By Professor Igor Shparlinski

Journal articles

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, http://dx.doi.org/10.1515/JMC.2010.007

Ostafe A; Pelican E; Shparlinski IE, 2010, 'On pseudorandom numbers from multivariate polynomial systems', Finite Fields and their Applications, 16, pp. 320 - 328, http://dx.doi.org/10.1016/j.ffa.2010.05.002

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, http://dx.doi.org/10.1016/j.jsc.2010.04.001

Bourgain J; Ford K; Konyagin SV; Shparlinski IE, 2010, 'On the divisibility of Fermat quotients', Michigan Mathematical Journal, 59, pp. 313 - 328, http://dx.doi.org/10.1307/mmj/1281531459

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, http://dx.doi.org/10.3934/amc.2010.4.369

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, http://dx.doi.org/10.1090/S0002-9939-10-10404-3

Shparlinski IE; Winterhof A, 2010, 'Partitions into two Lehmer numbers', Monatshefte fur Mathematik, 160, pp. 429 - 441, http://dx.doi.org/10.1007/s00605-009-0130-2

Glebsky L; Shparlinski IE, 2010, 'Short cycles in repeated exponentiation modulo a prime', Designs, Codes, and Cryptography, 56, pp. 35 - 42, http://dx.doi.org/10.1007/s10623-009-9339-2

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, http://dx.doi.org/10.1007/s13163-010-0029-4

Chan TH; Shparlinski IE, 2010, 'On the concentration of points on modular hyperbolas and exponential curves', Acta Arithmetica, 142, pp. 59 - 66, http://dx.doi.org/10.4064/aa142-1-5

Banks WD; Shparlinski IE, 2010, 'Sums with convolutions of Dirichlet characters', Manuscripta Mathematica, 133, pp. 105 - 114, http://dx.doi.org/10.1007/s00229-010-0364-2

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, http://dx.doi.org/10.1090/S0025-5718-09-02271-6

Ahmadi O; Shparlinski IE; Voloch JF, 2010, 'Multiplicative order of gauss periods', International Journal of Number Theory, 6, pp. 877 - 882, http://dx.doi.org/10.1142/S1793042110003290

Konyagin SV; Pomerance C; Shparlinski IE, 2010, 'On the distribution of pseudopowers', Canadian Journal of Mathematics, 62, pp. 582 - 594, http://dx.doi.org/10.4153/CJM-2010-020-4

Shparlinski IE, 2010, 'Tate-shafarevich groups and frobenius fields of reductions of elliptic curves', Quarterly Journal of Mathematics, 61, pp. 255 - 263, http://dx.doi.org/10.1093/qmath/hap001

Shparlinski IE, 2010, 'On the size of the Gelfond exponent', Journal of Number Theory, 130, pp. 1056 - 1060, http://dx.doi.org/10.1016/j.jnt.2009.09.005

Iosevich A; Shparlinski IE; Xiong M, 2010, 'Sets with integral distances in finite fields', Transactions of the American Mathematical Society, 362, pp. 2189 - 2204, http://dx.doi.org/10.1090/S0002-9947-09-05004-1

Iosevich A; Shparlinski IE; Xiong M, 2010, 'SETS WITH INTEGRAL DISTANCES IN FINITE FIELDS', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 362, pp. 2189 - 2204, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000275819200020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Shparlinski IE, 2010, 'Numbers at work and play', Notices of the American Mathematical Society, 57, pp. 334 - 342

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, http://dx.doi.org/10.1017/S0013091508000771

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, http://dx.doi.org/10.1017/S0004972709000719

Shparlinski IE, 2010, 'On quadratic fields generated by discriminants of irreducible trinomials', Proceedings of the American Mathematical Society, 138, pp. 125 - 132, http://dx.doi.org/10.1090/S0002-9939-09-10074-6

Cilleruelo J; Luca F; Quirós A; Shparlinski IE, 2010, 'On squares in polynomial products', Monatshefte fur Mathematik, 159, pp. 215 - 223, http://dx.doi.org/10.1007/s00605-008-0066-y

Loiperdinger SS; Shparlinski IE, 2010, 'ON THE DISTRIBUTION OF THE EULER FUNCTION OF SHIFTED SMOOTH NUMBERS', COLLOQUIUM MATHEMATICUM, 120, pp. 139 - 148, http://dx.doi.org/10.4064/cm120-1-10

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, http://dx.doi.org/10.4310/MRL.2010.v17.n4.a9

Rezaeian Farashahi R; Shparlinski IE, 2010, 'On the number of distinct elliptic curves in some families', Designs, Codes, and Cryptography, 54, pp. 83 - 99, http://dx.doi.org/10.1007/s10623-009-9310-2

Ostafe A; Shparlinski IE, 2010, 'Pseudorandom numbers and hash functions from iterations of multivariate polynomials', Cryptography and Communications, 2, pp. 49 - 67, http://dx.doi.org/10.1007/s12095-009-0016-0

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, http://dx.doi.org/10.4310/PAMQ.2010.v6.n1.a2

Shparlinski IE, 2010, 'Some counting questions for matrices with restricted entries', Linear Algebra and Its Applications, 432, pp. 155 - 160, http://dx.doi.org/10.1016/j.laa.2009.07.036

Broughan KA; Luca F; Shparlinski IE, 2010, 'Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem', Integers, 10, http://dx.doi.org/10.1515/integ.2010.041

Chan TH; Shparlinski IE, 2010, 'Visible Points on Modular Exponential Curves', Bulletin of the Polish Academy of Sciences Mathematics, 58, pp. 17 - 22, http://dx.doi.org/10.4064/ba58-1-2

Фридландер ДБ; Friedlander JB; Гонг K; Gong K; Шпарлинский ИЕ; Shparlinski IE, 2010, 'Суммы значений характеров на сдвинутых простых числах', Математические заметки, 88, pp. 605 - 619, http://dx.doi.org/10.4213/mzm8692

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, http://dx.doi.org/10.1216/RMJ-2009-39-5-1403

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, http://dx.doi.org/10.1093/imrn/rnp041

Banks WD; Shparlinski IE, 2009, 'Multiplicative character sums with twice-differentiable functions', Quarterly Journal of Mathematics, 60, pp. 401 - 411, http://dx.doi.org/10.1093/qmath/han023

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, http://dx.doi.org/10.1016/j.ffa.2009.08.002

Farashahi RR; Shparlinski IE; Voloch JF, 2009, 'On hashing into elliptic curves', Journal of Mathematical Cryptology, 3, pp. 353 - 360, http://dx.doi.org/10.1515/JMC.2009.022

Shparlinski IE, 2009, 'On the distribution of arguments of gauss sums', Kodai Mathematical Journal, 32, pp. 172 - 177, http://dx.doi.org/10.2996/kmj/1238594554

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, http://dx.doi.org/10.1137/090770746

Bourgain J; Konyagin SV; Pomerance C; Shparlinski IE, 2009, 'On the smallest pseudopower', Acta Arithmetica, 140, pp. 43 - 55, http://dx.doi.org/10.4064/aa140-1-3

Luca F; Shparlinski IE, 2009, 'On quadratic fields generated by the Shanks sequence', Proceedings of the Edinburgh Mathematical Society, 52, pp. 719 - 729, http://dx.doi.org/10.1017/S001309150700123X

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, http://dx.doi.org/10.1007/978-3-642-01877-0_8

Shparlinski IE, 2009, 'On a generalisation of a Lehmer problem', Mathematische Zeitschrift, 263, pp. 619 - 631, http://dx.doi.org/10.1007/s00209-008-0434-2

Friedlander JB; Shparlinski IE, 2009, 'On the density of some special primes', Journal of Mathematical Cryptology, 3, pp. 265 - 271, http://dx.doi.org/10.1515/JMC.2009.016

Von Zur Gathen J; Shparlinski IE, 2009, 'Subset sum pseudorandom numbers: Fast generation and distribution', Journal of Mathematical Cryptology, 3, pp. 149 - 163, http://dx.doi.org/10.1515/JMC.2009.007

Shparlinski IE, 2009, 'Bilinear sums with exponential functions', Proceedings of the American Mathematical Society, 137, pp. 2217 - 2224, http://dx.doi.org/10.1090/S0002-9939-09-09882-7

Shparlinski IE, 2009, 'On the values of Kloosterman sums', IEEE Transactions on Information Theory, 55, pp. 2599 - 2601, http://dx.doi.org/10.1109/TIT.2009.2018320

Cojocaru AC; Shparlinski IE, 2009, 'On the embedding degree of reductions of an elliptic curve', Information Processing Letters, 109, pp. 652 - 654, http://dx.doi.org/10.1016/j.ipl.2009.02.018

Balasuriya S; Shparlinski IE; Sutantyo D, 2009, 'Multiplicative character sums with the Euler function', Studia Scientiarum Mathematicarum Hungarica, 46, pp. 223 - 229, http://dx.doi.org/10.1556/SScMath.46.2009.2.1087

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, http://dx.doi.org/10.1017/S0004972709000033

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