 322, pp. 911 - 922,
    Journal articles | 2020
    Ricotta G; Royer E; Shparlinski I, 2020, 'Kloosterman paths of prime powers moduli, II', Bulletin de la Societe Mathematique de France, 148, pp. 173 - 188,
    Journal articles | 2020
    Shkredov ID; Shparlinski IE; Zaharescu A, 2020, 'On the distribution of modular square roots of primes', ,
    Journal articles | 2020
    Shparlinski I; Banks W, 2020, 'Congruences with intervals and arbitrary sets', Archiv der Mathematik, 114, pp. 527 - 539,
    Journal articles | 2020
    Shparlinski I; Banks W, 2020, 'Congruences with intervals and arbitrary sets', Archiv der Mathematik, 114, pp. 527 - 539,
    Journal articles | 2020
    Shparlinski I; Banks W, 2020, 'Sums with the Mobius function twisted by characters with powerful moduli', Trans. Amer. Math. Soc., pp. 249 - 272,
    Journal articles | 2020
    Shparlinski I; Chen C, 2020, 'Hausdorff dimension of the large values of Weyl sums', Journal of Number Theory, pp. 27 - 37,
    Journal articles | 2020
    Shparlinski I; Chen C, 2020, 'On large values of Weyl sums', Advances in Mathematics, 370, pp. 1 - 48,
    Journal articles | 2020
    Shparlinski I; Chen C, 2020, 'On large values of Weyl sums', Advances in Mathematics, 370, pp. 1 - 48,
    Journal articles | 2020
    Shparlinski I; Dunn A; Kerr B; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, 375, pp. 1 - 58,
    Journal articles | 2020
    Shparlinski I; Dunn A; Kerr B; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, 375, pp. 1 - 58,
    Journal articles | 2020
    Shparlinski I; Gomez-Perez D; Merai L, 2020, 'On the complexity of exact counting of dynamically irreducible polynomials', Journal of Symbolic Computation, 99, pp. 231 - 241,
    Journal articles | 2020
    Shparlinski I; Gomez-Perez D; Merai L, 2020, 'On the complexity of exact counting of dynamically irreducible polynomials', Journal of Symbolic Computation, 99, pp. 231 - 241,
    Journal articles | 2020
    Shparlinski I; Kerr B; Yau KH, 2020, 'A refinement of the Burgess bound for character sums', Michigan Mathematical Journal, 69, pp. 227 - 240,
    Journal articles | 2020
    Shparlinski I; Kerr B, 2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', Research in Number Theory, pp. 1 - 21,
    Journal articles | 2020
    Shparlinski I; Kerr B, 2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', Research in Number Theory, 6, pp. 1 - 21,
    Journal articles | 2020
    Shparlinski I; Korolev M, 2020, 'Sums of algebraic trace functions twisted by arithmetic functions.', Pacific J. Math., 304, pp. 505 - 18,
    Journal articles | 2020
    Shparlinski I; Korolev M, 2020, 'Sums of algebraic trace functions twisted by arithmetic functions.', Pacific J. Math., 304, pp. 505 - 18,
    Journal articles | 2020
    Shparlinski I; Pakovich F, 2020, 'Level curves of rational functions and unimodular points on rational curves.', Proceedings of the American Mathematical Society, 148, pp. 1829 - 1833,
    Journal articles | 2020
    Shparlinski I; Pakovich F, 2020, 'Level curves of rational functions and unimodular points on rational curves.', Proceedings of the American Mathematical Society, 148, pp. 1829 - 1833,
    Journal articles | 2020
    Shparlinski I; Voloch F, 2020, 'Binomial exponential sums', Annali della Scuola Normale Superiore di Pisa: Classe di Scienze, 21, pp. 931 - 941,
    Journal articles | 2020
    Shparlinski I; Voloch F, 2020, 'Binomial exponential sums', Annali della Scuola Normale Superiore di Pisa: Classe di Scienze, 21, pp. 931 - 941,
    Journal articles | 2020
    Shparlinski I; Voloch F, 2020, 'Value sets of sparse polynomials', Canad. Math. Bull., 63, pp. . 187 - 196,
    Journal articles | 2020
    Shparlinski I; Voloch F, 2020, 'Value sets of sparse polynomials', Canad. Math. Bull., 63, pp. . 187 - 196,
    Journal articles | 2020
    Shparlinski I, 2020, 'Lower bounds for periods of Ducci sequences', Bulletin of the Australian Mathematical Society, 102, pp. 31 - 38,
    Journal articles | 2020
    Shparlinski I, 2020, 'Lower bounds for periods of Ducci sequences', Bulletin of the Australian Mathematical Society, 102, pp. 31 - 38,
    Journal articles | 2020
    Shparlinski I, 2020, 'Unlikely intersections over finite fields: polynomial orbits in small subgroups', DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS., Ser.A, 40, pp. 1065 - 1073,
    Journal articles | 2020
    Shparlinski I, 2020, 'Unlikely intersections over finite fields: polynomial orbits in small subgroups', DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS., Ser.A, 40, pp. 1065 - 1073,
    Journal articles | 2020
    Shparlinski IE; Stewart CL, 2020, 'Counting solvable $S$-unit equations', ,
    Journal articles | 2020
    Shparlinski IE; Technau M, 2020, 'Kloosterman sums with twice-differentiable functions', Functiones et Approximatio Commentarii Mathematici, 63, pp. 113 - 124,
    Journal articles | 2020
    Shparlinski IE, 2020, 'Geometric progressions in vector sumsets over finite fields', Finite Fields and their Applications, 68,
    Journal articles | 2020
    Shparlinski IE, 2020, 'Orders of points in families of elliptic curves', Proceedings of the American Mathematical Society, 148, pp. 2371 - 2377,
    Journal articles | 2019
    Banks WD; Friedlander JB; Pomerance C; Shparlinski IE, 2019, 'Counting integers with a smooth totient', The Quarterly Journal of Mathematics, pp. 1371 - 1386,
    Journal articles | 2019
    Banks WD; Shparlinski IE, 2019, 'Bounds on short character sums and L-functions with characters to a powerful modulus', Journal D Analyse Mathematique, 139, pp. 239 - 263,
    Journal articles | 2019
    Bordell猫s O; Dai L; Heyman R; Pan H; Shparlinski IE, 2019, 'On a sum involving the Euler function', Journal of Number Theory, 202, pp. 278 - 297,
    Journal articles | 2019
    Bret猫che RDL; Kurlberg P; Shparlinski IE, 2019, 'On the number of products which form perfect powers and discriminants of multiquadratic extensions', International Mathematics Research Notices,
    Journal articles | 2019
    B茅rczes A; Ostafe A; Shparlinski IE; Silverman JH, 2019, 'Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups', International Mathematics Research Notices,
    Journal articles | 2019
    Chen C; Shparlinski IE, 2019, 'New bounds of Weyl sums', International Mathematics Research Notices,
    Journal articles | 2019
    Dietmann R; Ostafe A; Shparlinski IE, 2019, 'Discriminants of Fields Generated by Polynomials of Given Height', ,
    Journal articles | 2019
    El Abdalaoui EH; Shparlinski IE, 2019, 'Disjointness of the M枚bius Transformation and M枚bius Function', Research in the Mathematical Sciences, 6, pp. 17,
    Journal articles | 2019
    Konyagin SV; Sha M; Shparlinski IE; Stewart CL, 2019, 'On the distribution of multiplicatively dependent vectors', ,
    Journal articles | 2019
    Liu K; Shparlinski IE; Zhang T, 2019, 'CANCELLATIONS BETWEEN KLOOSTERMAN SUMS MODULO A PRIME POWER WITH PRIME ARGUMENTS', Mathematika, 65, pp. 475 - 487,
    Journal articles | 2019
    Macourt S; Shparlinski IE, 2019, 'Double sums of Kloosterman sums in finite fields', Finite Fields and their Applications, 60,
    Journal articles | 2019
    M茅rai L; Shparlinski IE, 2019, 'Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields', Acta Arithmetica, 188, pp. 401 - 411,
    Journal articles | 2019
    Ostafe A; Shparlinski I, 2019, 'Polynomial Values in Affine Subspaces of Finite Fields', Journal d'Analyse Mathematique, 138, pp. 49 - 81,
    Journal articles | 2019
    Petridis G; Shparlinski IE, 2019, 'Bounds on trilinear and quadrilinear exponential sums', Journal d'Analyse Math茅matique
    Journal articles | 2019
    Roche-Newton O; Shparlinski IE; Winterhof A, 2019, 'Analogues of the Balog鈥揥ooley Decomposition for Subsets of Finite Fields and Character Sums with Convolutions', Annals of Combinatorics, 23, pp. 183 - 205,
    Journal articles | 2019
    SHPARLINSKI I, 2019, 'ON FINDING SOLUTIONS TO EXPONENTIAL CONGRUENCES', Bulletin of the Australian Mathematical Society, 99, pp. 1 - 4,
    Journal articles | 2019
    Sha M; Shparlinski IE, 2019, 'M枚bius Randomness Law for Frobenius Traces', ,
    Journal articles | 2019
    Shparlinski I; Zannier U, 2019, 'Arithmetic properties of quadratic exponential polynomials', New York Journal of Mathematics, 25, pp. 207 - 218,
    Journal articles | 2019
    Shparlinski I, 2019, 'The Sato-Tate distribution in thin families of elliptic curves over high degree extensions of finite fields', International Journal of Number Theory, 15, pp. 469 - 477,
    Journal articles | 2019
    Shparlinski IE, 2019, 'Bilinear Forms with Kloosterman and Gauss Sums', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,
    Journal articles | 2019
    Shparlinski IE, 2019, 'Bounds on average values of double incomplete Kloosterman sums', Journal of Number Theory, 203, pp. 1 - 11,
    Journal articles | 2019
    Shparlinski IE, 2019, 'ON SHORT PRODUCTS OF PRIMES IN ARITHMETIC PROGRESSIONS', Proceedings of the American Mathematical Society, 147, pp. 977 - 986,
    Journal articles | 2018
    Banks WD; Guo VZ; Shparlinski IE, 2018, 'Some arithmetic properties of numbers of the form $\lfloor p^c\rfloor$', Indagationes Mathematicae, 27, pp. 423 - 436,
    Journal articles | 2018
    Bordell猫s O; Luca F; Moree P; Shparlinski IE, 2018, 'DENOMINATORS of BERNOULLI POLYNOMIALS', Mathematika, 64, pp. 519 - 541,
    Journal articles | 2018
    Bordell猫s O; Luca F; Shparlinski IE, 2018, 'On the error term of a lattice counting problem', Journal of Number Theory, 182, pp. 19 - 36,
    Journal articles | 2018
    Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2018, 'Multiplicative congruences with variables from short intervals', Journal d'Analyse Mathematique, 124, pp. 117 - 147,
    Journal articles | 2018
    Chang M-C; D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Orbits of Polynomial Dynamical Systems Modulo Primes', Proceedings of the American Mathematical Society, 146, pp. 2015 - 2025,
    Journal articles | 2018
    Chang MC; Kerr B; Shparlinski IE, 2018, 'On the exponential large sieve inequality for sparse sequences modulo primes', Journal of Mathematical Analysis and Applications, 459, pp. 53 - 81,
    Journal articles | 2018
    D鈥橝ndrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Reductions modulo primes of systems of polynomial equations and algebraic dynamical systems', Transactions of the American Mathematical Society, 371, pp. 1169 - 1198,
    Journal articles | 2018
    D鈥橝ndrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Reductions modulo primes of systems of polynomial equations and algebraic dynamical systems', Transactions of the American Mathematical Society, 371, pp. 1169 - 1198,
    Journal articles | 2018
    G贸mez-P茅rez D; Shparlinski IE, 2018, 'Arithmetic Properties of Integers in Chains and Reflections of g-ary Expansions', Experimental Mathematics, 27, pp. 184 - 192,
    Journal articles | 2018
    Heyman R; Shparlinski IE, 2018, 'On shifted Eisenstein polynomials', Periodica Mathematica Hungarica, 69, pp. 170 - 181,
    Journal articles | 2018
    Ivanyos G; Karpinski M; Santha M; Saxena N; Shparlinski IE, 2018, 'Polynomial Interpolation and Identity Testing from High Powers Over Finite Fields', Algorithmica, 80, pp. 560 - 575,
    Journal articles | 2018
    Karpinski M; M茅rai L; Shparlinski IE, 2018, 'Identity testing and interpolation from high powers of polynomials of large degree over finite fields', Journal of Complexity, 49, pp. 74 - 84,
    Journal articles | 2018
    LUCA F; RADZIWI艁艁 M; SHPARLINSKI IE, 2018, 'On the typical size and cancellations among the coefficients of some modular forms', Mathematical Proceedings of the Cambridge Philosophical Society, 166, pp. 173 - 189,
    Journal articles | 2018
    Liu K; Shparlinski IE; Zhang T, 2018, 'Bilinear forms with exponential sums with binomials', Journal of Number Theory, 188, pp. 172 - 185,
    Journal articles | 2018
    Liu K; Shparlinski IE; Zhang T, 2018, 'Divisor problem in arithmetic progressions modulo a prime power', Advances in Mathematics, 325, pp. 459 - 481,
    Journal articles | 2018
    Ostafe A; Sha M; Shparlinski IE; Zannier U, 2018, 'On abelian multiplicatively dependent points on a curve in a torus', The Quarterly Journal of Mathematics,
    Journal articles | 2018
    Ostafe A; Sha M; Shparlinski IE; Zannier U, 2018, 'On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem', MICHIGAN MATHEMATICAL JOURNAL, 5,
    Journal articles | 2018
    Pappalardi F; Sha M; Shparlinski IE; Stewart CL, 2018, 'On multiplicatively dependent vectors of algebraic numbers', Transactions of the American Mathematical Society, 370, pp. 6221 - 6244,
    Journal articles | 2018
    Pomerance C; Shparlinski I, 2018, 'CONNECTED COMPONENTS OF THE GRAPH GENERATED BY POWER MAPS IN PRIME FINITE FIELDS', Integers : Electronic Journal of Combinatorial Number Theory, 18A, pp. 1 - 8,
    Journal articles | 2018
    Sha M; Shparlinski IE, 2018, 'Effective results on linear dependence for elliptic curves', Pacific Journal of Mathematics, 295, pp. 123 - 144,
    Journal articles | 2018
    Sha M; Shparlinski IE, 2018, 'The Sato鈥揟ate distribution in families of elliptic curves with a rational parameter of bounded height', Indagationes Mathematicae, 28, pp. 306 - 320,
    Journal articles | 2018
    Shkredov ID; Shparlinski IE, 2018, 'Double Character Sums with Intervals and Arbitrary Sets', Proceedings of the Steklov Institute of Mathematics, 303, pp. 239 - 258
    Journal articles | 2018
    Shparlinski I; Voloch JF, 2018, 'Generators of Elliptic Curves over Finite Fields', Bulletin of the Institute of Mathematics Academia Sinica, 9, pp. 657 - 670,
    Journal articles | 2018
    Shparlinski IE; Sutherland AV, 2018, 'On the Distribution of Atkin and Elkies Primes', Foundations of Computational Mathematics, 14, pp. 285 - 297,
    Journal articles | 2018
    Shparlinski IE; Winterhof A, 2018, 'Codes correcting restricted errors', Designs, Codes, and Cryptography,
    Journal articles | 2018
    Shparlinski IE; Zhao L, 2018, 'Elliptic curves in isogeny classes', Journal of Number Theory, 191, pp. 194 - 212
    Journal articles | 2018
    Shparlinski IE; Zumalac谩rregui A, 2018, 'Sums of inverses in thin sets of finite fields', Proceedings of the American Mathematical Society, 146, pp. 1377 - 1388,
    Journal articles | 2018
    Shparlinski IE, 2018, 'Character sums with smooth numbers', Archiv Der Mathematik, 110, pp. 467 - 476,
    Journal articles | 2018
    Shparlinski IE, 2018, 'Constructing Dominating Sets in Circulant Graphs', Annals of Combinatorics, 22, pp. 201 - 211,
    Journal articles | 2018
    Shparlinski IE, 2018, 'Linear equations with rational fractions of bounded height and stochastic matrices', Quarterly Journal of Mathematics, 69, pp. 487 - 499,
    Journal articles | 2018
    Shparlinski IE, 2018, 'Multiplicative orders in orbits of polynomials over finite fields', Glasgow Mathematical Journal, 60, pp. 487 - 493,
    Journal articles | 2018
    Shparlinski IE, 2018, 'On Constructing Primitive Roots in Finite Fields With Advice', IEEE Transactions on Information Theory, 64, pp. 7132 - 7136,
    Journal articles | 2018
    Shparlinski IE, 2018, 'On the Gy艖ry-S谩rk枚zy-Stewart conjecture in function fields', Czechoslovak Mathematical Journal, 68, pp. 1067 - 1077,
    Journal articles | 2018
    Shparlinski IE, 2018, 'The Sato-Tate distribution in thin families of elliptic curves over high degree extensions of finite fields', International Journal of Number Theory, pp. 1 - 9,
    Journal articles | 2018
    Shparlinski IE, 2018, 'Trilinear forms with double Kloosterman sums', International Journal of Number Theory, 14, pp. 2195 - 2203,
    Journal articles | 2018
    Simon M; Shkredov I; Shparlinski I; Macourt S, 2018, 'Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields', Canadian Journal of Mathematics, 70, pp. 1319 - 1338,
    Journal articles | 2018
    Simon M; Shkredov I; Shparlinski I, 2018, 'Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields', Canadian Journal of Mathematics, 70, pp. 1319 - 1338,
    Journal articles | 2017
    Banks WD; Shparlinski IE, 2017, 'On coincidences among quadratic fields generated by the shanks sequence', Quarterly Journal of Mathematics, 68, pp. 465 - 484,
    Journal articles | 2017
    Bell J; Shparlinski IE, 2017, 'Power series approximations to Fekete polynomials', Journal of Approximation Theory, 222, pp. 132 - 142,
    Journal articles | 2017
    Dietmann R; Elsholtz C; Shparlinski IE, 2017, 'Prescribing the binary digits of squarefree numbers and quadratic residues', Transactions of the American Mathematical Society, 369, pp. 8369 - 8388,
    Journal articles | 2017
    Dubickas A; Sha M; Shparlinski IE, 2017, 'On distances in lattices from algebraic number fields', Moscow Mathematical Journal, 17, pp. 239 - 268,
    Journal articles | 2017
    Liu K; Shparlinski IE; Zhang T, 2017, 'Squares in Piatetski-Shapiro sequences', Acta Arithmetica, 181, pp. 239 - 252,
    Journal articles | 2017
    Luca F; Sha M; Shparlinski IE, 2017, 'On two functions arising in the study of the euler and carmichael quotients', Colloquium Mathematicum, 149, pp. 179 - 192,
    Journal articles | 2017
    Mans B; Sha M; Shparlinski IE; Sutantyo D, 2017, 'On Functional Graphs of Quadratic Polynomials', Experimental Mathematics, pp. 1 - 9,
    Journal articles | 2017
    Pomerance C; Shparlinski IE, 2017, 'Connected components of the graph generated by power maps in prime finite fields', Connected components of the graph generated by power maps in prime finite fields,
    Journal articles | 2017
    Shkredov ID; Shparlinski IE, 2017, 'ON SOME MULTIPLE CHARACTER SUMS', Mathematika, 63, pp. 553 - 560,
    Journal articles | 2017
    Shparlinski IE; Sutherland AV, 2017, 'Finding elliptic curves with a subgroup of prescribed size', International Journal of Number Theory, 13, pp. 133 - 152,
    Journal articles | 2017
    Shparlinski IE; Weingartner AJ, 2017, 'An explicit polynomial analogue of Romanoff's theorem', Finite Fields and their Applications, 44, pp. 22 - 33,
    Journal articles | 2017
    Shparlinski IE; Yau KH, 2017, 'Double exponential sums with exponential functions', International Journal of Number Theory, 13, pp. 2531 - 2543,
    Journal articles | 2017
    Shparlinski IE, 2017, 'On the convex hull of the points on multivariate modular hyperbolas', Journal of Number Theory, 171, pp. 71 - 78,
    Journal articles | 2016
    Banks WD; Guo VZ; Shparlinski IE, 2016, 'Almost primes of the form 鈱妏c鈱', Indagationes Mathematicae, 27, pp. 423 - 436,
    Journal articles | 2016
    Banks WD; Shparlinski IE, 2016, 'Fractional parts of Dedekind sums', International Journal of Number Theory, 12, pp. 1137 - 1147,
    Journal articles | 2016
    Banks WD; Shparlinski IE, 2016, 'On Gauss sums and the evaluation of Stechkin's constant', Mathematics of Computation, 85, pp. 2569 - 2581,
    Journal articles | 2016
    Banks WD; Shparlinski IE, 2016, 'On the number of distinct quadratic fields generated by the Shanks sequence', On the number of distinct quadratic fields generated by the Shanks sequence,
    Journal articles | 2016
    Camburu OM; Ciolan EA; Luca F; Moree P; Shparlinski IE, 2016, 'Cyclotomic coefficients: Gaps and jumps', Journal of Number Theory, 163, pp. 211 - 237,
    Journal articles | 2016
    Chang MC; Shparlinski IE, 2016, 'On the density of integer points on generalised Markoff鈥揌urwitz and Dwork hypersurfaces', Mathematische Zeitschrift, 282, pp. 935 - 954,
    Journal articles | 2016
    Chang MC; Shparlinski IE, 2016, 'On the density of integer points on generalised Markoff鈥揌urwitz and Dwork hypersurfaces', Mathematische Zeitschrift, 282, pp. 935 - 954,
    Journal articles | 2016
    Fit茅 F; Shparlinski IE, 2016, 'On the singularity of the demjanenko matrix of quotients of fermat curves', Proceedings of the American Mathematical Society, 144, pp. 55 - 63,
    Journal articles | 2016
    Harman G; Shparlinski IE, 2016, 'Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients', International Mathematics Research Notices, 2016, pp. 1424 - 1446,
    Journal articles | 2016
    Heyman R; Shparlinski IE, 2016, 'Counting irreducible binomials over finite fields', Finite Fields and their Applications, 38, pp. 1 - 12,
    Journal articles | 2016
    Koh D; Shen CY; Shparlinski I, 2016, 'Averaging Operators Over Homogeneous Varieties Over Finite Fields', Journal of Geometric Analysis, 26, pp. 1415 - 1441,
    Journal articles | 2016
    Koh D; Shen CY; Shparlinski I, 2016, 'Averaging Operators Over Homogeneous Varieties Over Finite Fields', Journal of Geometric Analysis, 26, pp. 1415 - 1441,
    Journal articles | 2016
    Konyagin SV; Luca F; Mans B; Mathieson L; Sha M; Shparlinski IE, 2016, 'Functional graphs of polynomials over finite fields', Journal of Combinatorial Theory Series B, 116, pp. 87 - 122,
    Journal articles | 2016
    Konyagin SV; Luca F; Mans B; Mathieson L; Sha M; Shparlinski IE, 2016, 'Functional graphs of polynomials over finite fields', Journal of Combinatorial Theory Series B, 116, pp. 87 - 122,
    Journal articles | 2016
    Munsch M; Shparlinski IE, 2016, 'Upper and Lower Bounds for Higher Moments of Theta Functions', Quarterly Journal of Mathematics, 67, pp. 53 - 73,
    Journal articles | 2016
    Nguyen PQ; Shparlinski IE, 2016, 'Counting Co-cyclic lattices', SIAM Journal on Discrete Mathematics, 30, pp. 1358 - 1370,
    Journal articles | 2016
    Rivat J; Shparlinski IE, 2016, 'Multiples of squares in short intervals', Functiones Et Approximatio Commentarii Mathematici, 54, pp. 57 - 63,
    Journal articles | 2016
    Shparlinski IE; Yau KH, 2016, 'Bounds of double multiplicative character sums and gaps between residues of exponential functions', Journal of Number Theory, 167, pp. 304 - 316,
    Journal articles | 2016
    Shparlinski IE; Zhang T, 2016, 'Cancellations amongst Kloosterman sums', Acta Arithmetica, 176, pp. 201 - 210,
    Journal articles | 2016
    Shparlinski IE, 2016, 'Groups generated by iterations of polynomials over finite fields', Proceedings of the Edinburgh Mathematical Society, 59, pp. 235 - 245,
    Journal articles | 2016
    Shparlinski IE, 2016, 'Linear congruences with ratios', Proceedings of the American Mathematical Society, 144, pp. 2837 - 2846,
    Journal articles | 2016
    Shparlinski IE, 2016, 'On bilinear exponential and character sums with reciprocals of polynomials', Mathematika, 62, pp. 842 - 859,
    Journal articles | 2016
    Shparlinski IE, 2016, 'On small gaps between the elements of multiplicative subgroups of finite fields', Designs Codes and Cryptography, 80, pp. 63 - 71,
    Journal articles | 2016
    Shparlinski IE, 2016, 'On the additive energy of the distance set in finite fields', Finite Fields and their Applications, 42, pp. 187 - 199,
    Journal articles | 2016
    Shparlinski IE, 2016, 'Polynomial values in small subgroups of finite fields', Revista Matematica Iberoamericana, 32, pp. 1127 - 1136,
    Journal articles | 2016
    Shparlinski IE, 2016, 'Ratios of Small Integers in Multiplicative Subgroups of Residue Rings', Experimental Mathematics, 25, pp. 273 - 280,
    Journal articles | 2016
    Shparlinski IE, 2016, 'SYSTEMS OF CONGRUENCES WITH PRODUCTS OF VARIABLES FROM SHORT INTERVALS', Bulletin of the Australian Mathematical Society, 93, pp. 364 - 371,
    Journal articles | 2015
    Blackburn SR; Konyagin SV; Shparlinski IE, 2015, 'Counting additive decompositions of quadratic residues in finite fields', Functiones Et Approximatio Commentarii Mathematici, 52, pp. 223 - 227,
    Journal articles | 2015
    Bourgain J; Konyagin SV; Shparlinski IE, 2015, 'Character sums and deterministic polynomial root finding in finite fields', Mathematics of Computation, 84, pp. 2969 - 2977,
    Journal articles | 2015
    Bret猫che RDL; Sha M; Shparlinski IE; Voloch JF, 2015, 'The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves', Mathematische Zeitschrift, 290, pp. 831 - 855,
    Journal articles | 2015
    Dubickas A; Sha M; Shparlinski I, 2015, 'Explicit form of Cassels' p-adic Embedding Theorem for Number Fields', Canadian Journal of Mathematics, 67, pp. 1046 - 1064,
    Journal articles | 2015
    G贸mez-P茅rez D; Shparlinski IE, 2015, 'Subgroups generated by rational functions in finite fields', Monatshefte Fur Mathematik, 176, pp. 241 - 253,
    Journal articles | 2015
    Heyman R; Shparlinski IE, 2015, 'On the greatest common divisor of shifted sets', Journal of Number Theory, 154, pp. 63 - 73,
    Journal articles | 2015
    Konyagin SV; Shparlinski IE, 2015, 'Quadratic non-residues in short intervals', Proceedings of the American Mathematical Society, 143, pp. 4261 - 4269,
    Journal articles | 2015
    Kurlberg P; Luca F; Shparlinski IE, 2015, 'On the fixed points of the map x鈫抶x modulo a prime', Mathematical Research Letters, 22, pp. 141 - 168,
    Journal articles | 2015
    Munsch M; Shparlinski IE, 2015, 'Congruences with intervals and subgroups modulo a prime', Michigan Mathematical Journal, 64, pp. 655 - 672,
    Journal articles | 2015
    Roche-Newton O; Shparlinski IE, 2015, 'Polynomial values in subfields and affine subspaces of finite fields', Quarterly Journal of Mathematics, 66, pp. 693 - 706,
    Journal articles | 2015
    Sha M; Shparlinski IE, 2015, 'Lang-trotter and sato-tate distributions in single and double parametric families of elliptic curves', Acta Arithmetica, 170, pp. 299 - 325,
    Journal articles | 2015
    Shparlinski I, 2015, 'Points on Varieties over Finite Fields in Small Boxes', Contemporary Mathematics, 655, pp. 209 - 233,
    Journal articles | 2015
    Shparlinski IE; Sutherland AV, 2015, 'On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average', Lms Journal of Computation and Mathematics, 18, pp. 308 - 322,
    Journal articles | 2015
    Shparlinski IE, 2015, 'Cayley graphs generated by small degree polynomials over finite fields', SIAM Journal on Discrete Mathematics, 29, pp. 376 - 381,
    Journal articles | 2015
    Shparlinski IE, 2015, 'Close values of shifted modular inversions and the decisional modular inversion hidden number problem', Advances in Mathematics of Communications, 9, pp. 169 - 176,
    Journal articles | 2015
    Shparlinski IE, 2015, 'Distribution of polynomial discriminants modulo a prime', Archiv Der Mathematik, 105, pp. 251 - 259,
    Journal articles | 2015
    Shparlinski IE, 2015, 'On the product of small Elkies primes', Proceedings of the American Mathematical Society, 143, pp. 1441 - 1448,
    Journal articles | 2015
    Shparlinski IE, 2015, 'Small discriminants of complex multiplication fields of elliptic curves over finite fields', Czechoslovak Mathematical Journal, 65, pp. 381 - 388,
    Journal articles | 2015
    Von Zur Gathen J; Shparlinski IE, 2015, 'Circulant graphs and GCD and LCM of subsets', Information Processing Letters, 115, pp. 134 - 138,
    Journal articles | 2014
    Ahmadi O; Shparlinski IE, 2014, 'Exponential sums over points of elliptic curves', Journal of Number Theory, 140, pp. 299 - 313,
    Journal articles | 2014
    Blake IF; Luca F; Shparlinski IE, 2014, 'VSH and multiplicative modular relations between small primes with polynomial exponents', Applicable Algebra in Engineering, Communications and Computing, 25, pp. 181 - 188,
    Journal articles | 2014
    Chang M-C; Shparlinski IE, 2014, 'On the Density of Integer Points on Generalised Markoff-Hurwitz and Dwork Hypersurfaces', ,
    Journal articles | 2014
    Chang MC; Cilleruelo J; Garaev MZ; Hern谩ndez J; Shparlinski IE; Zumalac谩rregui A, 2014, 'Points on curves in small boxes and applications', Michigan Mathematical Journal, 63, pp. 503 - 534,
    Journal articles | 2014
    Chang MC; Kerr B; Shparlinski IE; Zannier U, 2014, 'Elements of large order on varieties over prime finite fields', Journal De Theorie Des Nombres De Bordeaux, 26, pp. 579 - 593,
    Journal articles | 2014
    Chang MC; Shparlinski IE, 2014, 'Double character sums over subgroups and intervals', Bulletin of the Australian Mathematical Society, 90, pp. 376 - 390,
    Journal articles | 2014
    Chen Z; Shparlinski IE; Winterhof A, 2014, 'Covering sets for limited-magnitude errors', IEEE Transactions on Information Theory, 60, pp. 5315 - 5321,
    Journal articles | 2014
    Friedlander JB; Shparlinski IE, 2014, 'Enumeration of certain varieties over a finite field', Proceedings of the American Mathematical Society, 142, pp. 2615 - 2623,
    Journal articles | 2014
    Garcia-Morchon O; Rietman R; Shparlinski IE; Tolhuizen L, 2014, 'Interpolation and approximation of polynomials in finite fields over a short interval from noisy values', Experimental Mathematics, 23, pp. 241 - 260,
    Journal articles | 2014
    G贸mez-P茅rez D; Ostafe A; Shparlinski I, 2014, 'Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators', Mathematics of Computation, 83, pp. 1535 - 1550,
    Journal articles | 2014
    G贸mez-P茅rez D; Ostafe A; Shparlinski IE, 2014, 'On irreducible divisors of iterated polynomials', Revista Matematica Iberoamericana, 30, pp. 1123 - 1134,
    Journal articles | 2014
    Ling S; Shparlinski I; Wang H, 2014, 'On the multidimensional distribution of the Naor-Reingold pseudo-random function', Mathematics of Computation, 83, pp. 2429 - 2434,
    Journal articles | 2014
    Luca F; Shparlinski IE, 2014, 'On the counting function of elliptic carmichael numbers', Canadian Mathematical Bulletin, 57, pp. 105 - 112,
    Journal articles | 2014
    Mans B; Shparlinski I, 2014, 'Random walks, bisections and gossiping in circulant graphs', Algorithmica, 70, pp. 301 - 325
    Journal articles | 2014
    Shparlinski IE; Sutantyo D, 2014, 'Distribution of elliptic twin primes in isogeny and isomorphism classes', Journal of Number Theory, 137, pp. 1 - 15,
    Journal articles | 2014
    Shparlinski IE; Sutherland AV, 2014, 'On the Distribution of Atkin and Elkies Primes', Foundations of Computational Mathematics, pp. 1 - 13,
    Journal articles | 2014
    Shparlinski IE, 2014, 'Distribution of exponential functions modulo a prime power', Journal of Number Theory, 143, pp. 224 - 231,
    Journal articles | 2014
    Shparlinski IE, 2014, 'Evasive properties of sparse graphs and some linear equations in primes', Theoretical Computer Science, 547, pp. 117 - 121,
    Journal articles | 2014
    Shparlinski IE, 2014, 'Evasive properties of sparse graphs and some linear equations in primes', Theoretical Computer Science, 547, pp. 117 - 121,
    Journal articles | 2014
    Shparlinski IE, 2014, 'Multiple exponential and character sums with monomials', Mathematika, 60, pp. 363 - 373,
    Journal articles | 2014
    Shparlinski IE, 2014, 'On solutions to some polynomial congruences in small boxes', Bulletin of the Australian Mathematical Society, 89, pp. 300 - 307,
    Journal articles | 2014
    Shparlinski IE, 2014, 'On the distribution of points on the generalized markoff-hurwitz and dwork hypersurfaces', International Journal of Number Theory, 10, pp. 151 - 160,
    Journal articles | 2014
    Shparlinski IE, 2014, 'Products with variables from low-dimensional affine spaces and shifted power identity testing in finite fields', Journal of Symbolic Computation, 64, pp. 35 - 41,
    Journal articles | 2014
    Shparlinski IE, 2014, 'Squarefree parts of discriminants of trinomials', Archiv Der Mathematik, 102, pp. 545 - 554,
    Journal articles | 2013
    Baker RC; Banks WD; Br眉dern J; Shparlinski IE; Weingartner AJ, 2013, 'Piatetski-Shapiro sequences', Acta Arithmetica, 157, pp. 37 - 68,
    Journal articles | 2013
    Borwein JM; Shparlinski I; Zudilin W, 2013, 'Number Theory and Related Fields: In Memory of Alf van der Poorten', Springer Proceedings in Mathematics and Statistics, 43
    Journal articles | 2013
    Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2013, 'On congruences with products of variables from short intervals and applications', Proceedings of the Steklov Institute of Mathematics, 280, pp. 61 - 90,
    Journal articles | 2013
    Cilleruelo J; Kumchev A; Luca F; Ru茅 J; Shparlinski IE, 2013, 'On the fractional parts of an/n', Bulletin of the London Mathematical Society, 45, pp. 249 - 256,
    Journal articles | 2013
    Cilleruelo J; Shparlinski I, 2013, 'Concentration of points on curves in finite fields', Monatshefte Fur Mathematik, 171, pp. 315 - 327,
    Journal articles | 2013
    Dietmann R; Elsholtz C; Shparlinski IE, 2013, 'On gaps between primitive roots in the hamming metric', Quarterly Journal of Mathematics, 64, pp. 1043 - 1055,
    Journal articles | 2013
    Dietmann R; Elsholtz C; Shparlinski IE, 2013, 'On gaps between quadratic non-residues in the Euclidean and Hamming metrics', Indagationes Mathematicae, 24, pp. 930 - 938,
    Journal articles | 2013
    Farashahi RR; Fouque PA; Shparlinski IE; Tibouchi M; Voloch JF, 2013, 'Indifferentiable deterministic hashing to elliptic and hyperelliptic curves', Mathematics of Computation, 82, pp. 491 - 512,
    Journal articles | 2013
    Gutierrez J; Ibeas A; G贸mez-P茅rez D; Shparlinski IE, 2013, 'Predicting masked linear pseudorandom number generators over finite fields', Designs Codes and Cryptography, 67, pp. 395 - 402,
    Journal articles | 2013
    Harvey D; Shparlinski IE, 2013, 'Statistics of different reduction types of fermat curves', Experimental Mathematics, 22, pp. 243 - 249,
    Journal articles | 2013
    Heyman R; Shparlinski IE, 2013, 'On the number of Eisenstein polynomials of bounded height', Applicable Algebra in Engineering Communications and Computing, 24, pp. 149 - 156,
    Journal articles | 2013
    Kerr B; Shparlinski IE, 2013, 'On the distribution of values and zeros of polynomial systems over arbitrary sets', Journal of Number Theory, 133, pp. 2863 - 2873,
    Journal articles | 2013
    Shparlinski I, 2013, 'Erratum: Sum-product estimates and multiplicative orders of螕 and 螕 + 螕-1 in finite fields (Bulletin of the Australian Mathematical Society)', Bulletin of the Australian Mathematical Society, 87, pp. 527 - 528,
    Journal articles | 2013
    Shparlinski IE; Steiner W, 2013, 'On digit patterns in expansions of rational numbers with prime denominator', Quarterly Journal of Mathematics, 64, pp. 1231 - 1238,
    Journal articles | 2013
    Shparlinski IE; Winterhof A, 2013, 'Distribution of values of polynomial Fermat quotients', Finite Fields and their Applications, 19, pp. 93 - 104,
    Journal articles | 2013
    Shparlinski IE, 2013, 'Additive decompositions of subgroups of finite fields', SIAM Journal on Discrete Mathematics, 27, pp. 1870 - 1879,
    Journal articles | 2013
    Shparlinski IE, 2013, 'Correcting noisy exponentiation black-boxes modulo a prime', Information Processing Letters, 113, pp. 414 - 417,
    Journal articles | 2013
    Shparlinski IE, 2013, 'Elliptic curves over finite fields: Number theoretic and cryptographic aspects', Fields Institute Communications, 66, pp. 65 - 90,
    Journal articles | 2013
    Shparlinski IE, 2013, 'On products of primes and almost primes in arithmetic progressions', Periodica Mathematica Hungarica, 67, pp. 55 - 61,
    Journal articles | 2013
    Shparlinski IE, 2013, 'On some exponential sums with exponential and rational functions', Rocky Mountain Journal of Mathematics, 43, pp. 361 - 371,
    Journal articles | 2013
    Shparlinski IE, 2013, 'On the Lang-Trotter and Sato-Tate conjectures on average for polynomial families of elliptic curves', Michigan Mathematical Journal, 62, pp. 491 - 505,
    Journal articles | 2013
    Shparlinski IE, 2013, 'On the Sato-Tate conjecture on average for some families of elliptic curves', Forum Mathematicum, 25, pp. 647 - 664,
    Journal articles | 2013
    Shparlinski IE, 2013, 'On the average number of square-free values of polynomials', Canadian Mathematical Bulletin, 56, pp. 844 - 849,
    Journal articles | 2013
    Shparlinski IE, 2013, 'On vanishing Fermat quotients and a bound of the Ihara sum', Kodai Mathematical Journal, 36, pp. 99 - 108,
    Journal articles | 2013
    Von Zur Gathen J; Shparlinski IE, 2013, 'Generating safe primes', Journal of Mathematical Cryptology, 7, pp. 333 - 365,
    Journal articles | 2012
    Ahmadi O; Luca F; Ostafe A; Shparlinski IE, 2012, 'On stable quadratic polynomials', Glasgow Mathematical Journal, 54, pp. 359 - 369,
    Journal articles | 2012
    Balog A; Broughan KA; Shparlinski IE, 2012, 'Sum-Products Estimates with Several Sets and Applications', Integers, 12,
    Journal articles | 2012
    Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2012, 'Exponential and character sums with mersenne numbers', Journal of the Australian Mathematical Society, 92, pp. 1 - 13,
    Journal articles | 2012
    Banks WD; Pappalardi F; Shparlinski IE, 2012, 'On group structures realized by elliptic curves over arbitrary finite fields', Experimental Mathematics, 21, pp. 11 - 25,
    Journal articles | 2012
    Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2012, 'On the hidden shifted power problem', SIAM Journal on Computing, 41, pp. 1524 - 1557,
    Journal articles | 2012
    Bourgain J; Konyagin SV; Shparlinski IE, 2012, 'Distribution of elements of cosets of small subgroups and applications', International Mathematics Research Notices, 2012, pp. 1968 - 2009,
    Journal articles | 2012
    Cilleruelo J; Garaev MZ; Ostafe A; Shparlinski IE, 2012, 'On the concentration of points of polynomial maps and applications', Mathematische Zeitschrift, 272, pp. 825 - 837,
    Journal articles | 2012
    Cilleruelo J; Shparlinski IE; Zumalac谩rregui A, 2012, 'Isomorphism classes of elliptic curves over a finite field in some thin families', Mathematical Research Letters, 19, pp. 335 - 343,
    Journal articles | 2012
    Cojocaru AC; Luca F; Shparlinski IE, 2012, 'Erratum: Pseudoprime reductions of elliptic curves (Mathematical Proceedings of the Cambridge Philosophical Society (2009) 146 (513-522))', Mathematical Proceedings of the Cambridge Philosophical Society, 152, pp. 571,
    Journal articles | 2012
    Farashahi RR; Shparlinski IE, 2012, 'On group structures realized by elliptic curves over a fixed finite field', Experimental Mathematics, 21, pp. 1 - 10,
    Journal articles | 2012
    Farashahi RR; Shparlinski IE, 2012, 'Pseudorandom bits from points on elliptic curves', IEEE Transactions on Information Theory, 58, pp. 1242 - 1247,
    Journal articles | 2012
    Gonz谩lez JJA; Luca F; Pomerance C; Shparlinski IE, 2012, 'On numbers n dividing the nth term of a linear recurrence', Proceedings of the Edinburgh Mathematical Society, 55, pp. 271 - 289,
    Journal articles | 2012
    Konyagin SV; Shparlinski IE, 2012, 'On the consecutive powers of a primitive root: Gaps and exponential sums', Mathematika, 58, pp. 11 - 20,
    Journal articles | 2012
    Ling S; Shparlinski IE; Steinfeld R; Wang H, 2012, 'On the modular inversion hidden number problem', Journal of Symbolic Computation, 47, pp. 358 - 367,
    Journal articles | 2012
    Mans B; Shparlinski IE, 2012, 'Random walks and bisections in random circulant graphs', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 7256 LNCS, pp. 542 - 555,
    Journal articles | 2012
    Ostafe A; Shparlinski I, 2012, 'Degree growth, linear independence and periods of a class of rational dynamical systems', ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY, 574, pp. 131 - 143,
    Journal articles | 2012
    Ostafe A; Shparlinski IE, 2012, 'Exponential sums over points of elliptic curves with reciprocals of primes', Mathematika, 58, pp. 21 - 33,
    Journal articles | 2012
    Ostafe A; Shparlinski IE, 2012, 'Multiplicative character sums and products of sparse integers in residue classes', Periodica Mathematica Hungarica, 64, pp. 247 - 255,
    Journal articles | 2012
    Ostafe A; Shparlinski IE, 2012, 'On the power generator and its multivariate analogue', Journal of Complexity, 28, pp. 238 - 249,
    Journal articles | 2012
    Shparlinski I, 2012, 'Sum-product estimates and multiplicative orders of 纬 and 纬+纬 -1 in finite fields', Bulletin of the Australian Mathematical Society, 85, pp. 505 - 508,
    Journal articles | 2012
    Shparlinski IE; Stange KE, 2012, 'Character sums with division polynomials', Canadian Mathematical Bulletin, 55, pp. 850 - 857,
    Journal articles | 2012
    Shparlinski IE, 2012, 'Modular hyperbolas', Japanese Journal of Mathematics, 7, pp. 235 - 294,
    Journal articles | 2012
    Shparlinski IE, 2012, 'On the convex hull of solutions to polynomial congruences', Journal of Number Theory, 132, pp. 254 - 257,
    Journal articles | 2012
    Shparlinski IE, 2012, 'On the distribution of solutions to polynomial congruences', Archiv Der Mathematik, 99, pp. 345 - 351,
    Journal articles | 2012
    Shparlinski IE, 2012, 'On the restricted divisor function in arithmetic progressions', Revista Matematica Iberoamericana, 28, pp. 231 - 238,
    Journal articles | 2012
    Shparlinski IE, 2012, 'On the value set of fermat quotients', Proceedings of the American Mathematical Society, 140, pp. 1199 - 1206,
    Journal articles | 2012
    Urroz JJ; Luca F; Shparlinski IE, 2012, 'On the number of isogeny classes of pairing-friendly elliptic curves and statistics of mnt curves', Mathematics of Computation, 81, pp. 1093 - 1110,
    Journal articles | 2011
    Balog A; Broughan KA; Shparlinski IE, 2011, 'On the number of solutions of exponential congruences', Acta Arithmetica, 148, pp. 93 - 103,
    Journal articles | 2011
    Bibak K; Shparlinski IE, 2011, 'On Fully Split Lacunary Polynomials in Finite Fields', Bulletin of the Polish Academy of Sciences Mathematics, 59, pp. 197 - 202,
    Journal articles | 2011
    Blackburn SR; Ostafe A; Shparlinski IE, 2011, 'On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves', On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves,
    Journal articles | 2011
    Blackburn SR; Ostafe A; Shparlinski IE, 2011, 'On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves', CoRR, abs/1102.1053
    Journal articles | 2011
    Fouvry E; Luca F; Pappalardi F; Shparlinski IE, 2011, 'Counting dihedral and quaternionic extensions', Transactions of the American Mathematical Society, 363, pp. 3233 - 3253,
    Journal articles | 2011
    Fouvry E; Shparlinski IE, 2011, 'On a ternary quadratic form over primes', Acta Arithmetica, 150, pp. 285 - 314,
    Journal articles | 2011
    Fouvry E; Shparlinski IE, 2011, 'Smooth shifted monomial products', Publicationes Mathematicae Debrecen, 79, pp. 423 - 432,
    Journal articles | 2011
    Konyagin SV; Shparlinski IE, 2011, 'On convex hull of points on modular hyperbolas', Moscow Journal of Combinatorics and Number Theory, 1, pp. 43 - 51
    Journal articles | 2011
    K艡铆啪ek M; Luca F; Shparlinski IE; Somer L, 2011, 'On the complexity of testing elite primes', Journal of Integer Sequences, 14, pp. 1 - 5
    Journal articles | 2011
    Luca F; Shparlinski IE, 2011, 'On the g-Ary expansions of middle binomial coefficients and catalan numbers', Rocky Mountain Journal of Mathematics, 41, pp. 1291 - 1301,
    Journal articles | 2011
    Ostafe A; Shparlinski IE; Winterhof A, 2011, 'Multiplicative character sums of a class of nonlinear recurrence vector sequences', International Journal of Number Theory, 7, pp. 1557 - 1571,
    Journal articles | 2011
    Ostafe A; Shparlinski IE, 2011, 'On the waring problem with Dickson polynomials in finite fields', Proceedings of the American Mathematical Society, 139, pp. 3815 - 3820,
    Journal articles | 2011
    Ostafe A; Shparlinski IE, 2011, 'Pseudorandomness and dynamics of fermat quotients*', SIAM Journal on Discrete Mathematics, 25, pp. 50 - 71,
    Journal articles | 2011
    Ostafe A; Shparlinski IE, 2011, 'Twisted exponential sums over points of elliptic curves', Acta Arithmetica, 148, pp. 77 - 92,
    Journal articles | 2011
    Shparlinski IE, 2011, 'Bounds of multiplicative character sums with Fermat quotients of primes', Bulletin of the Australian Mathematical Society, 83, pp. 456 - 462,
    Journal articles | 2011
    Shparlinski IE, 2011, 'Character sums with fermat quotients', Quarterly Journal of Mathematics, 62, pp. 1031 - 1043,
    Journal articles | 2011
    Shparlinski IE, 2011, 'Exponential sums with consecutive modular roots of an integer', Quarterly Journal of Mathematics, 62, pp. 207 - 213,
    Journal articles | 2011
    Shparlinski IE, 2011, 'Fermat quotients: Exponential sums, value set and primitive roots', Bulletin of the London Mathematical Society, 43, pp. 1228 - 1238,
    Journal articles | 2011
    Shparlinski IE, 2011, 'On small solutions to quadratic congruences', Journal of Number Theory, 131, pp. 1105 - 1111,
    Journal articles | 2011
    Shparlinski IE, 2011, 'On the average distribution of pseudorandom numbers generated by nonlinear permutations', Mathematics of Computation, 80, pp. 1053 - 1061,
    Journal articles | 2011
    Shparlinski IE, 2011, 'On the distribution of irreducible trinomials', Canadian Mathematical Bulletin, 54, pp. 748 - 756,
    Journal articles | 2010
    Ahmadi O; Shparlinski I, 2010, 'Bilinear character sums and sum-product problems on elliptic curves', Proceedings of the Edinburgh Mathematical Society, 53, pp. 1 - 12,
    Journal articles | 2010
    Ahmadi O; Shparlinski IE; Voloch JF, 2010, 'Multiplicative order of gauss periods', International Journal of Number Theory, 6, pp. 877 - 882,
    Journal articles | 2010
    Ahmadi O; Shparlinski IE, 2010, 'On the distribution of the number of points on algebraic curves in extensions of finite fields', Mathematical Research Letters, 17, pp. 689 - 699,
    Journal articles | 2010
    Banks WD; Shparlinski IE, 2010, 'Sums with convolutions of Dirichlet characters', Manuscripta Mathematica, 133, pp. 105 - 114,
    Journal articles | 2010
    Bourgain J; Ford K; Konyagin SV; Shparlinski IE, 2010, 'On the divisibility of Fermat quotients', Michigan Mathematical Journal, 59, pp. 313 - 328,
    Journal articles | 2010
    Broughan KA; Luca F; Shparlinski IE, 2010, 'Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem', Integers, 10,
    Journal articles | 2010
    Chan TH; Shparlinski IE, 2010, 'On the concentration of points on modular hyperbolas and exponential curves', Acta Arithmetica, 142, pp. 59 - 66,
    Journal articles | 2010
    Chan TH; Shparlinski IE, 2010, 'Visible Points on Modular Exponential Curves', Bulletin of the Polish Academy of Sciences Mathematics, 58, pp. 17 - 22,
    Journal articles | 2010
    Cilleruelo J; Luca F; Quir贸s A; Shparlinski IE, 2010, 'On squares in polynomial products', Monatshefte Fur Mathematik, 159, pp. 215 - 223,
    Journal articles | 2010
    Farashahi RR; Shparlinski IE, 2010, 'On pseudopoints of algebraic curves', Archiv Der Mathematik, 95, pp. 529 - 537,
    Journal articles | 2010
    Ferguson R; Hoffman C; Luca F; Ostafe A; Shparlinski IE, 2010, 'Some additive combinatorics problems in matrix rings', Revista Matematica Complutense, 23, pp. 501 - 513,
    Journal articles | 2010
    Ford K; Khan MR; Shparlinski IE, 2010, 'Geometric properties of points on modular hyperbolas', Proceedings of the American Mathematical Society, 138, pp. 4177 - 4185,
    Journal articles | 2010
    Friedlander JB; Gong K; Shparlinskii IE, 2010, 'Character sums over shifted primes', Mathematical Notes, 88, pp. 585 - 598,
    Journal articles | 2010
    Glebsky L; Shparlinski IE, 2010, 'Short cycles in repeated exponentiation modulo a prime', Designs Codes and Cryptography, 56, pp. 35 - 42,
    Journal articles | 2010
    Gutierrez J; Shparlinski IE, 2010, 'Expansion of orbits of some dynamical systems over finite fields', Bulletin of the Australian Mathematical Society, 82, pp. 232 - 239,
    Journal articles | 2010
    Iosevich A; Shparlinski IE; Xiong M, 2010, 'SETS WITH INTEGRAL DISTANCES IN FINITE FIELDS', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 362, pp. 2189 - 2204,
    Journal articles | 2010
    Iosevich A; Shparlinski IE; Xiong M, 2010, 'Sets with integral distances in finite fields', Transactions of the American Mathematical Society, 362, pp. 2189 - 2204,
    Journal articles | 2010
    Karabina K; Menezes A; Pomerance C; Shparlinski IE, 2010, 'On the asymptotic effectiveness of Weil descent attacks', Journal of Mathematical Cryptology, 4, pp. 175 - 191,
    Journal articles | 2010
    Konyagin SV; Pomerance C; Shparlinski IE, 2010, 'On the distribution of pseudopowers', Canadian Journal of Mathematics, 62, pp. 582 - 594,
    Journal articles | 2010
    Konyagin SV; Shparlinski IE, 2010, 'On the Convex Hull of the Points on Modular Hyperbolas', On the Convex Hull of the Points on Modular Hyperbolas,
    Journal articles | 2010
    Loiperdinger SS; Shparlinski IE, 2010, 'ON THE DISTRIBUTION OF THE EULER FUNCTION OF SHIFTED SMOOTH NUMBERS', COLLOQUIUM MATHEMATICUM, 120, pp. 139 - 148,
    Journal articles | 2010
    Luca F; Shparlinski IE, 2010, 'On the g-Ary Expansions of Ap茅ry, Motzkin, Schr枚der and Other Combinatorial Numbers', Annals of Combinatorics, 14, pp. 507 - 524,
    Journal articles | 2010
    Ostafe A; Pelican E; Shparlinski IE, 2010, 'On pseudorandom numbers from multivariate polynomial systems', Finite Fields and their Applications, 16, pp. 320 - 328,
    Journal articles | 2010
    Ostafe A; Shparlinski IE; Winterhof A, 2010, 'On the generalized joint linear complexity profile of a class of nonlinear pseudorandom multisequences', Advances in Mathematics of Communications, 4, pp. 369 - 379,
    Journal articles | 2010
    Ostafe A; Shparlinski IE, 2010, 'On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators', Mathematics of Computation, 79, pp. 501 - 511,
    Journal articles | 2010
    Ostafe A; Shparlinski IE, 2010, 'On the length of critical orbits of stable quadratic polynomials', Proceedings of the American Mathematical Society, 138, pp. 2653 - 2656,
    Journal articles | 2010
    Ostafe A; Shparlinski IE, 2010, 'Pseudorandom numbers and hash functions from iterations of multivariate polynomials', Cryptography and Communications, 2, pp. 49 - 67,
    Journal articles | 2010
    Pomerance C; Shparlinski IE, 2010, 'Rank statistics for a family of elliptic curves over a function field', Pure and Applied Mathematics Quarterly, 6, pp. 21 - 40,
    Journal articles | 2010
    Rezaeian Farashahi R; Shparlinski IE, 2010, 'On the number of distinct elliptic curves in some families', Designs Codes and Cryptography, 54, pp. 83 - 99,
    Journal articles | 2010
    Shparlinski IE; Winterhof A, 2010, 'Partitions into two Lehmer numbers', Monatshefte Fur Mathematik, 160, pp. 429 - 441,
    Journal articles | 2010
    Shparlinski IE, 2010, 'Numbers at work and play', Notices of the American Mathematical Society, 57, pp. 334 - 342
    Journal articles | 2010
    Shparlinski IE, 2010, 'On point sets in vector spaces over finite fields that determine only acute angle triangles', Bulletin of the Australian Mathematical Society, 81, pp. 114 - 120,
    Journal articles | 2010
    Shparlinski IE, 2010, 'On quadratic fields generated by discriminants of irreducible trinomials', Proceedings of the American Mathematical Society, 138, pp. 125 - 132,
    Journal articles | 2010
    Shparlinski IE, 2010, 'On the size of the Gelfond exponent', Journal of Number Theory, 130, pp. 1056 - 1060,
    Journal articles | 2010
    Shparlinski IE, 2010, 'Some counting questions for matrices with restricted entries', Linear Algebra and Its Applications, 432, pp. 155 - 160,
    Journal articles | 2010
    Shparlinski IE, 2010, 'Tate-shafarevich groups and frobenius fields of reductions of elliptic curves', Quarterly Journal of Mathematics, 61, pp. 255 - 263,
    Journal articles | 2010
    von zur Gathen J; Mignotte M; Shparlinski IE, 2010, 'Approximate polynomial gcd: Small degree and small height perturbations', Journal of Symbolic Computation, 45, pp. 879 - 886,
    Journal articles | 2010
    肖褉懈写谢邪薪写械褉 袛袘; Friedlander JB; 袚芯薪谐 K; Gong K; 楔锌邪褉谢懈薪褋泻懈泄 袠袝; Shparlinski IE, 2010, '小褍屑屑褘 蟹薪邪褔械薪懈泄 褏邪褉邪泻褌械褉芯胁 薪邪 褋写胁懈薪褍褌褘褏 锌褉芯褋褌褘褏 褔懈褋谢邪褏', 袦邪褌械屑邪褌懈褔械褋泻懈械 蟹邪屑械褌泻懈, 88, pp. 605 - 619,
    Journal articles | 2009
    Abercrombie AG; Banks WD; Shparlinski IE, 2009, 'Arithmetic functions on Beatty sequences', Acta Arithmetica, 136, pp. 81 - 89,
    Journal articles | 2009
    Ahmadi O; Alon N; Blake IF; Shparlinski IE, 2009, 'Graphs with integral spectrum', Linear Algebra and Its Applications, 430, pp. 547 - 552,
    Journal articles | 2009
    Balasuriya S; Shparlinski IE; Sutantyo D, 2009, 'Multiplicative character sums with the Euler function', Studia Scientiarum Mathematicarum Hungarica, 46, pp. 223 - 229,
    Journal articles | 2009
    Balasuriya S; Winterhof A; Shparlinski IE, 2009, 'An average bound for character sums with some counter-dependent recurrence sequences', Rocky Mountain Journal of Mathematics, 39, pp. 1403 - 1409,
    Journal articles | 2009
    Banks WD; Garaev MZ; Luca F; Shparlinski IE, 2009, 'Uniform Distribution of Fractional Parts Related to Pseudoprimes', Canadian Journal of Mathematics, 61, pp. 481 - 502,
    Journal articles | 2009
    Banks WD; Shparlinski IE, 2009, 'Multiplicative character sums with twice-differentiable functions', Quarterly Journal of Mathematics, 60, pp. 401 - 411,
    Journal articles | 2009
    Banks WD; Shparlinski IE, 2009, 'Prime numbers with beatty sequences', Colloquium Mathematicum, 115, pp. 147 - 157,
    Journal articles | 2009
    Banks WD; Shparlinski IE, 2009, 'Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height', Israel Journal of Mathematics, 173, pp. 253 - 277,
    Journal articles | 2009
    Bourgain J; Konyagin SV; Pomerance C; Shparlinski IE, 2009, 'On the smallest pseudopower', Acta Arithmetica, 140, pp. 43 - 55,
    Journal articles | 2009
    Bourgain J; Konyagin SV; Shparlinski IE, 2009, 'Erratum: Product sets of rationals, multiplicative translates of subgroups in residue rings and fixed points of the discrete logarithm (International Mathematics Research Notices)', International Mathematics Research Notices, 2009, pp. 3146 - 3147,
    Journal articles | 2009
    Cojocaru AC; Luca F; Shparlinski IE, 2009, 'Pseudoprime reductions of elliptic curves', Mathematical Proceedings of the Cambridge Philosophical Society, 146, pp. 513 - 522,
    Journal articles | 2009
    Cojocaru AC; Shparlinski IE, 2009, 'On the embedding degree of reductions of an elliptic curve', Information Processing Letters, 109, pp. 652 - 654,
    Journal articles | 2009
    Farashahi RR; Shparlinski IE; Voloch JF, 2009, 'On hashing into elliptic curves', Journal of Mathematical Cryptology, 3, pp. 353 - 360,
    Journal articles | 2009
    Ford K; Luca F; Shparlinski IE, 2009, 'On the largest prime factor of the mersenne numbers', Bulletin of the Australian Mathematical Society, 79, pp. 455 - 463,
    Journal articles | 2009
    Friedlander JB; Shparlinski IE, 2009, 'Elliptic twin prime conjecture', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 5557 LNCS, pp. 77 - 81,
    Journal articles | 2009
    Friedlander JB; Shparlinski IE, 2009, 'On the density of some special primes', Journal of Mathematical Cryptology, 3, pp. 265 - 271,
    Journal articles | 2009
    Igor S, 2009, 'Some special character sums over elliptic curves', Boletin De La Sociedad Matematica Mexicana, 15, pp. 37 - 40
    Journal articles | 2009
    Katz NM; Shparlinski IE; Xiong M, 2009, 'On character sums with distances on the upper half plane over a finite field', Finite Fields and their Applications, 15, pp. 738 - 747,
    Journal articles | 2009
    Luca F; Shparlinski IE, 2009, 'On quadratic fields generated by the Shanks sequence', Proceedings of the Edinburgh Mathematical Society, 52, pp. 719 - 729,
    Journal articles | 2009
    Pomerance C; Shparlinski IE, 2009, 'On Pseudosquares and Pseudopowers', COMBINATORIAL NUMBER THEORY, pp. 171 - +,
    Journal articles | 2009
    Shparlinski IE, 2009, 'Bilinear sums with exponential functions', Proceedings of the American Mathematical Society, 137, pp. 2217 - 2224,
    Journal articles | 2009
    Shparlinski IE, 2009, 'EXPONENTS OF MODULAR REDUCTIONS OF FAMILIES OF ELLIPTIC CURVES', REVISTA DE LA UNION MATEMATICA ARGENTINA, 50, pp. 69 - 74,
    Journal articles | 2009
    Shparlinski IE, 2009, 'Exponential Sums with Farey Fractions', Bulletin of the Polish Academy of Sciences Mathematics, 57, pp. 101 - 107,
    Journal articles | 2009
    Shparlinski IE, 2009, 'On a generalisation of a Lehmer problem', Mathematische Zeitschrift, 263, pp. 619 - 631,
    Journal articles | 2009
    Shparlinski IE, 2009, 'On some weighted average values of l-functions', Bulletin of the Australian Mathematical Society, 79, pp. 183 - 186,
    Journal articles | 2009
    Shparlinski IE, 2009, 'On the distribution of arguments of gauss sums', Kodai Mathematical Journal, 32, pp. 172 - 177,
    Journal articles | 2009
    Shparlinski IE, 2009, 'On the distribution of orbits of PGL2(q) in Fqn and the Klapper conjecture', SIAM Journal on Discrete Mathematics, 23, pp. 2093 - 2099,
    Journal articles | 2009
    Shparlinski IE, 2009, 'On the distribution of solutions to linear equations', Glasnik Matematicki, 44, pp. 7 - 10,
    Journal articles | 2009
    Shparlinski IE, 2009, 'On the values of Kloosterman sums', IEEE Transactions on Information Theory, 55, pp. 2599 - 2601,
    Journal articles | 2009
    Von Zur Gathen J; Shparlinski IE, 2009, 'Subset sum pseudorandom numbers: Fast generation and distribution', Journal of Mathematical Cryptology, 3, pp. 149 - 163,
    Journal articles | 2008
    Balasuriya S; Banks WD; Shparlinski IE, 2008, 'Congruences and exponential sums with the sum of aliquot divisors function', International Journal of Number Theory, 4, pp. 903 - 909,
    Journal articles | 2008
    Banks WD; Garaev MZ; Heath-Brown DR; Shparlinski IE, 2008, 'Density of non-residues in Burgess-type intervals and applications', Bulletin of the London Mathematical Society, 40, pp. 88 - 96,
    Journal articles | 2008
    Blackburn SR; Shparlinski IE, 2008, 'On the average energy of circulant graphs', Linear Algebra and Its Applications, 428, pp. 1956 - 1963,
    Journal articles | 2008
    Bourgain J; Konyagin SV; Shparlinski IE, 2008, 'Product sets of rationals, multiplicative translates of subgroups in residue rings, and fixed points of the discrete logarithm', International Mathematics Research Notices, 2008,
    Journal articles | 2008
    Bourgain J; Shparlinski IE, 2008, 'Distribution of consecutive modular roots of an integer', Acta Arithmetica, 134, pp. 83 - 91,
    Journal articles | 2008
    Cojocaru AC; Shparlinski IE, 2008, 'Distribution of farey fractions in residue classes and lang-trotter conjectures on average', Proceedings of the American Mathematical Society, 136, pp. 1977 - 1986,
    Journal articles | 2008
    Ford K; Shparlinski I, 2008, 'On curves over finite fields with Jacobians of small exponent', International Journal of Number Theory, 4, pp. 819 - 826,
    Journal articles | 2008
    Friedlander JB; Kurlberg P; Shparlinski IE, 2008, 'PRODUCTS IN RESIDUE CLASSES', MATHEMATICAL RESEARCH LETTERS, 15, pp. 1133 - 1147,
    Journal articles | 2008
    Friedlander JB; Kurlberg P; Shparlinski IE, 2008, 'Products in residue classes', Mathematical Research Letters, 15, pp. 1133 - 1147,
    Journal articles | 2008
    Friedlander JB; Shparlinski IE, 2008, 'Erratum: Least totient in a residue class (Bulletin of the London Mathematical Society (2007) 39 (425-432))', Bulletin of the London Mathematical Society, 40, pp. 532,
    Journal articles | 2008
    Graham SW; Shparlinski IE, 2008, 'On RSA moduli with almost half of the bits prescribed', Discrete Applied Mathematics, 156, pp. 3150 - 3154,
    Journal articles | 2008
    Khan MR; Shparlinski IE; Yankov CL, 2008, 'On the convex closure of the graph of modular inversions', Experimental Mathematics, 17, pp. 91 - 104,
    Journal articles | 2008
    Kohnen W; Lau YK; Shparlinski IE, 2008, 'On the number of sign changes of hecke eigenvalues of newforms', Journal of the Australian Mathematical Society, 85, pp. 87 - 94,
    Journal articles | 2008
    Luca F; Shparlinski IE; Thangadurai R, 2008, 'Quadratic non-residues versus primitive roots modulo p', Journal of the Ramanujan Mathematical Society, 23, pp. 97 - 104
    Journal articles | 2008
    Luca F; Shparlinski IE, 2008, 'Arithmetic properties of Ap茅ry numbers', Journal of the London Mathematical Society, 78, pp. 545 - 562,
    Journal articles | 2008
    Luca F; Shparlinski IE, 2008, 'On quadratic fields generated by polynomials', Archiv Der Mathematik, 91, pp. 399 - 408,
    Journal articles | 2008
    Luca F; Shparlinski IE, 2008, 'On the values of the divisor function', Monatshefte Fur Mathematik, 154, pp. 59 - 69,
    Journal articles | 2008
    Naccache D; Shparlinski IE, 2008, 'Divisibility, Smoothness and Cryptographic Applications', Divisibility, Smoothness and Cryptographic Applications,
    Journal articles | 2008
    Shparlinski I, 2008, 'Bilinear character sums over elliptic curves', Finite Fields and their Applications, 14, pp. 132 - 141,
    Journal articles | 2008
    Shparlinski I, 2008, 'On the elliptic curve analogue of the sum-product problem', Finite Fields and their Applications, 14, pp. 721 - 726,
    Journal articles | 2008
    Shparlinski I, 2008, 'On the exponential sum-product problem', Indagationes Mathematicae, 19, pp. 325 - 331,
    Journal articles | 2008
    Shparlinski I, 2008, 'On the size of the Jacobians of curves over finite fields', Bulletin of the Brazilian Mathematical Society, 39, pp. 587 - 595,
    Journal articles | 2008
    Shparlinski IE; Voloch JF, 2008, 'Average distribution of prime ideals in families of number fields', Bulletin of the Brazilian Mathematical Society, 39, pp. 417 - 425,
    Journal articles | 2008
    Shparlinski IE; Winterhof A, 2008, 'On the number of distances between the coordinates of points on modular hyperbolas', Journal of Number Theory, 128, pp. 1224 - 1230,
    Journal articles | 2008
    Shparlinski IE; Winterhof A, 2008, 'Visible points on multidimensional modular hyperbolas', Journal of Number Theory, 128, pp. 2695 - 2703,
    Journal articles | 2008
    Shparlinski IE, 2008, 'Approximation by several rationals', Bulletin of the Australian Mathematical Society, 77, pp. 325 - 329,
    Journal articles | 2008
    Shparlinski IE, 2008, 'Arithmetic and geometric progressions in product sets over finite fields', Bulletin of the Australian Mathematical Society, 78, pp. 357 - 364,
    Journal articles | 2008
    Shparlinski IE, 2008, 'Distribution of modular inverses and multiples of small integers and the Sato-Tate conjecture on average', Michigan Mathematical Journal, 56, pp. 99 - 111,
    Journal articles | 2008
    Shparlinski IE, 2008, 'Exponential sums and prime divisors of sparse integers', Periodica Mathematica Hungarica, 57, pp. 93 - 99,
    Journal articles | 2008
    Shparlinski IE, 2008, 'Infinite hilbert class field towers over cyclotomic fields', Glasgow Mathematical Journal, 50, pp. 27 - 32,
    Journal articles | 2008
    Shparlinski IE, 2008, 'On a Generalised Lehmer Problem for Arbitrary Powers', On a Generalised Lehmer Problem for Arbitrary Powers,
    Journal articles | 2008
    Shparlinski IE, 2008, 'On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas', Bulletin of the Polish Academy of Sciences Mathematics, 56, pp. 1 - 7,
    Journal articles | 2008
    Shparlinski IE, 2008, 'On the distribution of Kloosterman sums', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 136, pp. 419 - 425,
    Journal articles | 2008
    Shparlinski IE, 2008, 'On the distribution of kloosterman sums', Proceedings of the American Mathematical Society, 136, pp. 419 - 425,
    Journal articles | 2008
    Shparlinski IE, 2008, 'On the solvability of bilinear equations in finite fields', Glasgow Mathematical Journal, 50, pp. 523 - 529,
    Journal articles | 2008
    Shparlinski IE, 2008, 'Pseudorandom graphs from elliptic curves', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 4957 LNCS, pp. 284 - 292,
    Journal articles | 2008
    Van Dam W; Shparlinski IE, 2008, 'Classical and quantum algorithms for exponential congruences', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 5106 LNCS, pp. 1 - 10,
    Journal articles | 2008
    Von Zur Gathen J; Shparlinski IE, 2008, 'Approximate polynomial gcd: Small degree and small height perturbations', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 4957 LNCS, pp. 276 - 283,
    Journal articles | 2007
    Ahmadi O; Shparlinski IE, 2007, 'Distribution of matrices with restricted entries over finite fields', Indagationes Mathematicae, 18, pp. 327 - 337,
    Journal articles | 2007
    Ahmadi O; Shparlinski IE, 2007, 'Geometric progressions in sumsets over finite fields', Monatshefte Fur Mathematik, 152, pp. 177 - 185,
    Journal articles | 2007
    Balasuriya S; Luca F; Shparlinski IE, 2007, 'Prime Divisors Of Some Recurrence Sequence', Periodica Mathematica Hungarica, 54, pp. 215 - 227,
    Journal articles | 2007
    Balasuriya S; Shparlinski IE, 2007, 'Character sums with subsequence sums', Periodica Mathematica Hungarica, 55, pp. 215 - 221,
    Journal articles | 2007
    Banks WD; Luca F; Shparlinski IE, 2007, 'Estimates for Wieferich numbers', Ramanujan Journal, 14, pp. 361 - 378,
    Journal articles | 2007
    Banks WD; Luca F; Shparlinski IE, 2007, 'On rough and smooth neighbors', REVISTA MATEMATICA COMPLUTENSE, 20, pp. 109 - 118,
    Journal articles | 2007
    Banks WD; Shparlinski IE, 2007, 'On values taken by the largest prime factor of shifted primes', Journal of the Australian Mathematical Society, 82, pp. 133 - 147,
    Journal articles | 2007
    Banks WD; Shparlinski IE, 2007, 'Prime divisors in Beatty sequences', Journal of Number Theory, 123, pp. 413 - 425,
    Journal articles | 2007
    Becheanu M; Luca F; Shparlinski IE, 2007, 'On the sums of complementary divisors', INTERNATIONAL JOURNAL OF NUMBER THEORY, 3, pp. 635 - 648,
    Journal articles | 2007
    Blackburn SR; Shparlinski IE, 2007, 'Erratum to "Character sums and nonlinear recurrence sequences". [Discrete Math. 306 (2006) 1126-1131] (DOI:10.1016/j.disc.2006.02.012)', Discrete Mathematics, 307, pp. 1218 - 1219,
    Journal articles | 2007
    Blake IF; Shparlinski IE, 2007, 'Statistical distribution and collisions of VSH', JOURNAL OF MATHEMATICAL CRYPTOLOGY, 1, pp. 329 - 349,
    Journal articles | 2007
    Friedlander JB; Shparlinski IE, 2007, 'Least totient in a residue class', Bulletin of the London Mathematical Society, 39, pp. 425 - 432,
    Journal articles | 2007
    Garaev MZ; Luca F; Shparlinski IE, 2007, 'Exponential sums with Catalan numbers and middle binomial coefficients', Indagationes Mathematicae, 18, pp. 23 - 37,
    Journal articles | 2007
    Lange T; Shparlinski IE, 2007, 'Distribution of some sequences of points on elliptic curves', Journal of Mathematical Cryptology, 1, pp. 1 - 11,
    Journal articles | 2007
    Luca F; Shparlinski IE, 2007, 'Arithmetic functions with linear recurrence sequences', Journal of Number Theory, 125, pp. 459 - 472,
    Journal articles | 2007
    Luca F; Shparlinski IE, 2007, 'Discriminants of complex multiplication fields of elliptic curves over finite fields', Canadian Mathematical Bulletin, 50, pp. 409 - 417,
    Journal articles | 2007
    Luca F; Shparlinski IE, 2007, 'On finite fields for pairing based cryptography', ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 1, pp. 281 - 286,
    Journal articles | 2007
    Luca F; Shparlinski IE, 2007, 'On the square-free parts of 鈱奺n!鈱', Glasgow Mathematical Journal, 49, pp. 391 - 403,
    Journal articles | 2007
    Luca F; Shparlinski IE, 2007, 'PSEUDOPRIMES IN CERTAIN LINEAR RECURRENCES', Albanian Journal of Mathematics, 1,
    Journal articles | 2007
    Luca F; Shparlinski IE, 2007, 'Pseudoprime Cullen and Woodall numbers', Colloquium Mathematicum, 107, pp. 35 - 43,
    Journal articles | 2007
    Saxena N; Severini S; Shparlinski I, 2007, 'Parameters of integral circulant graphs and periodic quantum dynamics', International Journal of Quantum Information, 5, pp. 417 - 430,
    Journal articles | 2007
    Shparlinski I, 2007, 'A computational introduction to number theory and algebra', MATHEMATICS OF COMPUTATION, 76, pp. 1697 - 1698,
    Journal articles | 2007
    Shparlinski IE; Steinfeld R, 2007, 'Chinese remaindering with multiplicative noise', Theory of Computing Systems, 40, pp. 33 - 41,
    Journal articles | 2007
    Shparlinski IE; Sutantyo D, 2007, 'On the set of the largest prime divisors', Publicationes Mathematicae Debrecen, 71, pp. 95 - 100,
    Journal articles | 2007
    Shparlinski IE; Voloch JF, 2007, 'Visible Points on Curves over Finite Fields', Bulletin of the Polish Academy of Sciences Mathematics, 55, pp. 193 - 199,
    Journal articles | 2007
    Shparlinski IE; Winterhof A, 2007, 'Quantum period reconstruction of approximate sequences', Information Processing Letters, 103, pp. 211 - 215,
    Journal articles | 2007
    Shparlinski IE, 2007, 'Bounds of incomplete multiple Kloosterman sums', JOURNAL OF NUMBER THEORY, 126, pp. 68 - 73,
    Journal articles | 2007
    Shparlinski IE, 2007, 'Bounds of incomplete multiple Kloosterman sums', Journal of Number Theory, 126, pp. 68 - 73,
    Journal articles | 2007
    Shparlinski IE, 2007, 'Bounds on the Fourier coefficients of the weighted sum function', Information Processing Letters, 103, pp. 83 - 87,
    Journal articles | 2007
    Shparlinski IE, 2007, 'Character sums over shifted smooth numbers', Proceedings of the American Mathematical Society, 135, pp. 2699 - 2705,
    Journal articles | 2007
    Shparlinski IE, 2007, 'Communication complexity of some number theoretic functions', Applied Mathematics Letters, 20, pp. 872 - 875,
    Journal articles | 2007
    Shparlinski IE, 2007, 'Distribution of roots of polynomial congruences', International Journal of Mathematics and Mathematical Sciences, 2007,
    Journal articles | 2007
    Shparlinski IE, 2007, 'On some dynamical systems in finite fields and residue rings', Discrete and Continuous Dynamical Systems, 17, pp. 901 - 917,
    Journal articles | 2007
    Shparlinski IE, 2007, 'On the distribution of angles of the sali茅 sums', Bulletin of the Australian Mathematical Society, 75, pp. 221 - 227,
    Journal articles | 2007
    Shparlinski IE, 2007, 'On the distribution of points on multidimensional modular hyperbolas', Proceedings of the Japan Academy Series A Mathematical Sciences, 83, pp. 5 - 9,
    Journal articles | 2006
    Banks MK, 2006, 'Editor鈥檚 Note', Journal of Environmental Engineering, 132, pp. 157 - 157,
    Journal articles | 2006
    Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2006, 'Character sums with exponential functions over smooth numbers', Indagationes Mathematicae, 17, pp. 157 - 168,
    Journal articles | 2006
    Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2006, 'Double character sums over elliptic curves and finite fields', PURE AND APPLIED MATHEMATICS QUARTERLY, 2, pp. 179 - 197,
    Journal articles | 2006
    Banks WD; Friedlander JB; Konyagin SV; Shparlinski IE, 2006, 'Incomplete exponential sums and Diffie-Hellman triples', Mathematical Proceedings of the Cambridge Philosophical Society, 140, pp. 193 - 206,
    Journal articles | 2006
    Banks WD; Friedlander JB; Luca F; Pappalardi F; Shparlinski IE, 2006, 'Coincidences in the values of the Euler and Carmichael functions', Acta Arithmetica, 122, pp. 207 - 234,
    Journal articles | 2006
    Banks WD; Luca F; Shparlinski IE, 2006, 'Arithmetic properties of 蠁(n)/位(n) and the structure of the multiplicative group modulo n', Commentarii Mathematici Helvetici, 81, pp. 1 - 22,
    Journal articles | 2006
    Banks WD; Luca F; Shparlinski IE, 2006, 'Common divisors of the Euler function at related arguments', ACTA SCIENTIARUM MATHEMATICARUM, 72, pp. 525 - 536,
    Journal articles | 2006
    Banks WD; Shparlinski IE, 2006, 'Average Value of the Euler Function on Binary Palindromes', Bulletin of the Polish Academy of Sciences Mathematics, 54, pp. 95 - 101,
    Journal articles | 2006
    Banks WD; Shparlinski IE, 2006, 'Character sums with Beatty sequences on Burgess-type intervals', Character sums with Beatty sequences on Burgess-type intervals,
    Journal articles | 2006
    Banks WD; Shparlinski IE, 2006, 'Congruences and rational exponential sums with the euler function', Rocky Mountain Journal of Mathematics, 36, pp. 1415 - 1426,
    Journal articles | 2006
    Banks WD; Shparlinski IE, 2006, 'Integers with a large smooth divisor', Integers with a large smooth divisor,
    Journal articles | 2006
    Banks WD; Shparlinski IE, 2006, 'Multiplicative character sums with the sum of g-ary digits function', Ramanujan Journal, 11, pp. 215 - 219,
    Journal articles | 2006
    Banks WD; Shparlinski IE, 2006, 'Non-residues and primitive roots in beatty sequences', Bulletin of the Australian Mathematical Society, 73, pp. 433 - 443,
    Journal articles | 2006
    Banks WD; Shparlinski IE, 2006, 'Short character sums with beatty sequences', Mathematical Research Letters, 13, pp. 539 - 547,
    Journal articles | 2006
    Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Reconstructing noisy polynomial evaluation in residue rings', JOURNAL OF ALGORITHMS-COGNITION INFORMATICS AND LOGIC, 61, pp. 47 - 59,
    Journal articles | 2006
    Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Reconstructing noisy polynomial evaluation in residue rings', Journal of Algorithms, 61, pp. 47 - 59,
    Journal articles | 2006
    Blackburn SR; Shparlinski IE, 2006, 'Character sums and nonlinear recurrence sequences', Discrete Mathematics, 306, pp. 1126 - 1131,
    Journal articles | 2006
    Blake IF; Garefalakis T; Shparlinski IE, 2006, 'On the bit security of the Diffie-Hellman key', Applicable Algebra in Engineering Communications and Computing, 16, pp. 397 - 404,
    Journal articles | 2006
    Contini S; Croot E; Shparlinski IE, 2006, 'Complexity of inverting the Euler function', Mathematics of Computation, 75, pp. 983 - 996,
    Journal articles | 2006
    Coppersmith D; Howgrave-Graham N; Nguy峄卬 PQ; Shparlinski IE, 2006, 'Testing set proportionality and the 脕d谩m isomorphism of circulant graphs', Journal of Discrete Algorithms, 4, pp. 324 - 335,
    Journal articles | 2006
    El-Mahassni ED; Shparlinski IE; Winterhof A, 2006, 'Distribution of nonlinear congruential pseudorandom numbers modulo almost squarefree integers', Monatshefte Fur Mathematik, 148, pp. 297 - 307,
    Journal articles | 2006
    Garaev MZ; Luca F; Shparlinski IE; Winterhof A, 2006, 'On the lower bound of the linear complexity over Fp of Sidelnikov sequences', IEEE Transactions on Information Theory, 52, pp. 3299 - 3304,
    Journal articles | 2006
    Garaev MZ; Luca F; Shparlinski IE, 2006, 'Catalan and Ap茅ry numbers in residue classes', Journal of Combinatorial Theory Series A, 113, pp. 851 - 865,
    Journal articles | 2006
    Garaev MZ; Luca F; Shparlinski IE, 2006, 'Distribution of harmonic sums and Bernoulli polynomials modulo a prime', Mathematische Zeitschrift, 253, pp. 855 - 865,
    Journal articles | 2006
    Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Exponential sums with Dickson polynomials', Finite Fields and their Applications, 12, pp. 16 - 25,
    Journal articles | 2006
    Luca F; McKee J; Shparlinsk IE, 2006, 'Small exponent point groups on elliptic curves', Journal De Theorie Des Nombres De Bordeaux, 18, pp. 471 - 476,
    Journal articles | 2006
    Luca F; Shparlinski IE, 2006, 'Arithmetic properties of the Ramanujan function', Proceedings of the Indian Academy of Sciences Mathematical Sciences, 116, pp. 1 - 8,
    Journal articles | 2006
    Luca F; Shparlinski IE, 2006, 'Elliptic curves with low embedding degree', Journal of Cryptology, 19, pp. 553 - 562,
    Journal articles | 2006
    Luca F; Shparlinski IE, 2006, 'ON THE NUMBER OF POLYNOMIAL MAPS INTO Z(n)', TSUKUBA JOURNAL OF MATHEMATICS, 30, pp. 431 - 441,
    Journal articles | 2006
    Luca F; Shparlinski IE, 2006, 'On the number of polynomial maps into $\mathbb{Z}_{n}$', Tsukuba Journal of Mathematics, 30,
    Journal articles | 2006
    Luca F; Shparlinski IE, 2006, 'Pseudoprime values of the Fibonacci sequence, polynomials and the Euler function', Indagationes Mathematicae, 17, pp. 611 - 625,
    Journal articles | 2006
    Luca F; Shparlinski IE, 2006, 'Some divisibilities amongst the terms of linear recurrences', Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, 76, pp. 143 - 156,
    Journal articles | 2006
    Luca F; Shparlinski IE, 2006, 'Uniformity of distribution modulo 1 of the geometric mean prime divisor', Boletin De La Sociedad Matematica Mexicana, 12, pp. 155 - 163
    Journal articles | 2006
    Shparlinski I, 2006, 'On the energy of some circulant graphs', Linear Algebra and Its Applications, 414, pp. 378 - 382,
    Journal articles | 2006
    Shparlinski I, 2006, 'On the set of distances between two sets over finite fields', International Journal of Mathematics and Mathematical Sciences, 2006,
    Journal articles | 2006
    Shparlinski IE; Winterhof A, 2006, 'Constructions of approximately mutually unbiased bases', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 3887 LNCS, pp. 793 - 799,
    Journal articles | 2006
    Shparlinski IE; Winterhof A, 2006, 'On the discrepancy and linear complexity of some counter-dependent recurrence sequences', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 4086 LNCS, pp. 295 - 303,
    Journal articles | 2006
    Shparlinski IE; Winterhof A, 2006, 'On the nonlinearity of linear recurrence sequences', Applied Mathematics Letters, 19, pp. 340 - 344,
    Journal articles | 2006
    Shparlinski IE, 2006, 'On RSA moduli with prescribed bit patterns', Designs Codes and Cryptography, 39, pp. 113 - 122,
    Journal articles | 2006
    Shparlinski IE, 2006, 'On some generalisations of the Erdos distance problem over finite fields', Bulletin of the Australian Mathematical Society, 73, pp. 285 - 292,
    Journal articles | 2006
    Shparlinski IE, 2006, 'On the sum of iterations of the Euler function', Journal of Integer Sequences, 9, pp. 1 - 5
    Journal articles | 2006
    Shparlinski IE, 2006, 'Primitive Points on a Modular Hyperbola', Bulletin of the Polish Academy of Sciences Mathematics, 54, pp. 193 - 200,
    Journal articles | 2006
    Shparlinski IE, 2006, 'Truncations of L-functions in residue classes', Glasgow Mathematical Journal, 48, pp. 347 - 350,
    Journal articles | 2006
    Von Zur Gathen J; Shparlinski IE, 2006, 'GCD of random linear combinations', Algorithmica New York, 46, pp. 137 - 148,
    Journal articles | 2005
    Banks WD; Ford K; Luca F; Pappalardi F; Shparlinski IE, 2005, 'Values of the Euler function in various sequences', Monatshefte Fur Mathematik, 146, pp. 1 - 19,
    Journal articles | 2005
    Banks WD; Garaev MZ; Luca F; Shparlinski IE, 2005, 'Uniform Distribution of the Fractional Part of the Average Prime Divisor', Forum Mathematicum, 17, pp. 885 - 901,
    Journal articles | 2005
    Banks WD; Harman G; Shparlinski IE, 2005, 'Distributional properties of the largest prime factor', Michigan Mathematical Journal, 53, pp. 665 - 681,
    Journal articles | 2005
    Banks WD; Heath-Brown R; Shparlinski IE, 2005, 'On the average value of divisor sums in arithmetic progressions', International Mathematics Research Notices, pp. 1 - 25,
    Journal articles | 2005
    Banks WD; Luca F; Saidak F; Shparlinski IE, 2005, 'Values of arithmetical functions equal to a sum of two squares', Quarterly Journal of Mathematics, 56, pp. 123 - 139,
    Journal articles | 2005
    Banks WD; Luca F; Shparlinski IE, 2005, 'Irrationality of power series for various number theoretic functions', Manuscripta Mathematica, 117, pp. 183 - 197,
    Journal articles | 2005
    Banks WD; Luca F; Shparlinski IE, 2005, 'Some divisibility properties of the Euler function', Glasgow Mathematical Journal, 47, pp. 517 - 528,
    Journal articles | 2005
    Banks WD; Shparlinski IE, 2005, 'Prime divisors of palindromes', Periodica Mathematica Hungarica, 51, pp. 1 - 10,
    Journal articles | 2005
    Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2005, 'Predicting nonlinear pseudorandom number generators', Mathematics of Computation, 74, pp. 1471 - 1494,
    Journal articles | 2005
    Cohen SD; Dewar M; Friedlander JB; Panario D; Shparlinski IE, 2005, 'Polynomial gauss sums', Proceedings of the American Mathematical Society, 133, pp. 2225 - 2231,
    Journal articles | 2005
    Contini S; Shparlinski IE, 2005, 'On Stern's attack against secret truncated linear congruential generators', Lecture Notes in Computer Science, 3574, pp. 52 - 60,
    Journal articles | 2005
    De Koninck JM; Luca F; Shparlinski IE, 2005, 'Powerful numbers in short intervals', Bulletin of the Australian Mathematical Society, 71, pp. 11 - 16,
    Journal articles | 2005
    Everest G; Shparlinski IE, 2005, 'Prime divisors of sequences associated to elliptic curves', Glasgow Mathematical Journal, 47, pp. 115 - 122,
    Journal articles | 2005
    Ford K; Khan MR; Shparlinski IE; Yankov CL, 2005, 'On the maximal difference between an element and its inverse in residue rings', Proceedings of the American Mathematical Society, 133, pp. 3463 - 3468,
    Journal articles | 2005
    Friedlander JB; Pomerance C; Shparlinski IE, 2005, 'Finding the group structure of elliptic curves over finite fields', Bulletin of the Australian Mathematical Society, 72, pp. 251 - 263,
    Journal articles | 2005
    Garaev MZ; Luca F; Shparlinski IE, 2005, 'Exponential sums and congruences with factorials', Journal Fur Die Reine Und Angewandte Mathematik, pp. 29 - 44,
    Journal articles | 2005
    Garaev MZ; Luca F; Shparlinski IE, 2005, 'Waring problem with factorials', Bulletin of the Australian Mathematical Society, 71, pp. 259 - 264,
    Journal articles | 2005
    Garaev MZ; Shparlinski IE, 2005, 'The large sieve inequality with exponential functions and the distribution of mersenne numbers modulo primes', International Mathematics Research Notices, pp. 2391 - 2403,
    Journal articles | 2005
    Granville A; Shparlinski IE; Zaharescu A, 2005, 'On the distribution of rational functions along a curve over F-P and residue races', JOURNAL OF NUMBER THEORY, 112, pp. 216 - 237,
    Journal articles | 2005
    Granville A; Shparlinski IE; Zaharescu A, 2005, 'On the distribution of rational functions along a curve over Fp and residue races', Journal of Number Theory, 112, pp. 216 - 237,
    Journal articles | 2005
    Hallgren S; Russell A; Shparlinski IE, 2005, 'Quantum noisy rational function reconstruction', Lecture Notes in Computer Science, 3595, pp. 420 - 429,
    Journal articles | 2005
    Hess F; Shparlinski IE, 2005, 'On the linear complexity and multidimensional distribution of congruential generators over elliptic curves', Designs Codes and Cryptography, 35, pp. 111 - 117,
    Journal articles | 2005
    Klappenecker A; R枚tteler M; Shparlinski IE; Winterhof A, 2005, 'On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states', Journal of Mathematical Physics, 46,
    Journal articles | 2005
    Lange T; Shparlinski I, 2005, 'Collisions in fast generation of ideal classes and points on hyperelliptic and elliptic curves', Applicable Algebra in Engineering Communications and Computing, 15, pp. 329 - 337,
    Journal articles | 2005
    Lange T; Shparlinski IE, 2005, 'Certain exponential sums and random walks on elliptic curves', Canadian Journal of Mathematics, 57, pp. 338 - 350,
    Journal articles | 2005
    Levieil E; Luca F; Shparlinski IE, 2005, 'Bounding the number of solutions of some congruences', Boletin De La Sociedad Matematica Mexicana, 11, pp. 175 - 180
    Journal articles | 2005
    Levieil E; Luca F; Shparlinski IE, 2005, 'Prime divisors of some shifted products', International Journal of Mathematics and Mathematical Sciences, 2005, pp. 3057 - 3073,
    Journal articles | 2005
    Luca F; Shparlinski IE, 2005, 'On the exponent of the group of points on elliptic curves in extension fields', International Mathematics Research Notices, pp. 1391 - 1409,
    Journal articles | 2005
    Luca F; Shparlinski IE, 2005, 'On the largest prime factor of n! + 2n 鈭 1', Journal De Theorie Des Nombres De Bordeaux, 17, pp. 859 - 870,
    Journal articles | 2005
    Luca F; Shparlinski IE, 2005, 'Prime divisors of shifted factorials', Bulletin of the London Mathematical Society, 37, pp. 809 - 817,
    Journal articles | 2005
    Shparlinski I; Winterhof A, 2005, 'A hidden number problem in small subgroups', Mathematics of Computation, 74, pp. 2073 - 2080,
    Journal articles | 2005
    Shparlinski I; Winterhof A, 2005, 'Noisy interpolation of sparse polynomials in finite fields', Applicable Algebra in Engineering Communications and Computing, 16, pp. 307 - 317,
    Journal articles | 2005
    Shparlinski I, 2005, 'Book Review: Report on global methods for combinatorial isoperimetric problems', Mathematics of Computation, 74, pp. 1033 - 1052,
    Journal articles | 2005
    Shparlinski IE; Winterhof A, 2005, 'On the linear complexity of bounded integer sequences over different moduli', Information Processing Letters, 96, pp. 175 - 177,
    Journal articles | 2005
    Shparlinski IE, 2005, 'On the nonlinearity of the sequence of signs of Kloosterman sums', Bulletin of the Australian Mathematical Society, 71, pp. 405 - 409,
    Journal articles | 2005
    Shparlinski IE, 2005, 'On the singularity of generalised Vandermonde matrices over finite fields', Finite Fields and their Applications, 11, pp. 193 - 199,
    Journal articles | 2005
    Shparlinski IE, 2005, 'On the value set of the Ramanujan function', Archiv Der Mathematik, 85, pp. 508 - 513,
    Journal articles | 2005
    von zur Gathen J; Shparlinski IE; Stichtenoth H, 2005, 'Finite Fields: Theory and Applications', Oberwolfach Reports, 1, pp. 2913 - 2970,
    Journal articles | 2004
    Banks WD; Conflitti A; Friedlander JB; Shparlinski IE, 2004, 'Exponential sums over Mersenne numbers', Compositio Mathematica, 140, pp. 15 - 30,
    Journal articles | 2004
    Banks WD; Conflitti A; Shparlinski IE, 2004, 'Number theoretic designs for directed regular graphs of small diameter', SIAM Journal on Discrete Mathematics, 17, pp. 377 - 383,
    Journal articles | 2004
    Banks WD; Harcharras A; Shparlinski IE, 2004, 'Smooth values of shifted primes in arithmetic progressions', Michigan Mathematical Journal, 52, pp. 603 - 618,
    Journal articles | 2004
    Banks WD; Shparlinski IE, 2004, 'Arithmetic properties of numbers with restricted digits', Acta Arithmetica, 112, pp. 313 - 332,
    Journal articles | 2004
    Chou WS; Shparlinski IE, 2004, 'On the cycle structure of repeated exponentiation modulo a prime', Journal of Number Theory, 107, pp. 345 - 356,
    Journal articles | 2004
    Conflitti A; Shparlinski IE, 2004, 'On the multidimensional distribution of the subset sum generator of pseudorandom numbers', Mathematics of Computation, 73, pp. 1005 - 1011,
    Journal articles | 2004
    Dewar M; Panario D; Shparlinski IE, 2004, 'Distribution of exponential functions with k-full exponent modulo a prime', Indagationes Mathematicae, 15, pp. 497 - 503,
    Journal articles | 2004
    Frandsen GS; Shparlinski IE, 2004, 'On Reducing a System of Equations to a Single Equation', BRICS Report Series, 11,
    Journal articles | 2004
    Frandsen GS; Shparlinski IE, 2004, 'On reducing a system of equations to a single equation', Proceedings of the International Symposium on Symbolic and Algebraic Computation ISSAC, pp. 163 - 166,
    Journal articles | 2004
    Galbraith SD; Hopkins HJ; Shparlinski IE, 2004, 'Secure bilinear Diffie-Hellman bits', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 3108, pp. 370 - 378,
    Journal articles | 2004
    Garaev MZ; Luca F; Shparlinski IE, 2004, 'Character sums and congruences with n!', Transactions of the American Mathematical Society, 356, pp. 5089 - 5102,
    Journal articles | 2004
    Goresky M; Klapper A; Murty R; Shparlinski I, 2004, 'On decimations of 鈩-sequences', SIAM Journal on Discrete Mathematics, 18, pp. 130 - 140,
    Journal articles | 2004
    Luca F; Mireles DJ; Shparlinski IE, 2004, 'Florianptic curves', Illinois Journal of Mathematics, 48, pp. 1041 - 1052,
    Journal articles | 2004
    Luca F; Mireles DJ; Shparlinski IE, 2004, 'Mov attack in various subgroups on elliptic curves', ILLINOIS JOURNAL OF MATHEMATICS, 48, pp. 1041 - 1052,
    Journal articles | 2004
    Mans B; Shparlinski I, 2004, 'Bisecting and gossiping in circulant graphs', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2976, pp. 589 - 598,
    Journal articles | 2004
    Russell A; Shparlinski IE, 2004, 'Classical and quantum function reconstruction via character evaluation', Journal of Complexity, 20, pp. 404 - 422,
    Journal articles | 2004
    Shparlinski IE; Steinfield R, 2004, 'Noisy Chinese remaindering in the Lee norm', Journal of Complexity, 20, pp. 423 - 437,
    Journal articles | 2004
    Shparlinski IE; Winterhof A, 2004, 'A nonuniform algorithm for the hidden number problem in subgroups', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2947, pp. 416 - 424,
    Journal articles | 2004
    Shparlinski IE, 2004, 'Bounds of Gauss sums in finite fields', Proceedings of the American Mathematical Society, 132, pp. 2817 - 2824,
    Journal articles | 2004
    Shparlinski IE, 2004, 'Distribution of exponential functions with squarefull exponent in residue rings', Indagationes Mathematicae, 15, pp. 283 - 289,
    Journal articles | 2004
    Shparlinski IE, 2004, 'Exponential function analogue of kloosterman sums', Rocky Mountain Journal of Mathematics, 34, pp. 1497 - 1502,
    Journal articles | 2004
    Shparlinski IE, 2004, 'On the uniformity of distribution of the decryption exponent in fixed encryption exponent RSA', Information Processing Letters, 92, pp. 143 - 147,
    Journal articles | 2004
    Shparlinski IE, 2004, 'Security of polynomial transformations of the Diffie-Hellman key', Finite Fields and their Applications, 10, pp. 123 - 131,
    Journal articles | 2004
    Vasco MIG; N盲slund M; Shparlinski IE, 2004, 'New results on the hardness of diffie-hellman bits', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2947, pp. 159 - 172
    Journal articles | 2004
    Von Gathen JZ; Shparlinski IE, 2004, 'GCD of random linear forms', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 3341, pp. 464 - 469
    Journal articles | 2004
    Von Gathen JZ; Shparlinski IE, 2004, 'Predicting Subset Sum Pseudorandom Generators', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3357, pp. 241 - 251
    Journal articles | 2004
    Von Gathen JZ; Shparlinski IE, 2004, 'Predicting Subset Sum Pseudorandom Generators', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 3357, pp. 241 - 251
    Journal articles | 2004
    Von Zur Gathen J; Shparlinski IE, 2004, 'Polynomial Interpolation from Multiples', Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms, 15, pp. 1125 - 1130
    Journal articles | 2004
    von zur Gathen J; Knopfmacher A; Luca F; Lucht LG; Shparlinski IE, 2004, 'Average order in cyclic groups', Journal De Theorie Des Nombres De Bordeaux, 16, pp. 107 - 123,
    Journal articles | 2003
    Allender E; Bernasconi A; Damm C; Von Zur Gathen J; Saks M; Shparlinski I, 2003, 'Complexity of some arithmetic problems for binary polynomials', Computational Complexity, 12, pp. 23 - 47,
    Journal articles | 2003
    Banks WD; Harcharras A; Shparlinski IE, 2003, 'Short Kloosterman sums for polynomials over finite fields', Canadian Journal of Mathematics, 55, pp. 225 - 246,
    Journal articles | 2003
    Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2003, 'Predicting the Inversive Generator', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2898, pp. 264 - 275,
    Journal articles | 2003
    Guruswami V; Shparlinski I, 2003, 'Unconditional proof of tightness of Johnson bound', Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms, pp. 754 - 755
    Journal articles | 2003
    Gutierrez J; Shparlinski IE; Winterhof A, 2003, 'On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators', IEEE Transactions on Information Theory, 49, pp. 60 - 64,
    Journal articles | 2003
    Howgrave-Graham NA; Nguyen PQ; Shparlinski IE, 2003, 'Hidden number problem with hidden multipliers, timed-release crypto, and noisy exponentiation', Mathematics of Computation, 72, pp. 1473 - 1485,
    Journal articles | 2003
    Khan MR; Shparlinski IE, 2003, 'On the maximal difference between an element and its inverse modulo n', Periodica Mathematica Hungarica, 47, pp. 111 - 117,
    Journal articles | 2003
    Konyagin S; Lange T; Shparlinski I, 2003, 'Linear complexity of the discrete logarithm', Designs Codes and Cryptography, 28, pp. 135 - 146,
    Journal articles | 2003
    Luca F; Shparlinski IE, 2003, 'Average multiplicative orders of elements modulo n', Acta Arithmetica, 109, pp. 387 - 411,
    Journal articles | 2003
    Nguyen PQ; Shparlinski IE, 2003, 'The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces', Designs Codes and Cryptography, 30, pp. 201 - 217,
    Journal articles | 2003
    Nguyen PQ; Shparlinski IE, 2003, 'The insecurity of the digital signature algorithm with partially known nonces', Journal of Cryptology, 15, pp. 151 - 176,
    Journal articles | 2003
    Niederreiter H; Shparlinski IE, 2003, 'Dynamical systems generated by rational functions', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2643, pp. 6 - 17,
    Journal articles | 2003
    Niederreiter H; Shparlinski IE, 2003, 'On the distribution of power residues and primitive elements in some nonlinear recurring sequences', Bulletin of the London Mathematical Society, 35, pp. 522 - 528,
    Journal articles | 2003
    Niederreiter H; Shparlinski IE, 2003, 'Periodic sequences with maximal linear complexity and almost maximal k-rrror linear complexity', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2898, pp. 183 - 189,
    Journal articles | 2003
    N盲slund M; Shparlinski IE; Whyte W, 2003, 'On the bit security of NTRUEncrypt', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2567, pp. 62 - 70,
    Journal articles | 2003
    Pappalardi F; Saidak F; Shparlinski IE, 2003, 'Square-free values of the Carmichael function', Journal of Number Theory, 103, pp. 122 - 131,
    Journal articles | 2003
    Shparlinski IE, 2003, 'Prime divisors of sparse integers', Periodica Mathematica Hungarica, 46, pp. 215 - 222,
    Journal articles | 2003
    Von Zur Gathen J; Shparlinski I; Sinclair A, 2003, 'Finding points on curves over finite fields', SIAM Journal on Computing, 32, pp. 1436 - 1448,
    Journal articles | 2002
    Banks WD; Conflitti A; Shparlinski IE, 2002, 'Character sums over integers with restricted g-ary digits', Illinois Journal of Mathematics, 46, pp. 819 - 836,
    Journal articles | 2002
    Banks WD; Shparlinski IE, 2002, 'Average normalisations of elliptic curves', Bulletin of the Australian Mathematical Society, 66, pp. 353 - 358,
    Journal articles | 2002
    Banks WD; Shparlinski IE, 2002, 'On the number of sparse RSA exponents', JOURNAL OF NUMBER THEORY, 95, pp. 340 - 350,
    Journal articles | 2002
    Banks WD; Shparlinski IE, 2002, 'On the number of sparse RSA exponents', Journal of Number Theory, 95, pp. 340 - 350,
    Journal articles | 2002
    Codenotti B; Shparlinski IE; Winterhof A, 2002, 'On the hardness of approximating the permanent of structured matrices', Computational Complexity, 11, pp. 158 - 170,
    Journal articles | 2002
    El Mahassni E; Shparlinski I, 2002, 'On the Uniformity of Distribution of the Elliptic Curve ElGamal Signature', Finite Fields and Their Applications, 8, pp. 589 - 596,
    Journal articles | 2002
    El Mahassni E; Shparlinski I, 2002, 'On the uniformity of distribution of the elliptic curve ElGamal signature', Finite Fields and their Applications, 8, pp. 589 - 596,
    Journal articles | 2002
    Friedlander JB; Konyagin S; Shparllnski IE, 2002, 'Some doubly exponential sums over 鈩', Acta Arithmetica, 105, pp. 349 - 370,
    Journal articles | 2002
    Friedlander JB; Pomerance C; Shparlinski IE, 2002, 'Erratum: Period of the power generator and small values of Carmichael's function (Mathematics of Computation)', Mathematics of Computation, 71, pp. 1803 - 1806,
    Journal articles | 2002
    Mans B; Pappalardi F; Shparlinski I, 2002, 'On the spectral 脕d谩m property for circulant graphs', Discrete Mathematics, 254, pp. 309 - 329,
    Journal articles | 2002
    Niederreiter H; Shparlinski IE, 2002, 'On the Average Distribution of Inversive Pseudorandom Numbers', Finite Fields and Their Applications, 8, pp. 491 - 503,
    Journal articles | 2002
    Niederreiter H; Shparlinski IE, 2002, 'On the average distribution of inversive pseudorandom numbers', Finite Fields and their Applications, 8, pp. 491 - 503,
    Journal articles | 2002
    Shparlinski IE, 2002, 'On a question of Erdos and Graham', Archiv Der Mathematik, 78, pp. 445 - 448,
    Journal articles | 2002
    Shparlinski IE, 2002, 'On the distribution of the Diffie-Hellman pairs', Finite Fields and their Applications, 8, pp. 131 - 141,
    Journal articles | 2002
    Shparlinski IE, 2002, 'On the uniformity of distribution of the EIGamal signature', Applicable Algebra in Engineering Communications and Computing, 13, pp. 9 - 16,
    Journal articles | 2002
    Shparlinski IE, 2002, 'Security of most significant bits of gx(2)', Information Processing Letters, 83, pp. 109 - 113,
    Journal articles | 2002
    Vasco MIG; Shparlinski IE, 2002, 'Security of the most significant bits of the Shamir message passing scheme', Mathematics of Computation, 71, pp. 333 - 342,
    Journal articles | 2001
    Banks WD; Shparlinski IE, 2001, 'Distribution of inverses in polynomial rings', Indagationes Mathematicae, 12, pp. 303 - 315,
    Journal articles | 2001
    Bernasconi A; Damm C; Shparlinski I, 2001, 'Circuit and decision tree complexity of some number theoretic problems', Information and Computation, 168, pp. 113 - 124,
    Journal articles | 2001
    Boneh D; Shparlinski IE, 2001, 'On the unpredictability of bits of the elliptic curve Diffie-Hellman scheme', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2139 LNCS, pp. 201 - 212,
    Journal articles | 2001
    Cohen SD; Niederreiter H; Shparlinski IE; Zieve M, 2001, 'Incomplete character sums and a special class of permutations', Journal De Theorie Des Nombres De Bordeaux, 13, pp. 53 - 63,
    Journal articles | 2001
    El Mahassni E; Shparlinski I, 2001, 'On Some Uniformity of Distribution Properties of ESIGN', Electronic Notes in Discrete Mathematics, 6, pp. 132 - 139,
    Journal articles | 2001
    El Mahassni E; Shparlinski I, 2001, 'Polynomial representations of the Diffie-Hellman mapping', Bulletin of the Australian Mathematical Society, 63, pp. 467 - 473,
    Journal articles | 2001
    Friedlander JB; Pomerance C; Shparlinski IE, 2001, 'Period of the power generator and small values of Carmichael's function', Mathematics of Computation, 70, pp. 1591 - 1605,
    Journal articles | 2001
    Friedlander JB; Shparlinsk IE, 2001, 'On the distribution of Diffie-Hellman triples with sparse exponents', SIAM Journal on Discrete Mathematics, 14, pp. 162 - 169,
    Journal articles | 2001
    Friedlander JB; Shparlinski IE, 2001, 'Double exponential sums over thin sets', Proceedings of the American Mathematical Society, 129, pp. 1617 - 1621,
    Journal articles | 2001
    Friedlander JB; Shparlinski IE, 2001, 'On the distribution of the power generator', Mathematics of Computation, 70, pp. 1575 - 1589,
    Journal articles | 2001
    Lieman D; Shparlinski I, 2001, 'On a new exponential sum', Canadian Mathematical Bulletin, 44, pp. 87 - 92,
    Journal articles | 2001
    Niederreiter H; Shparlinski IE, 2001, 'On the distribution of inversive congruential pseudorandom numbers in parts of the period', Mathematics of Computation, 70, pp. 1569 - 1574,
    Journal articles | 2001
    Shparlinski I, 2001, 'On Some Properties of the Shrinking Generator', Designs Codes and Cryptography, 23, pp. 147 - 156,
    Journal articles | 2001
    Shparlinski I, 2001, 'On the Linear Complexity of the Power Generator', Designs Codes and Cryptography, 23, pp. 5 - 10,
    Journal articles | 2001
    Shparlinski I, 2001, 'On the Multiplicative Orders of 纬 and 纬+纬-1 over finite fields', Finite Fields and their Applications, 7, pp. 327 - 331,
    Journal articles | 2001
    Shparlinski IE; Silverman JH, 2001, 'On the Linear Complexity of the Naor-Reingold Pseudo-random Function from Elliptic Curves', Designs Codes and Cryptography, 24, pp. 279 - 289,
    Journal articles | 2001
    Shparlinski IE, 2001, 'On the Uniformity of Distribution of the Naor-Reingold Pseudo-Random Function', Finite Fields and their Applications, 7, pp. 318 - 326,
    Journal articles | 2001
    Shparlinski IE, 2001, 'On the uniformity of distribution of the RSA pairs', Mathematics of Computation, 70, pp. 801 - 808,
    Journal articles | 2001
    Shparlinski IE, 2001, 'Sparse polynomial approximation in finite fields', Conference Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 209 - 215,
    Journal articles | 2000
    Bernasconi A; Damm C; Shparlinski I, 2000, 'The average sensitivity of square-freeness', Computational Complexity, 9, pp. 39 - 51,
    Journal articles | 2000
    Canetti R; Friedlander J; Konyagin S; Larsen M; Lieman D; Shparlinski I, 2000, 'On the statistical properties of Diffie-Hellman distributions', Israel Journal of Mathematics, 120, pp. 23 - 46,
    Journal articles | 2000
    Coppersmith D; Shparlinski I, 2000, 'On polynomial approximation of the discrete logarithm and the Diffie-Hellman mapping', JOURNAL OF CRYPTOLOGY, 13, pp. 339 - 360,
    Journal articles | 2000
    El Mahassni E; Shparlinski I, 2000, 'On some uniformity of distribution properties of ESIGN', Electronic Notes in Discrete Mathematics, 6, pp. 1 - 8
    Journal articles | 2000
    Friedlander JB; Hansen J; Shparlinski IE, 2000, 'Character sums with exponential functions', Mathematika, 47, pp. 75 - 85,
    Journal articles | 2000
    Griffin F; Shparlinski IE, 2000, 'On the linear complexity profile of the power generator', IEEE Transactions on Information Theory, 46, pp. 2159 - 2162,
    Journal articles | 2000
    Gutierrez J; Niederreiter H; Shparlinski IE, 2000, 'On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period', Monatshefte Fur Mathematik, 129, pp. 31 - 36,
    Journal articles | 2000
    Karpinski M; Van Der Poorten A; Shparlinski I, 2000, 'Zero testing of p-adic and modular polynomials', Theoretical Computer Science, 233, pp. 309 - 317,
    Journal articles | 2000
    Niederreiter H; Shparlinski IE, 2000, 'Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus', Acta Arithmetica, 92, pp. 89 - 98,
    Journal articles | 2000
    Niederreiter H; Shparlinski IE, 2000, 'On the distribution of pseudorandom numbers and vectors generated by inversive methods', Applicable Algebra in Engineering Communications and Computing, 10, pp. 189 - 202,
    Journal articles | 2000
    Shparlinski IE, 2000, 'Communication complexity and fourier coefficients of the Diffie-Hellman key', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 1776 LNCS, pp. 259 - 268,
    Journal articles | 2000
    Shparlinski IE, 2000, 'Computing Jacobi Symbols modulo Sparse Integers and Polynomials and Some Applications', Journal of Algorithms, 36, pp. 241 - 252,
    Journal articles | 2000
    Shparlinski IE, 2000, 'Linear complexity of the Naor-Reingold pseudo-random function', Information Processing Letters, 76, pp. 95 - 99,
    Journal articles | 2000
    Shparlinski IE, 2000, 'On the Naor-Reingold pseudo-random function from elliptic curves', Applicable Algebra in Engineering Communications and Computing, 11, pp. 27 - 34,
    Journal articles | 2000
    Von Zur Gathen J; Shparlinski IE, 2000, 'CREW PRAM complexity of modular inversion', SIAM Journal on Computing, 29, pp. 1839 - 1857,
    Journal articles | 1999
    Canetti R; Friedlander J; Shparlinski I, 1999, 'On certain exponential sums and the distribution of Diffie-Hellman triples', Journal of the London Mathematical Society, 59, pp. 799 - 812,
    Journal articles | 1999
    Everest GR; Shparlinski IE, 1999, 'Counting the values taken by algebraic exponential polynomials', Proceedings of the American Mathematical Society, 127, pp. 665 - 675,
    Journal articles | 1999
    Friedlander J; Larsen M; Lieman D; Shparlinski I, 1999, 'On the Correlation of Binary M-sequences', Designs Codes and Cryptography, 16, pp. 249 - 256,
    Journal articles | 1999
    Niederreiter H; Shparlinski IE, 1999, 'On the distribution and lattice structure of nonlinear congruential pseudorandom numbers', Finite Fields and their Applications, 5, pp. 246 - 253,
    Journal articles | 1999
    Von Zur Gathen J; Shparlinski I, 1999, 'Computing components and projections of curves over finite fields', SIAM Journal on Computing, 28, pp. 822 - 840,
    Journal articles | 1998
    Von Zur Gathen J; Shparlinski I, 1998, 'Orders of Gauss periods in finite fields', Applicable Algebra in Engineering Communications and Computing, 9, pp. 15 - 24,
    Journal articles | 1996
    Everest GR; Shparlinski IE, 1996, 'Divisor sums of generalised exponential polynomials', Canadian Mathematical Bulletin, 39, pp. 35 - 46,
    Journal articles | 1996
    Karpinski M; Shparlinski I, 1996, 'On some approximation problems concerning sparse polynomials over finite fields', Theoretical Computer Science, 157, pp. 259 - 266,
    Journal articles | 1996
    Shparlinski I, 1996, 'On exponential sums with sparse polynomials and rational functions', Journal of Number Theory, 60, pp. 233 - 244,
    Journal articles | 1996
    Shparlinski I, 1996, 'On finding primitive roots in finite fields', Theoretical Computer Science, 157, pp. 273 - 275,
    Journal articles | 1996
    Shparlinski IE, 1996, 'On irreducible polynomials of small height over finite fields', APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 7, pp. 427 - 431,
    Journal articles | 1996
    Shparlinski IE, 1996, 'On irreducible polynomials of small height over finite fields', Applicable Algebra in Engineering Communications and Computing, 7, pp. 427 - 431,
    Journal articles | 1996
    Van Der Poorten AJ; Shparlinski IE, 1996, 'On linear recurrence sequences with polynomial coefficients', Glasgow Mathematical Journal, 38, pp. 147 - 155,
    Journal articles | 1996
    Von Zur Gathen J; Karpinski M; Shparlinski I, 1996, 'Counting curves and their projections', Computational Complexity, 6, pp. 64 - 99,
    Journal articles | 1995
    Pappalardi F; Shparlinski I, 1995, 'On artin鈥瞫 conjecture over function fields', Finite Fields and their Applications, 1, pp. 399 - 404,
    Journal articles | 1993
    MULLEN GL; SHPARLINSKI I, 1993, 'VALUES OF LINEAR RECURRING SEQUENCES OF VECTORS OVER FINITE-FIELDS', ACTA ARITHMETICA, 65, pp. 221 - 226,
    Journal articles | 1993
    Shparlinski IE, 1993, 'Finding irreducible and primitive polynomials', Applicable Algebra in Engineering Communication and Computing, 4, pp. 263 - 268,
    Journal articles | 1993
    Shparlinski IE, 1993, 'On bivariate polynomial factorization over finite fields', Mathematics of Computation, 60, pp. 787 - 791,
    Journal articles | 1993
    Shparlinski IE, 1993, 'On parameters of some graphs from finite fields', European Journal of Combinatorics, 14, pp. 589 - 591,
    Journal articles | 1992
    Galiev VI; Polupanov AF; Shparlinski IE, 1992, 'Distances from differences of roots of polynomials to the nearest integers', Information Processing Letters, 43, pp. 143 - 146,
    Journal articles | 1992
    Galiev VI; Polupanov AF; Shparlinski IE, 1992, 'On the construction of solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity', Journal of Computational and Applied Mathematics, 39, pp. 151 - 163,
    Journal articles | 1992
    SHPARLINSKI IE; TSFASMAN MA; VLADUT SG, 1992, 'CURVES WITH MANY POINTS AND MULTIPLICATION IN FINITE-FIELDS', LECTURE NOTES IN MATHEMATICS, 1518, pp. 145 - 169,
    Journal articles | 1992
    SHPARLINSKI IE, 1992, 'ON GAUSSIAN SUMS FOR FINITE-FIELDS AND ELLIPTIC-CURVES', LECTURE NOTES IN COMPUTER SCIENCE, 573, pp. 5 - 15,
    Journal articles | 1992
    Shparlinski IE, 1992, 'A deterministic test for permutation polynomials', Computational Complexity, 2, pp. 129 - 132,
    Journal articles | 1992
    Shparlinski沫 IE, 1992, 'On primitive elements in finite fields and on elliptic curves', Mathematics of the USSR Sbornik, 71, pp. 41 - 50,
    Journal articles | 1992
    Stepanov SA; Shparlinskii IE, 1992, 'An estimate of incomplete multiplicative character sum of polynomials', Discrete Mathematics and Applications, 2, pp. 169 - 174,
    Journal articles | 1992
    Van Der Poorten AJ; Shparlinski IE, 1992, 'On the number of zeros of exponential polynomials and related questions', Bulletin of the Australian Mathematical Society, 46, pp. 401 - 412,
    Journal articles | 1991
    Shparlinskii IE, 1991, 'Estimates of Gaussian sums', Mathematical Notes of the Academy of Sciences of the USSR, 50, pp. 740 - 746,
    Journal articles | 1991
    Shparlinskiy IE, 1991, 'On the Distribution of Values of Recurring Sequences and the Bell Numbers in Finite Fields', European Journal of Combinatorics, 12, pp. 81 - 87,
    Journal articles | 1990
    Perel'muter GI; Shparlinskii IE, 1990, 'The distribution of primitive roots in finite fields', Russian Mathematical Surveys, 45, pp. 223 - 224,
    Journal articles | 1990
    Shparlinskii IE, 1990, 'Generalization of Chebyshev polynomials', Siberian Mathematical Journal, 31, pp. 183 - 185,
    Journal articles | 1990
    Shparlinskii IE, 1990, 'Some arithmetic properties of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, 47, pp. 612 - 617,
    Journal articles | 1990
    Shparlinski沫 IE; Skorobogatov AN, 1990, 'Exponential sums and rational points on complete intersections', Mathematika, 37, pp. 201 - 208,
    Journal articles | 1990
    Stepanov SA; Shparlinskii IE, 1990, 'On the construction of a primitive normal basis in a finite field', Mathematics of the USSR Sbornik, 67, pp. 527 - 533,
    Journal articles | 1989
    Shparlinskii IE, 1989, 'Dimension of BCH codes', Problems of Information Transmission, 25, pp. 77 - 80
    Journal articles | 1989
    Shparlinskii IE, 1989, 'On arithmetical properties of solutions of norm equations', Russian Mathematical Surveys, 44, pp. 216 - 217,
    Journal articles | 1989
    Shparlinskii IE, 1989, 'On distribution of values of recurrence sequences', Problems of Information Transmission, 25, pp. 120 - 125
    Journal articles | 1989
    Shparlinski沫 IE, 1989, 'On polynomials of prescribed height in finite fields', Mathematics of the USSR Sbornik, 63, pp. 247 - 255,
    Journal articles | 1988
    Shparlinskii IE, 1988, 'Residue classes modulo a prime number in a field of algebraic numbers', Mathematical Notes of the Academy of Sciences of the USSR, 43, pp. 249 - 252,
    Journal articles | 1987
    Shparlinskii IE, 1987, 'Number of different prime divisors of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, 42, pp. 773 - 780,
    Journal articles | 1986
    Shparlinskii IE, 1986, 'WEIGHT SPECTRA OF SOME CODES.', Problems of Information Transmission, 22, pp. 111 - 116
    Journal articles | 1985
    Kosachevskaya LL; Romanovtsev VV; Shparlinskii IE, 1985, 'On one sequence of iteration parameters', USSR Computational Mathematics and Mathematical Physics, 25, pp. 89 - 93,
    Journal articles | 1985
    Shparlinskii IE, 1985, 'Coefficients of primitive polynomials', Mathematical Notes of the Academy of Sciences of the USSR, 38, pp. 951 - 954,
    Journal articles | 1985
    Shparlinskii IE, 1985, 'Number of prime divisors of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, 38, pp. 529 - 532,
    Journal articles | 1984
    Kosachevskaya LL; Shparlinskii IE, 1984, 'The rate of convergence of some iterational processes', USSR Computational Mathematics and Mathematical Physics, 24, pp. 81 - 84,
    Journal articles | 1984
    Shparlinskii IE, 1984, 'Communications of the moscow mathematical society: On the note of convergence of Newton's interpolation process and the power of certain codes', Russian Mathematical Surveys, 39, pp. 199 - 200,
    Journal articles | 1984
    Shparlinskii IE, 1984, 'On a multiplicative generator of pseudorandom numbers', USSR Computational Mathematics and Mathematical Physics, 24, pp. 79 - 81,
    Journal articles | 1983
    Kosachevskaya LL; Romanovtsev VV; Shparlinskiy IE, 1983, 'On the spline-based method for experimental data deconvolution', Computer Physics Communications, 29, pp. 227 - 230,
    Journal articles | 1983
    Shparlinskii IE, 1983, 'On one property of a multiplicative transducer of pseudo-random numbers', USSR Computational Mathematics and Mathematical Physics, 23, pp. 158 - 159,
    Journal articles | 1982
    Kosachevskaya LL; Romanovtsev VV; Shparlinskii IE, 1982, 'On an iterative process for the numerical solution of systems of linear algebraic equations', USSR Computational Mathematics and Mathematical Physics, 22, pp. 232 - 237,
    Journal articles | 1982
    Kosachevskaya LL; Romanovtsev VV; Shparlinskiy IE; Vystavkin AN, 1982, 'New improved algorithm for the iterative solution of a system of linear algebraic equations', Computer Physics Communications, 27, pp. 87 - 89,
    Journal articles | 1981
    Shparlinskii IE, 1981, 'The distribution of the fractional parts of recurrent sequences', USSR Computational Mathematics and Mathematical Physics, 21, pp. 231 - 235,
    Journal articles | 1979
    Levin MB; Shparlinskii IE, 1979, 'The uniform distribution of fractional parts of recurrent sequences', Russian Mathematical Surveys, 34, pp. 207 - 208,
    Journal articles | 1979
    Shparlinskii IE, 1979, 'On a completely uniform distribution', USSR Computational Mathematics and Mathematical Physics, 19, pp. 249 - 253,
    Journal articles | 1978
    Shparlinskii IE, 1978, 'Distribution of nonresidues and primitive roots in recurrent sequences', Mathematical Notes of the Academy of Sciences of the USSR, 24, pp. 823 - 828,
  • Working Papers | 2021
    Chen C; Shparlinski IE, 2021, On a hybrid version of the Vinogradov mean value theorem,
    Working Papers | 2021
    Chen C; Shparlinski IE, 2021, Restricted Mean Value Theorems and the Metric Theory of Restricted Weyl Sums,
    Working Papers | 2020
    Banks WD; Shparlinski IE, 2020, Sums with the M枚bius function twisted by characters with powerful moduli,
    Working Papers | 2020
    Kerr B; Shparlinski IE; Yau KH, 2020, A refinement of the burgess bound for character sums,
    Working Papers | 2020
    Munsch M; Shparlinski IE, 2020, On smooth square-free numbers in arithmetic progressions,
    Working Papers | 2019
    D膮browski A; Pomyka艂a J; Shparlinski IE, 2019, On oracle factoring of integers, ,
    Working Papers | 2017
    Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2017, On the new bound for the number of solutions of polynomial equations in subgroups and the structure of graphs of Markoff triples, ,
  • Preprints | 2025
    B脙漏rczes A; Bhakta S; Hajdu L; Ostafe A; Shparlinski IE, 2025, Multiplicative dependence in the denominators of points of elliptic curves
    Preprints | 2025
    B茅rczes A; Hajdu L; Ostafe A; Shparlinski IE, 2025, Multiplicative dependence in linear recurrence sequences,
    Preprints | 2025
    Koh D; Shparlinski IE, 2025, Mean value theorems for rational exponential sums,
    Preprints | 2025
    Manning A; Ostafe A; Shparlinski IE, 2025, Counting matrices over finite rank multiplicative groups,
    Preprints | 2025
    Ostafe A; Pomerance C; Shparlinski IE, 2025, Counting solvable $\mathcal S$-unit equations and linear recurrence sequences with zeros,
    Preprints | 2025
    Ostafe A; Shparlinski IE, 2025, Counting integer matrices with square-free determinants,
    Preprints | 2024
    Afifurrahman M; Kuperberg V; Ostafe A; Shparlinski IE, 2024, Statistics of ranks, determinants and characteristic polynomials of rational matrices,
    Preprints | 2024
    Bhakta S; Shparlinski I, 2024, Exponential Sums with Sparse Polynomials and Distribution of the Power Generator,
    Preprints | 2024
    Blomer V; Risager MS; Shparlinski IE, 2024, Triple sums of Kloosterman sums and the discrepancy of modular inverses,
    Preprints | 2024
    Drappeau S; Shparlinski IE, 2024, Exponential sums over integers without large prime divisors,
    Preprints | 2024
    Fouvry 脡; Shparlinski IE; Xi P, 2024, Estimates for trilinear and quadrilinear character sums,
    Preprints | 2024
    Garaev MZ; Pardo JC; Shparlinski IE, 2024, Binary and ternary congruences involving intervals and sets modulo a prime,
    Preprints | 2024
    Iyer S; Shparlinski I, 2024, Character sums over elements of extensions of finite fields with restricted coordinates
    Preprints | 2024
    Klurman O; Shparlinski IE; Ter盲v盲inen J, 2024, On Artin's conjecture on average and short character sums,
    Preprints | 2024
    Kurlberg P; Ostafe A; Rudnick Z; Shparlinski IE, 2024, On quantum ergodicity for higher dimensional cat maps,
    Preprints | 2024
    Ostafe A; Shparlinski IE, 2024, On the frequency of primes preserving dynamical irreducibility of polynomials,
    Preprints | 2024
    Shao X; Shparlinski IE; Wijaya LP, 2024, Sums of Kloosterman sums over square-free and smooth integers,
    Preprints | 2024
    Shkredov ID; Shparlinski IE, 2024, On the determinants of matrices with elements from arbitrary sets,
    Preprints | 2024
    Shparlinski IE; Voloch JF, 2024, On the Waring problem with Dickson polynomials modulo a prime,
    Preprints | 2023
    Borda B; Munsch M; Shparlinski I, 2023, Pointwise and correlation bounds on Dedekind sums over small subgroups,
    Preprints | 2023
    Brandes J; Chen C; Shparlinski IE, 2023, Local mean value estimates for Weyl sums, ,
    Preprints | 2023
    Browning T; Shparlinski I, 2023, Square-free values of random polynomials, ,
    Preprints | 2023
    Bulinski K; Ostafe A; Shparlinski IE, 2023, Counting embeddings of free groups into $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups,
    Preprints | 2023
    Bulinski K; Shparlinski IE, 2023, Counting elements of the congruence subgroup,
    Preprints | 2023
    Dartyge C; Martin B; Rivat J; Shparlinski IE; Swaenepoel C, 2023, Reversible primes,
    Preprints | 2023
    Dubickas A; Sha M; Shparlinski IE, 2023, Euclidean minima of algebraic number fields,
    Preprints | 2023
    Garaev M; Rudnick Z; Shparlinski I, 2023, On a family of sparse exponential sums,
    Preprints | 2023
    Garaev MZ; Shparlinski IE, 2023, On some congruences and exponential sums, ,
    Preprints | 2023
    Garaev MZ; Shparlinski IE, 2023, On the distribution of modular inverses from short intervals, ,
    Preprints | 2023
    Kerr B; Mohammadi A; Shparlinski IE, 2023, Additive energy of polynomial images, ,
    Preprints | 2023
    Mohammadi A; Ostafe A; Shparlinski I, 2023, On some matrix counting problems,
    Preprints | 2023
    Munsch M; Shparlinski IE, 2023, Moments and non-vanishing of $L$-functions over thin subgroups,
    Preprints | 2023
    M茅rai L; Shparlinski IE, 2023, Distribution of recursive matrix pseudorandom number generator modulo prime powers,
    Preprints | 2023
    M茅rai L; Shparlinski IE, 2023, Number of characteristic polynomials of matrices with bounded height,
    Preprints | 2023
    Ostafe A; Shparlinski IE, 2023, On the sparsity of non-diagonalisable integer matrices and matrices with a given discriminant,
    Preprints | 2023
    Shparlinski IE; Wijaya LP, 2023, On Nonzero Coefficients of Binary Cyclotomic Polynomials,
    Preprints | 2023
    Shparlinski IE, 2023, On the number of Diophantine $m$-tuples in finite fields, ,
    Preprints | 2022
    Abdalaoui EHE; Shparlinski IE; Steiner RS, 2022, Chowla and Sarnak Conjectures for Kloosterman Sums,
    Preprints | 2022
    Banks W; Shparlinski IE, 2022, On the greatest common divisor of integer parts of polynomials, ,
    Preprints | 2022
    Fouvry 脡; Shparlinski IE, 2022, On character sums with determinants, ,
    Preprints | 2022
    Habegger P; Ostafe A; Shparlinski IE, 2022, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices,
    Preprints | 2022
    Hauck M; Shparlinski IE, 2022, Smooth numbers with few non-zero binary digits, ,
    Preprints | 2022
    Kerr B; Shparlinski IE; Wu X; Xi P, 2022, Bounds on bilinear forms with Kloosterman sums,
    Preprints | 2022
    Mans B; Sha M; Shparlinski IE; Sutantyo D, 2022, Functional graphs of families of quadratic polynomials,
    Preprints | 2022
    M茅rai L; Shparlinski IE; Winterhof A, 2022, Character sums over sparse elements of finite fields,
    Preprints | 2022
    Ostafe A; Shparlinski IE; Voloch JF, 2022, Weil Sums over Small Subgroups,
    Preprints | 2022
    Shparlinski IE, 2022, Multiplicative Properties of Hilbert Cubes, ,
    Preprints | 2021
    Bag N; Shparlinski IE, 2021, Bounds on bilinear sums of Kloosterman sums,
    Preprints | 2021
    Bagshaw C; Shparlinski IE, 2021, Energy bounds, bilinear sums and their applications in function fields,
    Preprints | 2021
    Baker RC; Chen C; Shparlinski IE, 2021, Bounds on the Norms of Maximal Operators on Weyl Sums,
    Preprints | 2021
    Baker RC; Chen C; Shparlinski IE, 2021, Large Weyl sums and Hausdorff dimension,
    Preprints | 2021
    Baker RC; Munsch M; Shparlinski IE, 2021, Additive energy and a large sieve inequality for sparse sequences,
    Preprints | 2021
    Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, On sparsity of representations of polynomials as linear combinations of exponential functions,
    Preprints | 2021
    Ghioca D; Shparlinski I, 2021, Order of torsion for reduction of linearly independent points for a family of Drinfeld modules,
    Preprints | 2021
    Kaminski M; Shparlinski IE; Waldschmidt M, 2021, On sets of linear forms of maximal complexity,
    Conference Papers | 2021
    Kaminski M; Shparlinski IE, 2021, 'Sets of Linear Forms Which Are Hard to Compute', in Leibniz International Proceedings in Informatics Lipics,
    Preprints | 2021
    Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2021, Energy bounds for modular roots and their applications,
    Preprints | 2021
    Ostafe A; Shparlinski IE; Voloch JF, 2021, Equations and character sums with matrix powers, Kloosterman sums over small subgroups and quantum ergodicity,
    Preprints | 2021
    Ostafe A; Shparlinski IE, 2021, Additive energy of cyclic matrix groups and character sums with matrix exponential functions,
    Preprints | 2021
    Shparlinski IE; Thuswaldner JM, 2021, Weyl sums over integers with digital restrictions,
    Preprints | 2021
    Shparlinski IE; Thuswaldner JM, 2021, Weyl sums over integers with digital restrictions, ,
    Preprints | 2021
    Shparlinski IE, 2021, On the Glasner property for matrices with polynomial entries,
    Preprints | 2020
    Banks W; Shparlinski I, 2020, On a conjecture of Soundararajan,
    Preprints | 2020
    Benedetto DD; Garaev MZ; Garc铆a VC; Gonz谩lez-S谩nchez D; Shparlinski IE; Trujillo CA, 2020, New estimates for exponential sums over multiplicative subgroups and intervals in prime fields,
    Preprints | 2020
    Brandes J; Shparlinski IE, 2020, Two-dimensional Weyl sums failing square-root cancellation along lines,
    Preprints | 2020
    Brandes J; Shparlinski IE, 2020, Two-dimensional Weyl sums failing square-root cancellation along lines, ,
    Preprints | 2020
    Chen C; Kerr B; Maynard J; Shparlinski I, 2020, Metric theory of Weyl sums,
    Preprints | 2020
    Chen C; Kerr B; Shparlinski I, 2020, Metric theory of lower bounds on Weyl sums,
    Preprints | 2020
    Chen C; Shparlinski IE, 2020, Hybrid bounds on two-parametric family Weyl sums along smooth curves,
    Preprints | 2020
    Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2020, A sparsity result for the Dynamical Mordell-Lang Conjecture in positive characteristic,
    Preprints | 2020
    Karpinski M; Shparlinski I, 2020, Noisy polynomial interpolation modulo prime powers,
    Preprints | 2020
    Kerr B; Mello J; Shparlinski I, 2020, An effective local-global principle for algebraic varieties and the sum product problem in finite fields,
    Preprints | 2020
    Kerr B; Mello J; Shparlinski IE, 2020, On elements of large order of elliptic curves and multiplicative dependent images of rational functions over finite fields,
    Preprints | 2020
    Kerr B; M茅rai L; Shparlinski IE, 2020, On digits of Mersenne numbers,
    Preprints | 2020
    Konyagin SV; Shparlinski IE; Vyugin IV, 2020, Polynomial Equations in Subgroups and Applications,
    Preprints | 2020
    Li R; Shparlinski IE, 2020, Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers,
    Preprints | 2020
    Macourt S; Petridis G; Shkredov ID; Shparlinski IE, 2020, Bounds of Trilinear and Trinomial Exponential Sums,
    Preprints | 2020
    M茅rai L; Shparlinski IE, 2020, On the Dynamical System Generated by the M枚bius transformation at Prime Times,
    Preprints | 2020
    Ostafe A; Shparlinski I, 2020, On the Skolem problem and some related questions for parametric families of linear recurrence sequences,
    Preprints | 2020
    Shkredov ID; Shparlinski IE; Zaharescu A, 2020, On the distribution of modular square roots of primes,
    Preprints | 2020
    Shkredov ID; Shparlinski IE; Zaharescu A, 2020, On the distribution of modular square roots of primes, ,
    Preprints | 2020
    Shparlinski IE; Stewart CL, 2020, Counting solvable $S$-unit equations,
    Preprints | 2020
    Shparlinski IE; Wang Q, 2020, Exponential sums with sparse polynomials over finite fields,
    Preprints | 2019
    Banks W; Shparlinski I, 2019, Congruences with intervals and arbitrary sets,
    Preprints | 2019
    Bret猫che RDL; Kurlberg P; Shparlinski IE, 2019, On the number of products which form perfect powers and discriminants of multiquadratic extensions,
    Preprints | 2019
    Breuer F; Shparlinski IE, 2019, Lower bounds for periods of Ducci sequences,
    Preprints | 2019
    Chen C; Shparlinski IE, 2019, Hausdorff dimension of the large values of Weyl sums,
    Preprints | 2019
    Chen C; Shparlinski IE, 2019, New bounds of Weyl sums,
    Preprints | 2019
    Chen C; Shparlinski IE, 2019, On Large Values of Weyl Sums,
    Preprints | 2019
    Chen C; Shparlinski IE, 2019, On a Hybrid Version of the Vinogradov Mean Value Theorem,
    Preprints | 2019
    Chen C; Shparlinski IE, 2019, Restricted mean value theorems and metric theory of restricted Weyl sums,
    Preprints | 2019
    Chen C; Shparlinski IE, 2019, Small values of Weyl sums,
    Preprints | 2019
    Dietmann R; Ostafe A; Shparlinski IE, 2019, Discriminants of Fields Generated by Polynomials of Given Height,
    Preprints | 2019
    Dietmann R; Ostafe A; Shparlinski IE, 2019, Discriminants of Fields Generated by Polynomials of Given Height, ,
    Preprints | 2019
    Dunn A; Kerr B; Shparlinski IE; Zaharescu A, 2019, Bilinear forms in Weyl sums for modular square roots and applications,
    Preprints | 2019
    D膮browski A; Pomyka艂a J; Shparlinski IE, 2019, On oracle factoring of integers,
    Preprints | 2019
    Konyagin SV; Sha M; Shparlinski IE; Stewart CL, 2019, On the distribution of multiplicatively dependent vectors,
    Preprints | 2019
    Macourt S; Shparlinski IE, 2019, Double Sums of Kloosterman Sums in Finite Fields,
    Preprints | 2019
    M茅rai L; Ostafe A; Shparlinski IE, 2019, Dynamical irreducibility of polynomials modulo primes,
    Preprints | 2019
    M茅rai L; Shparlinski IE, 2019, Unlikely intersections over finite fields: polynomial orbits in small subgroups,
    Preprints | 2019
    Ostafe A; Pottmeyer L; Shparlinski IE, 2019, Perfect powers in value sets and orbits of polynomials,
    Preprints | 2019
    Sha M; Shparlinski IE, 2019, M枚bius Randomness Law for Frobenius Traces,
    Preprints | 2019
    Sha M; Shparlinski IE, 2019, M枚bius Randomness Law for Frobenius Traces, ,
    Preprints | 2019
    Shparlinski IE; Technau M, 2019, Kloosterman sums with twice-differentiable functions,
    Preprints | 2018
    Banks WD; Friedlander JB; Pomerance C; Shparlinski IE, 2018, Counting integers with a smooth totient,
    Preprints | 2018
    Banks WD; Shparlinski IE, 2018, Sums with the Mobius function twisted by characters with powerful moduli,
    Preprints | 2018
    Bordell猫s O; Dai L; Heyman R; Pan H; Shparlinski IE, 2018, On a sum involving the Euler function,
    Preprints | 2018
    B茅rczes A; Ostafe A; Shparlinski IE; Silverman JH, 2018, Multiplicative dependence among iterated values of rational functions modulo finitely generated groups,
    Preprints | 2018
    Kerr B; Shparlinski IE, 2018, Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions,
    Preprints | 2018
    Korolev MA; Shparlinski IE, 2018, Sums of algebraic trace functions twisted by arithmetic functions,
    Preprints | 2018
    Munsch M; Shparlinski IE; Yau KH, 2018, Smooth squarefree and square-full integers in arithmetic progressions,
    Preprints | 2018
    M茅rai L; Shparlinski IE, 2018, Distribution of short subsequences of inversive congruential pseudorandom numbers modulo $2^t$,
    Preprints | 2018
    M茅rai L; Shparlinski IE, 2018, Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields,
    Preprints | 2018
    Pakovich F; Shparlinski IE, 2018, Level curves of rational functions and unimodular points on rational curves,
    Preprints | 2018
    Ricotta G; Royer E; Shparlinski I, 2018, Kloosterman paths of prime powers moduli, II,
    Preprints | 2018
    Shkredov ID; Shparlinski IE, 2018, Double Character Sums with Intervals and Arbitrary Sets in Finite Fields,
    Preprints | 2018
    Shparlinski IE; Voloch JF, 2018, Binomial exponential sums,
    Preprints | 2018
    Shparlinski IE; Voloch JF, 2018, Value sets of sparse polynomials,
    Preprints | 2018
    Shparlinski IE; Winterhof A, 2018, Codes correcting restricted errors,
    Preprints | 2017
    Abdalaoui EHE; Shparlinski IE, 2017, Disjointness of the M枚bius Transformation and M枚bius Function,
    Preprints | 2017
    Bordell猫s O; Luca F; Moree P; Shparlinski IE, 2017, Denominators of Bernoulli polynomials,
    Preprints | 2017
    Chang M-C; D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2017, Orbits of Polynomial Dynamical Systems Modulo Primes,
    Preprints | 2017
    Chang M-C; Kerr B; Shparlinski IE, 2017, On the exponential large sieve inequality for sparse sequences modulo primes,
    Preprints | 2017
    Dubickas A; Sha M; Shparlinski IE, 2017, On distances in lattices from algebraic number fields,
    Preprints | 2017
    G贸mez-P茅rez D; M茅rai L; Shparlinski IE, 2017, On the Complexity of Exact Counting of Dynamically Irreducible Polynomials,
    Preprints | 2017
    Karpinski M; M茅rai L; Shparlinski IE, 2017, Identity Testing and Interpolation from High Powers of Polynomials of Large Degree over Finite Fields,
    Preprints | 2017
    Kerr B; Shparlinski IE; Yau KH, 2017, A refinement of the Burgess bound for character sums,
    Preprints | 2017
    Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2017, On the new bound for the number of solutions of polynomial equations in subgroups and the structure of graphs of Markoff triples,
    Preprints | 2017
    Luca F; Sha M; Shparlinski IE, 2017, On two functions arising in the study of the Euler and Carmichael quotients,
    Preprints | 2017
    Luca F; Shparlinski IE, 2017, On the error term of a lattice counting problem,
    Preprints | 2017
    Macourt S; Shkredov ID; Shparlinski IE, 2017, Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields,
    Preprints | 2017
    Mans B; Sha M; Shparlinski IE; Sutantyo D, 2017, On Functional Graphs of Quadratic Polynomials,
    Preprints | 2017
    Munsch M; Shparlinski IE, 2017, On smooth square-free numbers in arithmetic progressions,
    Preprints | 2017
    Ostafe A; Sha M; Shparlinski IE; Zannier U, 2017, On abelian multiplicatively dependent points on a curve in a torus,
    Preprints | 2017
    Ostafe A; Sha M; Shparlinski IE; Zannier U, 2017, On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem,
    Preprints | 2017
    Pomerance C; Shparlinski IE, 2017, Connected components of the graph generated by power maps in prime finite fields,
    Preprints | 2017
    Roche-Newton O; Shparlinski I; Winterhof A, 2017, Analogues of the Balog--Wooley Decomposition for Subsets of Finite Fields and Character Sums with Convolutions,
    Preprints | 2017
    Shparlinski I, 2017, Trilinear forms with double Kloosterman sums,
    Preprints | 2017
    Shparlinski IE, 2017, Character sums with smooth numbers,
    Preprints | 2017
    Shparlinski IE, 2017, On short products of primes in arithmetic progressions,
    Preprints | 2016
    Banks W; Shparlinski I, 2016, Bounds on short character sums and L-functions for characters with a smooth modulus,
    Preprints | 2016
    Banks WD; Shparlinski IE, 2016, On the number of distinct quadratic fields generated by the Shanks sequence,
    Preprints | 2016
    Bell J; Shparlinski IE, 2016, Power Series Approximations to Fekete Polynomials,
    Preprints | 2016
    Dietmann R; Elsholtz C; Shparlinski IE, 2016, Prescribing the binary digits of squarefree numbers and quadratic residues,
    Preprints | 2016
    G贸mez-P茅rez D; Shparlinski IE, 2016, Arithmetic Properties of Integers in Chains and Reflections of $g$-ary Expansions,
    Conference Papers | 2016
    Kohel D; Shparlinski I, 2016, 'Preface', in Contemporary Mathematics, pp. vii - viii
    Preprints | 2016
    Liu K; Shparlinski IE; Zhang T, 2016, Bilinear Forms with Exponential Sums with Binomials,
    Preprints | 2016
    Liu K; Shparlinski IE; Zhang T, 2016, Cancellations between Kloosterman sums modulo a prime power with prime arguments,
    Preprints | 2016
    Liu K; Shparlinski IE; Zhang T, 2016, Divisor problem in arithmetic progressions modulo a prime power,
    Preprints | 2016
    Liu K; Shparlinski IE; Zhang T, 2016, Squares in Piatetski--Shapiro Sequences,
    Preprints | 2016
    Pappalardi F; Sha M; Shparlinski IE; Stewart CL, 2016, On multiplicatively dependent vectors of algebraic numbers,
    Preprints | 2016
    Petridis G; Shparlinski IE, 2016, Bounds on trilinear and quadrilinear exponential sums,
    Preprints | 2016
    Shkredov ID; Shparlinski IE, 2016, On Some Multiple Character Sums,
    Conference Papers | 2016
    Shparlinski I; Childs AM; van Dam W, 2016, 'Optimal Quantum Algorithm for Polynomial Interpolation', in Ioannis Chatzigiannakis MMYRADS (ed.), Proceedings of the 43rd International Colloquium on Automata, Languages, and Programming, DROPS, Rome, pp. 16:1 - 16:13, presented at 43rd International Colloquium on Automata, Languages, and Programming, Rome, 11 July 2016 - 15 July 2016,
    Preprints | 2016
    Shparlinski IE; Zhang TP, 2016, Cancellations Amongst Kloosterman Sums,
    Preprints | 2016
    Shparlinski IE; Zhao L, 2016, Elliptic curves in isogeny classes,
    Preprints | 2016
    Shparlinski IE; Zumalac谩rregui A, 2016, Sums of inverses in thin sets of finite fields,
    Conference Papers | 2016
    Shparlinski IE, 2016, 'Dynamical systems of non-algebraic origin: Fixed points and orbit lengths', pp. 261 - 283,
    Preprints | 2016
    Shparlinski IE, 2016, Bilinear Forms with Kloosterman and Gauss Sums,
    Preprints | 2016
    Shparlinski IE, 2016, Constructing Dominating Sets in Circulant Graphs,
    Preprints | 2015
    Banks WD; Guo VZ; Shparlinski IE, 2015, Some arithmetic properties of numbers of the form $\lfloor p^c\rfloor$,
    Preprints | 2015
    Camburu O-M; Ciolan E-A; Luca F; Moree P; Shparlinski IE, 2015, Cyclotomic coefficients: gaps and jumps,
    Preprints | 2015
    Childs AM; Dam WV; Hung S-H; Shparlinski IE, 2015, Optimal quantum algorithm for polynomial interpolation,
    Preprints | 2015
    D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2015, Reductions Modulo Primes of Systems of Polynomial Equations and Algebraic Dynamical Systems,
    Preprints | 2015
    Heyman R; Shparlinski IE, 2015, Counting irreducible binomials over finite fields,
    Preprints | 2015
    Ivanyos G; Karpinski M; Santha M; Saxena N; Shparlinski I, 2015, Polynomial Interpolation and Identity Testing from High Powers over Finite Fields,
    Preprints | 2015
    Munsch M; Shparlinski IE, 2015, Upper and lower bounds for higher moments of theta functions,
    Preprints | 2015
    Nguyen PQ; Shparlinski IE, 2015, Counting Co-Cyclic Lattices,
    Preprints | 2015
    Sha M; Shparlinski IE, 2015, The Sato--Tate Distribution in Families of Elliptic Curves with a Rational Parameter of Bounded Height,
    Preprints | 2015
    Shparlinski IE; Weingartner AJ, 2015, An explicit polynomial analogue of Romanoff's theorem,
    Preprints | 2015
    Shparlinski IE, 2015, Linear Congruences with Ratios,
    Preprints | 2015
    Shparlinski IE, 2015, Linear Equations with Rational Fractions of Bounded Height and Stochastic Matrices,
    Preprints | 2015
    Shparlinski IE, 2015, On Bilinear Exponential and Character Sums with Reciprocals of Polynomials,
    Preprints | 2015
    de la Bret猫che R; Sha M; Shparlinski IE; Voloch JF, 2015, The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves,
    Preprints | 2014
    Banks WD; Shparlinski IE, 2014, Fractional parts of Dedekind sums,
    Preprints | 2014
    Blackburn SR; Konyagin SV; Shparlinski IE, 2014, Counting Additive Decompositions of Quadratic Residues in Finite Fields,
    Preprints | 2014
    Chang M-C; Shparlinski IE, 2014, Double Character Sums over Subgroups and Intervals,
    Preprints | 2014
    Chang M-C; Shparlinski IE, 2014, On the Density of Integer Points on Generalised Markoff-Hurwitz and Dwork Hypersurfaces,
    Preprints | 2014
    Dubickas A; Sha M; Shparlinski IE, 2014, Explicit form of Cassels' $p$-adic embedding theorem for number fields,
    Preprints | 2014
    Fite F; Shparlinski IE, 2014, On the singularity of the Demjanenko matrix of quotients of Fermat curves,
    Preprints | 2014
    Garcia-Morchon O; Rietman R; Shparlinski IE; Tolhuizen L, 2014, Interpolation and Approximation of Polynomials in Finite Fields over a Short Interval from Noisy Values,
    Preprints | 2014
    Gathen JVZ; Shparlinski IE, 2014, Circulant graphs and GCD and LCM of Subsets,
    Preprints | 2014
    Harman G; Shparlinski IE, 2014, Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients,
    Preprints | 2014
    Heyman R; Shparlinski IE, 2014, On the Greatest Common Divisor of Shifted Sets,
    Preprints | 2014
    Kurlberg P; Luca F; Shparlinski I, 2014, On the Fixed Points of the Map x -> x^x Modulo a Prime,
    Preprints | 2014
    Munsch M; Shparlinski I, 2014, Congruences with intervals and subgroups modulo a prime,
    Preprints | 2014
    Ostafe A, 2014, Polynomial Values in Affine Subspaces of Finite Fields,
    Preprints | 2014
    Roche-Newton O; Shparlinski I, 2014, Polynomial Values in Subfields and Affine Subspaces of Finite Fields,
    Preprints | 2014
    Sha M; Shparlinski IE, 2014, Effective results on linear dependence for elliptic curves,
    Preprints | 2014
    Sha M; Shparlinski IE, 2014, Lang-Trotter and Sato-Tate Distributions in Single and Double Parametric Families of Elliptic Curves,
    Preprints | 2014
    Shparlinski IE; Sutherland AV, 2014, Finding elliptic curves with a subgroup of prescribed size,
    Preprints | 2014
    Shparlinski IE; Sutherland AV, 2014, On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average,
    Preprints | 2014
    Shparlinski IE, 2014, Cayley graphs generated by small degree polynomials over finite fields,
    Preprints | 2014
    Shparlinski IE, 2014, On the Density of Integer Points on the Generalised Markoff-Hurwitz and Dwork Hypersurfaces,
    Preprints | 2014
    Shparlinski IE, 2014, Polynomial Values in Small Subgroups of Finite Fields,
    Preprints | 2013
    Ahmadi O; Shparlinski IE, 2013, Exponential Sums over Points of Elliptic Curves,
    Preprints | 2013
    Banks WD; Shparlinski IE, 2013, On Gauss sums and the evaluation of Stechkin's constant,
    Preprints | 2013
    Bourgain J; Konyagin S; Shparlinski I, 2013, Character Sums and Deterministic Polynomial Root Finding in Finite Fields,
    Preprints | 2013
    Chen Z; Shparlinski IE; Winterhof A, 2013, Covering sets for limited-magnitude errors,
    Preprints | 2013
    Gomez-Perez D; Shparlinski IE, 2013, Subgroups Generated by Rational Functions in Finite Fields,
    Preprints | 2013
    Heyman R; Shparlinski IE, 2013, On Shifted Eisenstein Polynomials,
    Preprints | 2013
    Heyman R; Shparlinski IE, 2013, On the Number of Eisenstein Polynomials of Bounded Height,
    Preprints | 2013
    Kaszian J; Moree P; Shparlinski IE, 2013, Periodic Structure of the Exponential Pseudorandom Number Generator,
    Preprints | 2013
    Koh D; Shen C-Y; Shparlinski I, 2013, Averaging operators over homogeneous varieties over finite fields,
    Preprints | 2013
    Konyagin SV; Luca F; Mans B; Mathieson L; Sha M; Shparlinski IE, 2013, Functional Graphs of Polynomials over Finite Fields,
    Preprints | 2013
    Konyagin SV; Shparlinski IE, 2013, Quadratic Non-residues in Short Intervals,
    Preprints | 2013
    Luca F; Radziwill M; Shparlinski IE, 2013, On the Typical Size and Cancelations Among the Coefficients of Some Modular Forms,
    Preprints | 2013
    Shparlinski I, 2013, Additive Decompositions of Subgroups of Finite Fields, ,
    Preprints | 2013
    Shparlinski I, 2013, Evasive Properties of Sparse Graphs and Some Linear Equations in Primes,
    Preprints | 2013
    Shparlinski I, 2013, Multiple Exponential and Character Sums with Monomials,
    Preprints | 2013
    Shparlinski I, 2013, On the Product of Small Elkies Primes,
    Preprints | 2013
    Shparlinski IE, 2013, On Solutions to Some Polynomial Congruences in Small Boxes,
    Preprints | 2012
    Baker RC; Banks WD; Br眉dern J; Shparlinski IE; Weingartner AJ, 2012, Piatetski-Shapiro sequences,
    Preprints | 2012
    Bourgain J; Garaev M; Konyagin S; Shparlinski I, 2012, On Congruences with Products of Variables from Short Intervals and Applications,
    Preprints | 2012
    Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2012, Multiplicative Congruences with Variables from Short Intervals,
    Preprints | 2012
    Dietmann R; Elsholtz C; Shparlinski IE, 2012, On Gaps Between Primitive Roots in the Hamming Metric,
    Preprints | 2012
    Harvey D; Shparlinski I, 2012, Statistics of Different Reduction Types of Fermat Curves, ,
    Preprints | 2012
    Kerr B; Shparlinski IE, 2012, On the Distribution of Values and Zeros of Polynomial Systems over Arbitrary Sets,
    Preprints | 2012
    Luca F; Shparlinski IE, 2012, On the Counting Function of Elliptic Carmichael Numbers,
    Preprints | 2012
    Shparlinski IE; Steiner W, 2012, On digit patterns in expansions of rational numbers with prime denominator,
    Preprints | 2012
    Shparlinski IE, 2012, On the Lang-Trotter and Sato-Tate Conjectures on Average for Polynomial Families of Elliptic Curves,
    Preprints | 2011
    Bibak K; Shparlinski IE, 2011, On fully split lacunary polynomials in finite fields,
    Preprints | 2011
    Blackburn SR; Ostafe A; Shparlinski IE, 2011, On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves,
    Preprints | 2011
    Blackburn SR; Ostafe A; Shparlinski IE, 2011, On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves,
    Preprints | 2011
    Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2011, On the Hidden Shifted Power Problem,
    Preprints | 2011
    Bourgain J; Konyagin SV; Shparlinski IE, 2011, Distribution of Elements of Cosets of Small Subgroups and Applications,
    Preprints | 2011
    Chang M-C; Cilleruelo J; Garaev MZ; Hern谩ndez J; Shparlinski IE; Zumalac谩rregui A, 2011, Points on curves in small boxes en applications,
    Preprints | 2011
    Ostafe A; Shparlinski I, 2011, Degree Growth, Linear Independence and Periods of a Class of Rational Dynamical Systems,
    Preprints | 2011
    Shparlinski IE; Sutherland AV, 2011, On the Distribution of Atkin and Elkies Primes,
    Preprints | 2011
    Shparlinski IE, 2011, Fermat quotients: Exponential sums, value set and primitive roots,
    Preprints | 2011
    Shparlinski IE, 2011, Modular Hyperbolas,
    Preprints | 2011
    Shparlinski IE, 2011, On vanishing Fermat quotients and a bound of the Ihara sum,
    Preprints | 2010
    Balog A; Broughan KA; Shparlinski IE, 2010, On the Number of Solutions of Exponential Congruences,
    Preprints | 2010
    Banks WD; Pappalardi F; Shparlinski IE, 2010, On group structures realized by elliptic curves over arbitrary finite fields,
    Preprints | 2010
    Farashahi RR; Shparlinski IE, 2010, On Pseudopoints of Algebraic Curves,
    Preprints | 2010
    Farashahi RR; Shparlinski IE, 2010, On group structures realized by elliptic curves over a fixed finite field,
    Preprints | 2010
    Farashahi RR; Shparlinski IE, 2010, Pseudorandom Bits From Points on Elliptic Curves,
    Preprints | 2010
    Gonzalez JJA; Luca F; Pomerance C; Shparlinski I, 2010, On numbers $n$ dividing the $n$th term of a linear recurrence,
    Preprints | 2010
    Konyagin SV; Shparlinski IE, 2010, On the Convex Hull of the Points on Modular Hyperbolas,
    Preprints | 2010
    Ostafe A; Shparlinski IE, 2010, Pseudorandomness and Dynamics of Fermat Quotients,
    Preprints | 2010
    Shparlinski I, 2010, On Small Solutions to Quadratic Congruences,
    Preprints | 2010
    Shparlinski IE, 2010, On the Restricted Divisor Function in Arithmetic Progressions,
    Preprints | 2009
    Ahmadi O; Shparlinski IE, 2009, On the Distribution of the Number of Points on Algebraic Curves in Extensions of Finite Fields,
    Preprints | 2009
    Ferguson R; Hoffman C; Luca F; Ostafe A; Shparlinski I, 2009, Some Additive Combinatorics Problems in Matrix Rings,
    Preprints | 2009
    Glebsky L; Shparlinski IE, 2009, Short Cycles in Repeated Exponentiation Modulo a Prime,
    Preprints | 2009
    Ostafe A; Shparlinski I, 2009, On the Degree Growth in Some Polynomial Dynamical Systems and Nonlinear Pseudorandom Number Generators,
    Preprints | 2009
    Ostafe A; Shparlinski IE, 2009, On the Length of Critical Orbits of Stable Quadratic Polynomials,
    Preprints | 2009
    Ostafe A; Shparlinski IE, 2009, Pseudorandom Numbers and Hash Functions from Iterations of Multivariate Polynomials,
    Preprints | 2009
    Pomerance C; Shparlinski IE, 2009, Rank statistics for a family of elliptic curves over a function field,
    Preprints | 2009
    Shparlinski IE; Stange KE, 2009, Character sums with division polynomials,
    Preprints | 2009
    Shparlinski IE, 2009, On Point Sets in Vector Spaces over Finite Fields That Determine Only Acute Angle Triangles,
    Preprints | 2008
    Ahmadi O; Shparlinski I, 2008, On the Sum-Product Problem on Elliptic Curves,
    Preprints | 2008
    Loiperdinger SS; Shparlinski IE, 2008, On the Distribution of the Euler Function of Shifted Smooth Numbers,
    Preprints | 2008
    Naccache D; Shparlinski IE, 2008, Divisibility, Smoothness and Cryptographic Applications,
    Preprints | 2008
    Shparlinski I, 2008, On Some Weighted Average Values of L-functions,
    Conference Papers | 2008
    Shparlinski IE, 2008, 'OPEN PROBLEMS ON EXPONENTIAL AND CHARACTER SUMS', in Aoki T; Kanemitsu S; Liu JY (eds.), NUMBER THEORY: DREAMING IN DREAMS, WORLD SCIENTIFIC PUBL CO PTE LTD, JAPAN, Kinki Univ, Higashiosaka, pp. 222 - 242, presented at 5th China-Japan Seminar on Number Theory, JAPAN, Kinki Univ, Higashiosaka, 27 August 2008 - 31 August 2008,
    Conference Papers | 2008
    Shparlinski IE, 2008, 'Pseudorandom Points on Elliptic Curves over Finite Fields', in Algebraic Geometry and Its Applications, WORLD SCIENTIFIC, pp. 116 - 134, presented at Proceedings of the First SAGA Conference,
    Preprints | 2008
    Shparlinski IE, 2008, On Quadratic Fields Generated by Discriminants of Irreducible Trinomials,
    Preprints | 2008
    Shparlinski IE, 2008, On a Generalised Lehmer Problem for Arbitrary Powers,
    Preprints | 2008
    van Dam W; Shparlinski IE, 2008, Classical and Quantum Algorithms for Exponential Congruences,
    Preprints | 2007
    Ahmadi O; Shparlinski IE; Voloch JF, 2007, Multiplicative Order of Gauss Periods,
    Preprints | 2007
    Banks WD; Shparlinski IE, 2007, Prime numbers with Beatty sequences,
    Preprints | 2007
    Cojocaru AC; Shparlinski IE, 2007, Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average,
    Conference Papers | 2007
    EI-Mahassni E; Shparlinski IE, 2007, 'On the distribution of the elliptic curve power generator', in Mullen GL; Panario D; Shparlinski IE (eds.), FINITE FIELDS AND APPLICATIONS, AMER MATHEMATICAL SOC, AUSTRALIA, Melbourne, pp. 111 - 118, presented at 8th International Conference on Finite Fields and Applications, AUSTRALIA, Melbourne, 09 July 2007 - 13 July 2007,
    Preprints | 2007
    Ford K; Luca F; Shparlinski IE, 2007, On the largest prime factor of the Mersenne numbers,
    Preprints | 2007
    Friedlander JB; Kurlberg P; Shparlinski IE, 2007, Products in Residue Classes,
    Preprints | 2007
    Graham SW; Shparlinski IE, 2007, On RSA Moduli with Almost Half of the Bits Prescribed,
    Preprints | 2007
    Khan MR; Shparlinski IE; Yankov CL, 2007, On the Convex Closure of the Graph of Modular Inversions,
    Preprints | 2007
    Konyagin SV; Pomerance C; Shparlinski IE, 2007, On the Distribution of Pseudopowers,
    Conference Papers | 2007
    Luca F; Shparlinski IE, 2007, 'On Special Finite Fields', in Lachaud G; Ritzenthaler C; Tsfasman MA (eds.), ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY, AMER MATHEMATICAL SOC, FRANCE, Ctr Int Rencontres Math, Marseilles, pp. 163 - 167, presented at 11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory, FRANCE, Ctr Int Rencontres Math, Marseilles, 05 November 2007 - 09 November 2007,
    Preprints | 2007
    Pomerance C; Shparlinski IE, 2007, On Pseudosquares and Pseudopowers,
    Preprints | 2007
    Saxena N; Severini S; Shparlinski I, 2007, Parameters of Integral Circulant Graphs and Periodic Quantum Dynamics, ,
    Conference Papers | 2007
    Shparlinski IE; Steinfeld R, 2007, 'Collision in the DSA Function', in Li Y; Ling S; Niederreiter H; Wang H; Xing C; Zhang S (eds.), CODING AND CRYPTOLOGY, WORLD SCIENTIFIC PUBL CO PTE LTD, PEOPLES R CHINA, Fujian Normal Univ, Wuui Mt, pp. 226 - 232, presented at 1st International Workshop on Coding and Cryptology, PEOPLES R CHINA, Fujian Normal Univ, Wuui Mt, 11 June 2007 - 15 June 2007,
    Preprints | 2007
    Shparlinski IE; Voloch JF, 2007, Visible Points on Curves over Finite Fields,
    Preprints | 2007
    Shparlinski IE, 2007, Approximation by Several Rationals,
    Preprints | 2007
    Shparlinski IE, 2007, Arithmetic and Geometric Progressions in Productsets over Finite Fields,
    Preprints | 2007
    Shparlinski IE, 2007, On The Solvability of Bilinear Equations in Finite Fields,
    Preprints | 2007
    Shparlinski IE, 2007, Tate-Shafarevich Groups and Frobenius Fields of Reductions of Elliptic Curves,
    Preprints | 2006
    Banks WD; Garaev MZ; Heath-Brown DR; Shparlinski IE, 2006, Density of non-residues in Burgess-type intervals and applications,
    Preprints | 2006
    Banks WD; Shparlinski IE, 2006, Character sums with Beatty sequences on Burgess-type intervals,
    Preprints | 2006
    Banks WD; Shparlinski IE, 2006, Integers with a large smooth divisor,
    Preprints | 2006
    Banks WD; Shparlinski IE, 2006, Sato--Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height,
    Preprints | 2006
    Ford K; Shparlinski I, 2006, On curves over finite fields with Jacobians of small exponent, ,
    Preprints | 2006
    Luca F; Shparlinski IE, 2006, Arithmetic properties of the Ramanujan function,
    Preprints | 2006
    Shparlinski I, 2006, On a Generalisation of a Lehmer Problem,
    Conference Papers | 2006
    Shparlinski IE, 2006, 'Bounds on the Fourier Coefficients of the Weighted Sum Function', in Dagstuhl Seminar Proceedings
    Conference Papers | 2006
    Shparlinski IE, 2006, 'DISTRIBUTION OF POINTS ON MODULAR HYPERBOLAS', in Kanemitsu S; Liu JY (ed.), NUMBER THEORY: SAILING ON THE SEA OF NUMBER THEORY, WORLD SCIENTIFIC PUBL CO PTE LTD, PEOPLES R CHINA, Weihai, pp. 155 - 189, presented at 4th China-Japan Seminar on Number Theory, PEOPLES R CHINA, Weihai, 30 August 2006 - 03 September 2006,
    Preprints | 2006
    Shparlinski IE, 2006, Distribution of modular inverses and multiples of small integers and the Sato--Tate conjecture on average,
    Preprints | 2006
    Shparlinski IE, 2006, On Some Dynamical Systems in Finite Fields and Residue Rings,
    Preprints | 2006
    Shparlinski IE, 2006, On the distribution of Kloosterman sums,
    Preprints | 2005
    Banks WD; Garaev MZ; Luca F; Shparlinski IE, 2005, Uniform Distribution of Fractional Parts Related to Pseudoprimes,
    Preprints | 2005
    Klappenecker A; Roetteler M; Shparlinski I; Winterhof A, 2005, On Approximately Symmetric Informationally Complete Positive Operator-Valued Measures and Related Systems of Quantum States,
    Conference Papers | 2005
    Shparlinski IE, 2005, 'Pseudorandom Number Generators from Elliptic Curves', in Luengo I (ed.), RECENT TRENDS IN CRYPTOGRAPHY, AMER MATHEMATICAL SOC, SPAIN, Real Soc Mat Espanola, Santander, pp. 121 - 141, presented at Summer School on Recent Trends in Cryptography, SPAIN, Real Soc Mat Espanola, Santander, 11 July 2005 - 15 July 2005,
    Preprints | 2004
    Contini S; Croot E; Shparlinski I, 2004, Complexity of Inverting the Euler Function,
    Preprints | 2004
    Everest G; Shparlinski IE, 2004, Prime divisors of sequences associated to elliptic curves,
    Preprints | 2004
    Garaev MZ; Luca F; Shparlinski IE, 2004, Character Sums and Congruences with n!,
    Preprints | 2004
    Garaev MZ; Luca F; Shparlinski IE, 2004, Exponential Sums and Congruences with Factorials,
    Conference Papers | 2003
    Banks WD; Friedlander JB; Pomerance C; Shparlinski IE, 2003, 'Multiplicative structure of values of the Euler function', in VanDerPoorten A; Stein A (ed.), HIGH PRIMES AND MISDEMEANOURS: LECTURES IN HONOUR OF THE 60TH BIRTHDAY OF HUGH COWIE WILLIAMS, AMER MATHEMATICAL SOC, CANADA, Banff, pp. 29 - 47, presented at Conference in Number Theory in Honour of Hugh C Williams, CANADA, Banff, 24 May 2003 - 30 May 2003,
    Conference Papers | 2003
    Banks WD; Shparlinski IE, 2003, 'Congruences and exponential sums with the Euler function', in VanDerPoorten A; Stein A (ed.), HIGH PRIMES AND MISDEMEANOURS: LECTURES IN HONOUR OF THE 60TH BIRTHDAY OF HUGH COWIE WILLIAMS, AMER MATHEMATICAL SOC, CANADA, Banff, pp. 49 - 59, presented at Conference in Number Theory in Honour of Hugh C Williams, CANADA, Banff, 24 May 2003 - 30 May 2003,
    Conference Papers | 2003
    Shparlinski IE, 2003, 'Orders of points on elliptic curves', in Gutierrez J; Shpilrain V; Yu JT (eds.), AFFINE ALGEBRAIC GEOMETRY, AMER MATHEMATICAL SOC, SPAIN, Seville, pp. 245 - 251, presented at 1st RSME-AMS Joint Meeting, SPAIN, Seville, 19 June 2003 - 21 June 2003,
    Conference Papers | 2003
    Shparlinski IE, 2003, 'Playing "hide-and-seek" with numbers: The hidden number problem, lattices and exponential sums', in Garret P; Lieman D (ed.), PUBLIC-KEY CRYPTOGRAPHY, AMER MATHEMATICAL SOC, MD, Baltimore, pp. 153 - 177, presented at Joint Annual Meeting of the American-Mathematical-Society/Mathematical-Association-of-America, MD, Baltimore, 17 January 2003,
    Conference Papers | 2003
    Von Zur Gathen J; Shokrollahi A; Shparlinski I, 2003, 'An authentication scheme based on roots of sparse polynomials', in Proceedings 2003 IEEE Information Theory Workshop Itw 2003, pp. 159 - 162,
    Conference Papers | 2002
    Banks WD; Shparlinski IE, 2002, 'A variant of NTRU with non-invertible polynomials', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 62 - 70,
    Conference Papers | 2002
    Lenstra AK; Shparlinski IE, 2002, 'Selective forgery of rsa signatures with fixed-pattern padding', in Lecture Notes in Computer Science, pp. 228 - 236,
    Conference Papers | 2002
    Li WCW; N盲slund M; Shparlinski IE, 2002, 'Hidden number problem with the trace and bit security of XTR and LUC', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 433 - 448,
    Conference Papers | 2002
    Pomerance C; Shparlinski IE, 2002, 'Smooth orders and cryptographic applications', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 338 - 348,
    Preprints | 2002
    Russell A; Shparlinski I, 2002, Classical and Quantum Polynomial Reconstruction via Legendre Symbol Evaluation, ,
    Conference Papers | 2002
    Shparlinski IE; Steinfeld R, 2002, 'Chinese remaindering for algebraic numbers in a hidden field', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 349 - 356,
    Conference Papers | 2002
    Vasco MIG; N盲slund M; Shparlinski IE, 2002, 'The hidden number problem in extension fields and its applications', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 105 - 117
    Conference Papers | 2001
    Allender E; Saks M; Shparlinski I, 2001, 'A lower bound for primality', in Journal of Computer and System Sciences, pp. 356 - 366,
    Conference Papers | 2001
    Banks WD; Lieman D; Shparlinski IE; Van To T, 2001, 'Cryptographic applications of sparse Polynomials over Finite Rings', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 206 - 220,
    Conference Papers | 2001
    El Mahassni E; Shparlinski I, 2001, 'On the uniformity of distribution of congruential generators over elliptic curves', in Helleseth T; Kumar PV; Yang K (eds.), SEQUENCES AND THEIR APPLICATIONS, PROCEEDINGS, SPRINGER-VERLAG LONDON LTD, NORWAY, BERGEN, pp. 257 - 264, presented at International Conference on Sequences and their Applications (SETA 01), NORWAY, BERGEN, 13 May 2001 - 17 May 2001,
    Conference Papers | 2001
    Lenstra AK; Shparlinski IE, 2001, 'On the security of Lenstra鈥檚 variant of DSA without long inversions', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 64 - 72,
    Conference Papers | 2001
    Mahassni EE; Nguyen PQ; Shparlinski IE, 2001, 'The insecurity of nyberg鈥搑ueppel and other DSA-like signature schemes with partially known nonces', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 97 - 109,
    Conference Papers | 2001
    Nguyen PQ; Shparlinski IE, 2001, 'On the insecurity of a server-aided RSA protocol', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 21 - 35,
    Conference Papers | 2001
    Plaku E; Shparlinski IE, 2001, 'On polynomial representations of boolean functions related to some number theoretic problems', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 305 - 316,
    Conference Papers | 2001
    Shparlinski IE, 2001, 'Exponential sums and lattice reduction: Applications to cryptography', in Mullen GL; Stichtenoth H; TapiaRecillas H (eds.), FINITE FIELDS WITH APPLICATIONS TO CODING THEORY, CRYPTOGRAPHY AND RELATED AREAS, SPRINGER-VERLAG BERLIN, MEXICO, OAXACA, pp. 286 - 298, presented at 6th International Conference on Finite Fields and Applications (Fq6), MEXICO, OAXACA, 21 May 2001 - 26 May 2001,
    Conference Papers | 2001
    Shparlinski IE, 2001, 'On the generalised hidden number problem and bit security of XTR', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 268 - 277,
    Conference Papers | 2000
    Banks WD; Griffin F; Lieman D; Shparlinski IE, 2000, 'Non-linear complexity of the naor-reingold pseudo-random function', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 53 - 59,
    Conference Papers | 2000
    Banks WD; Lieman D; Shparlinski IE, 2000, 'An Extremely Small and Efficient identification scheme', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 378 - 384,
    Conference Papers | 2000
    Banks WD; Lieman D; Shparlinski IE, 2000, 'An identification scheme based on sparse polynomials', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 68 - 74,
    Conference Papers | 2000
    Friedlander JB; Hansen JSD; Shparlinski IE, 2000, 'On the distribution of the power generator modulo a prime power', in Nathanson MB (ed.), UNUSUAL APPLICATIONS OF NUMBER THEORY, AMER MATHEMATICAL SOC, NJ, Piscataway, pp. 71 - 79, presented at DIMACS Workshop on Unusual Applications of Number Theory, NJ, Piscataway, 10 January 2000 - 14 January 2000,
    Conference Papers | 2000
    Kohel DR; Shparlinski IE, 2000, 'On exponential sums and group generators for elliptic curves over finite fields', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 395 - 404,
    Conference Papers | 2000
    Niederreiter H; Shparlinski IE, 2000, 'Recent advances in the theory of nonlinear pseudorandom number generators', in Fang KT; Hickernell FJ; Niederreiter H (eds.), MONTE CARLO AND QUASI-MONTE CARLO METHODS 2000, SPRINGER-VERLAG BERLIN, PEOPLES R CHINA, HONG KONG BAPTIST UNIV, HONG KONG, pp. 86 - 102, presented at 4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2000), PEOPLES R CHINA, HONG KONG BAPTIST UNIV, HONG KONG, 27 November 2000 - 01 December 2000,
    Conference Papers | 1999
    Alexandris N; Burmester M; Chrissikopoulos V; Desmedt Y, 1999, 'Designated 2-verifier proofs and their application to electronic commerce', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 149 - 163, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Allender E; Saks M; Shparlinski I, 1999, 'Lower bound for primality', in Proceedings of the Annual IEEE Conference on Computational Complexity, pp. 10 - 14
    Conference Papers | 1999
    Alonso C; Gutierrez J; Rubio R, 1999, 'On the dimension and the number of parameters of a unirational variety', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 3 - 9, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Bernasconi A; Damm C; Shparlinski IE, 1999, 'On the average sensitivity of testing square-free numbers', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 291 - 299,
    Conference Papers | 1999
    Bernasconi A; Shparlinski I, 1999, 'Circuit complexity of testing square-free numbers', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 47 - 56,
    Conference Papers | 1999
    Cai JY; Havas G; Mans B; Nerurkar A; Seifert JP; Shparlinski I, 1999, 'On routing in circulant graphs', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 360 - 369,
    Conference Papers | 1999
    Conflitti A, 1999, 'On elements of high order in finite fields', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 11 - 14, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Dawson E; Simpson L; Golic J, 1999, 'A survey of divide and conquer attacks on certain irregularly clocked stream ciphers', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 165 - 185, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    De Bonis A; De Santis A, 1999, 'New results on the randomness of visual cryptography schemes', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 187 - 201, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Ding CS; Kohel DR; Ling S, 1999, 'Counting the number of points on affine diagonal curves', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 15 - 24, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Friedlander JB; Pomerance C; Shparlinski IE, 1999, 'Small values of the Carmichael function and cryptographic applications', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 25 - 32, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Gollmann D, 1999, 'Authentication - Myths and misconceptions', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 203 - 225, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Griffin F; Niederreiter H; Shparlinski IE, 1999, 'On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 87 - 93,
    Conference Papers | 1999
    Griffin F; Shparlinski IE, 1999, 'On the linear complexity of the naor鈥攔eingold pseudo-random function', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 301 - 308,
    Conference Papers | 1999
    Han WB, 1999, 'The distribution of the coefficients of primitive polynomials over finite fields', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 43 - 57, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Hoffstein J; Lieman D, 1999, 'The distribution of the quadratic symbol in function fields and a faster mathematical stream cipher', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 59 - 68, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Hoffstein J; Silverman JH, 1999, 'Polynomial rings and efficient public key authentication II', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 269 - 286, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Karpinski M; Shparlinski I, 1999, 'On the computational hardness of testing square-freeness of sparse polynomials', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 492 - 497,
    Conference Papers | 1999
    Kohel DR, 1999, 'Rational groups of elliptic curves suitable for cryptography', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 69 - 80, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Lam KY; Sica F, 1999, 'Effective determination of the proportion of split primes in number fields', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 81 - 92, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Mihailescu P, 1999, 'Algorithms for generating, testing and proving primes: A survey', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 93 - 122, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Mihailescu P, 1999, 'Security of biased sources for cryptographic keys', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 287 - 302, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Naslund M; Russell A, 1999, 'Achieving optimal fairness from biased coinflips', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 303 - 319, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Nguyen PQ; Shparlinski IE; Stern J, 1999, 'Distribution of modular sums and the security of the server aided exponentiation', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 331 - 342, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Nguyen PQ, 1999, 'The dark side of the hidden number problem: Lattice attacks on DSA', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 321 - 330, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Peralta R, 1999, 'Elliptic curve factorization using a "partially oblivious" function', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 123 - 128, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Safavi-Naini R; Susilo W, 1999, 'A general construction for fail-stop signature using authentication codes', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 343 - 356, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Safavi-Naini R; Wang HX, 1999, 'Robust additive secret sharing schemes over Z(m)', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 357 - 368, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Silverman RD, 1999, 'RSA public key validation', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 369 - 378, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Vasco MIG; Naslund M, 1999, 'A survey of hard core functions', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 227 - 255, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Vasco MIG; Shparlinski IE, 1999, 'On the security of Diffie-Hellman bits', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 257 - 268, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    Von Zur Gathen J; Shparlinski I, 1999, 'Constructing elements of large order in finite fields', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 404 - 409,
    Conference Papers | 1999
    Xing CP, 1999, 'Applications of algebraic curves to constructions of sequences', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 137 - 146, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    van der Poorten A, 1999, 'The Hermite-Serret algorithm and 12(2)+33(2)', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 129 - 136, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    von zur Gathen J; Pappalardi F, 1999, 'Density estimates related to Gauss periods', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 33 - 41, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999,
    Conference Papers | 1999
    von zur Gathen J; Shparlinski I, 1999, 'Gauss periods in finite fields', in Jungnickel D; Niederreiter H (ed.), FINITE FIELDS AND APPLICATIONS, SPRINGER-VERLAG BERLIN, GERMANY, UNIV AUGSBURG, DEPT MATH, AUGSBURG, pp. 162 - 177, presented at 5th International Conference on Finite Fields and Applications, GERMANY, UNIV AUGSBURG, DEPT MATH, AUGSBURG, 02 August 1999 - 06 August 1999,
    Conference Papers | 1998
    Gathen JVZ; Shparlinski I, 1998, 'The crew pram complexity of modular inversion', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 305 - 315
    Conference Papers | 1998
    Grant D; Krastev K; Lieman D; Shparlinski I, 1998, 'A public key cryptosystem based on sparse polynomials', in Buchmann J; Hoholdt T; Stichtenoth H; TapiaRecillas H (eds.), CODING THEORY, CRYPTOGRAPHY AND RELATED AREAS, SPRINGER-VERLAG BERLIN, MEXICO, GUANAJUATO, pp. 114 - 121, presented at International Conference on Coding Theory, Cryptography and Related Areas, MEXICO, GUANAJUATO, 20 April 1998 - 24 April 1998,
    Conference Papers | 1998
    Mans B; Pappalardi F; Shparlinski I, 1998, 'On the 谩d谩m conjecture on circulant graphs', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 251 - 260,
    Conference Papers | 1995
    van der Poorten AJ; Shparlinski I; Zimmer HG, 1995, 'Number Theoretic and Algebraic Methods in Computer Science', in Number Theoretic and Algebraic Methods in Computer Science, WORLD SCIENTIFIC, pp. 1 - 214, presented at International Conference on NTAMCS '93,
    Conference Papers | 1995
    von zur Gathen J; Shparlinski I, 1995, 'Finding points on curves over finite fields extended abstract', in Annual Symposium on Foundations of Computer Science Proceedings, pp. 284 - 292
    Conference Papers | 1995
    von zur Gathen J; Shparlinski I, 1995, 'Orders of gauss periods in finite fields', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 208 - 215,
    Conference Papers | 1995
    vonzurGathen J; Shparlinski I, 1995, 'Finding points on curves over finite fields', in 36TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS, I E E E, COMPUTER SOC PRESS, WI, MILWAUKEE, pp. 284 - 292, presented at 36th Annual Symposium on Foundations of Computer Science (FOCS 95), WI, MILWAUKEE, 23 October 1995 - 25 October 1995,
    Conference Papers | 1994
    Shparlinski IE, 1994, 'On some applications of finitely generated semi-groups', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 265 - 279,
    Conference Papers | 1994
    Von Zur Gathen J; Shparlinski I, 1994, 'Components and projections of curves over finite fields', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 297 - 305,
    Conference Papers | 1993
    Von Zur Gathen J; Karpinski M; Shparlinski I, 1993, 'Counting curves and their projections', in Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 805 - 812,
    Conference Papers | 1992
    Shparlinski IE, 1992, 'On Gaussian sums for finite fields and elliptic curves', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 5 - 15,
    Conference Papers | 1991
    SHPARLINSKI IE; TSFASMAN MA; VLADUT SG, 1991, 'CURVES WITH MANY POINTS AND MULTIPLICATION IN FINITE-FIELDS', in Stichtenoth H; Tsfasman MA (ed.), CODING THEORY AND ALGEBRAIC GEOMETRY, SPRINGER-VERLAG BERLIN, FRANCE, CTR INT RENCONTRES MATH, LUMINY, pp. 145 - 169, presented at WORKSHOP ON ALGEBRAIC GEOMETRY AND CODING THEORY - 3 ( AGCT-3 ), FRANCE, CTR INT RENCONTRES MATH, LUMINY, 17 June 1991 - 21 June 1991,
    Conference Papers | 1991
    STEPANOV SA; SHPARLINSKI IE, 1991, 'ON NORMAL BASES OF ALGEBRAIC NUMBER-FIELDS', in Schweiger F; Manstavicius E (ed.), NEW TRENDS IN PROBABILITY AND STATISTICS, VOL 2, VSP BV, LITHUANIA, PALANGA, pp. 369 - 378, presented at INTERNATIONAL CONF ON ANALYTIC AND PROBABILISTIC METHODS IN NUMBER THEORY, IN HONOUR OF JONAS KUBILIUS ON THE OCCASION OF HIS 70TH BIRTHDAY, LITHUANIA, PALANGA, 24 September 1991 - 28 September 1991,
    Conference Papers | 1987
    Stepanov SA; Shparlinskiy IE, 1987, 'On structure complexity of normal basis of finite field', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 414 - 416,