By Professor Igor Shparlinski

Book Chapters

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, http://dx.doi.org/10.1007/978-3-031-05331-3_12

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, http://dx.doi.org/10.1090/conm/754/15150

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

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, http://dx.doi.org/10.1007/978-3-319-55357-3_18

Kaszián 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, http://dx.doi.org/10.1017/cbo9781139696456.012

Shparlinski IE, 2013, 'Additive Combinatorics over Finite Fields: New Results and Applications', in Finite Fields and Their Applications, DE GRUYTER, pp. 233 - 272, http://dx.doi.org/10.1515/9783110283600.233

Cillerueloa J; Lucab F; Shparlinskic IE, 2011, 'Power values of palindromes', in Frontiers of Combinatorics and Number Theory, pp. 103 - 110

Shparlinski I, 2011, 'Computational Diffie-Hellman Problem', in Encyclopedia of Cryptography and Security, Springer US, pp. 240 - 244, http://dx.doi.org/10.1007/978-1-4419-5906-5_882

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, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000267348300005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Shparlinski I, 2003, '1/M Generator', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 279 - 282, http://dx.doi.org/10.1007/978-3-0348-8037-4_26

Shparlinski I, 2003, 'Approximation of the Discrete Logarithm by Boolean Functions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 129 - 141, http://dx.doi.org/10.1007/978-3-0348-8037-4_11

Shparlinski I, 2003, 'Approximation of the Discrete Logarithm by Real Polynomials', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 143 - 156, http://dx.doi.org/10.1007/978-3-0348-8037-4_12

Shparlinski I, 2003, 'Approximation of the Discrete Logarithm Modulo p', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 109 - 122, http://dx.doi.org/10.1007/978-3-0348-8037-4_9

Shparlinski I, 2003, 'Approximation of the Discrete Logarithm Modulo p — 1', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 123 - 128, http://dx.doi.org/10.1007/978-3-0348-8037-4_10

Shparlinski I, 2003, 'Arithmetic Functions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 67 - 81, http://dx.doi.org/10.1007/978-3-0348-8037-4_6

Shparlinski I, 2003, 'Basic Notation and Definitions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 17 - 26, http://dx.doi.org/10.1007/978-3-0348-8037-4_2

Shparlinski I, 2003, 'Bit Security of NTRU', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 223 - 229, http://dx.doi.org/10.1007/978-3-0348-8037-4_21

Shparlinski I, 2003, 'Bit Security of the Diffie—Hellman Secret Key', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 189 - 194, http://dx.doi.org/10.1007/978-3-0348-8037-4_15

Shparlinski I, 2003, 'Bit Security of the RSA Encryption and the Shamir Message Passing Scheme', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 211 - 215, http://dx.doi.org/10.1007/978-3-0348-8037-4_19

Shparlinski I, 2003, 'Bit Security of the XTR and LUC Secret Keys', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 217 - 221, http://dx.doi.org/10.1007/978-3-0348-8037-4_20

Shparlinski I, 2003, 'Boolean Complexity of the Diffie-Hellman Secret Key', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 179 - 188, http://dx.doi.org/10.1007/978-3-0348-8037-4_14

Shparlinski I, 2003, 'Complexity Theory', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 103 - 106, http://dx.doi.org/10.1007/978-3-0348-8037-4_8

Shparlinski I, 2003, 'Concluding Remarks and Open Questions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 341 - 365, http://dx.doi.org/10.1007/978-3-0348-8037-4_33

Shparlinski I, 2003, 'Distribution and Discrepancy', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 61 - 65, http://dx.doi.org/10.1007/978-3-0348-8037-4_5

Shparlinski I, 2003, 'Distribution of the ElGamal Signature', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 207 - 210, http://dx.doi.org/10.1007/978-3-0348-8037-4_18

Shparlinski I, 2003, 'Distribution of the RSA and Exponential Pairs', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 231 - 237, http://dx.doi.org/10.1007/978-3-0348-8037-4_22

Shparlinski I, 2003, 'Exponential Sums', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 37 - 60, http://dx.doi.org/10.1007/978-3-0348-8037-4_4

Shparlinski I, 2003, 'Exponentiation and Inversion with Precomputation', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 239 - 245, http://dx.doi.org/10.1007/978-3-0348-8037-4_23

Shparlinski I, 2003, 'Introduction', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 1 - 14, http://dx.doi.org/10.1007/978-3-0348-8037-4_1

Shparlinski I, 2003, 'Inversive, Polynomial and Quadratic Exponential Generators', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 283 - 294, http://dx.doi.org/10.1007/978-3-0348-8037-4_27

Shparlinski I, 2003, 'Lattices and the Hidden Number Problem', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 83 - 102, http://dx.doi.org/10.1007/978-3-0348-8037-4_7

Shparlinski I, 2003, 'Naor—Reingold Function', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 271 - 277, http://dx.doi.org/10.1007/978-3-0348-8037-4_25

Shparlinski I, 2003, 'Polynomial Approximation and Arithmetic Complexity of the Diffie-Hellman Secret Key', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 159 - 177, http://dx.doi.org/10.1007/978-3-0348-8037-4_13

Shparlinski I, 2003, 'Polynomial Approximation, Permanents and Noisy Exponentiation in Finite Fields', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 325 - 332, http://dx.doi.org/10.1007/978-3-0348-8037-4_31

Shparlinski I, 2003, 'Polynomials and Recurrence Sequences', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 27 - 36, http://dx.doi.org/10.1007/978-3-0348-8037-4_3

Shparlinski I, 2003, 'RSA and Blum—Blum—Shub Generators', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 249 - 270, http://dx.doi.org/10.1007/978-3-0348-8037-4_24

Shparlinski I, 2003, 'Security Against the Cycling Attack on the RSA and Timed-release Crypto', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 197 - 200, http://dx.doi.org/10.1007/978-3-0348-8037-4_16

Shparlinski I, 2003, 'Special Polynomials and Boolean Functions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 333 - 339, http://dx.doi.org/10.1007/978-3-0348-8037-4_32

Shparlinski I, 2003, 'Square-Freeness Testing and Other Number-Theoretic Problems', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 303 - 308, http://dx.doi.org/10.1007/978-3-0348-8037-4_29

Shparlinski I, 2003, 'Subset Sum Generators', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 295 - 299, http://dx.doi.org/10.1007/978-3-0348-8037-4_28

Shparlinski I, 2003, 'The Insecurity of the Digital Signature Algorithm with Partially Known Nonces', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 201 - 206, http://dx.doi.org/10.1007/978-3-0348-8037-4_17

Shparlinski I, 2003, 'Trade-off Between the Boolean and Arithmetic Depths of Modulo p Functions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 309 - 323, http://dx.doi.org/10.1007/978-3-0348-8037-4_30

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, http://dx.doi.org/10.1142/9789812388841_0009

von zur Gathen J; Shparlinski I, 2001, 'Gauß Periods in Finite Fields', in Finite Fields and Applications, Springer Berlin Heidelberg, pp. 162 - 177, http://dx.doi.org/10.1007/978-3-642-56755-1_14

Friedlander JB; Lieman D; Shparlinski IE, 1999, 'On the Distribution of the RSA Generator', in Sequences and their Applications, Springer London, pp. 205 - 212, http://dx.doi.org/10.1007/978-1-4471-0551-0_14

Shparlinski I, 1996, 'Approximate constructions in finite fields', in Finite Fields and Applications, Cambridge University Press, pp. 313 - 332, http://dx.doi.org/10.1017/cbo9780511525988.024

Mullen GL; Shparlinski I, 1996, 'Open problems and conjectures in finite fields', in Finite Fields and Applications, Cambridge University Press, pp. 243 - 268, http://dx.doi.org/10.1017/cbo9780511525988.021

Shparlinski IE, 1995, 'On Some Characteristics of Uniformity of Distribution and Their Applications', in Computational Algebra and Number Theory, Springer Netherlands, pp. 227 - 241, http://dx.doi.org/10.1007/978-94-017-1108-1_16

Shparlinski IE, 'Diffie–Hellman Problem', in Encyclopedia of Cryptography and Security, Springer US, pp. 154 - 158, http://dx.doi.org/10.1007/0-387-23483-7_112

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