Select Publications

Journal articles

Farashahi RR; Shparlinski IE, 2012, 'Pseudorandom bits from points on elliptic curves', IEEE Transactions on Information Theory, 58, pp. 1242 - 1247, http://dx.doi.org/10.1109/TIT.2011.2170054

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, http://dx.doi.org/10.1090/conm/574/11426

Ostafe A; Shparlinski IE, 2012, 'Exponential sums over points of elliptic curves with reciprocals of primes', Mathematika, 58, pp. 21 - 33, http://dx.doi.org/10.1112/S0025579311001719

Cilleruelo J; Shparlinski IE; Zumalacárregui A, 2012, 'Isomorphism classes of elliptic curves over a finite field in some thin families', Mathematical Research Letters, 19, pp. 335 - 343, http://dx.doi.org/10.4310/MRL.2012.v19.n2.a6

Farashahi RR; Shparlinski IE, 2012, 'On group structures realized by elliptic curves over a fixed finite field', Experimental Mathematics, 21, pp. 1 - 10, http://dx.doi.org/10.1080/10586458.2012.632754

Banks WD; Pappalardi F; Shparlinski IE, 2012, 'On group structures realized by elliptic curves over arbitrary finite fields', Experimental Mathematics, 21, pp. 11 - 25, http://dx.doi.org/10.1080/10586458.2011.606075

Konyagin SV; Shparlinski IE, 2012, 'On the consecutive powers of a primitive root: Gaps and exponential sums', Mathematika, 58, pp. 11 - 20, http://dx.doi.org/10.1112/S0025579311002117

Shparlinski IE, 2012, 'On the convex hull of solutions to polynomial congruences', Journal of Number Theory, 132, pp. 254 - 257, http://dx.doi.org/10.1016/j.jnt.2011.06.016

Ostafe A; Shparlinski IE, 2012, 'On the power generator and its multivariate analogue', Journal of Complexity, 28, pp. 238 - 249, http://dx.doi.org/10.1016/j.jco.2011.10.010

Shparlinski IE, 2012, 'On the restricted divisor function in arithmetic progressions', Revista Matematica Iberoamericana, 28, pp. 231 - 238, http://dx.doi.org/10.4171/rmi/675

Balog A; Broughan KA; Shparlinski IE, 2012, 'Sum-Products Estimates with Several Sets and Applications', Integers, 12, http://dx.doi.org/10.1515/integers-2012-0012

Shparlinski IE, 2011, 'Character sums with fermat quotients', Quarterly Journal of Mathematics, 62, pp. 1031 - 1043, http://dx.doi.org/10.1093/qmath/haq028

Shparlinski IE, 2011, 'Fermat quotients: Exponential sums, value set and primitive roots', Bulletin of the London Mathematical Society, 43, pp. 1228 - 1238, http://dx.doi.org/10.1112/blms/bdr058

Shparlinski IE, 2011, 'On the distribution of irreducible trinomials', Canadian Mathematical Bulletin, 54, pp. 748 - 756, http://dx.doi.org/10.4153/CMB-2011-053-0

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, http://dx.doi.org/10.1090/S0002-9939-2011-10843-8

Fouvry E; Shparlinski IE, 2011, 'On a ternary quadratic form over primes', Acta Arithmetica, 150, pp. 285 - 314, http://dx.doi.org/10.4064/aa150-3-5

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, http://dx.doi.org/10.1216/RMJ-2011-41-4-1291

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, http://dx.doi.org/10.1142/S1793042111004484

Balog A; Broughan KA; Shparlinski IE, 2011, 'On the number of solutions of exponential congruences', Acta Arithmetica, 148, pp. 93 - 103, http://dx.doi.org/10.4064/aa148-1-7

Ostafe A; Shparlinski IE, 2011, 'Twisted exponential sums over points of elliptic curves', Acta Arithmetica, 148, pp. 77 - 92, http://dx.doi.org/10.4064/aa148-1-6

Ostafe A; Shparlinski IE, 2011, 'Pseudorandomness and dynamics of fermat quotients*', SIAM Journal on Discrete Mathematics, 25, pp. 50 - 71, http://dx.doi.org/10.1137/100798466

Shparlinski IE, 2011, 'Bounds of multiplicative character sums with Fermat quotients of primes', Bulletin of the Australian Mathematical Society, 83, pp. 456 - 462, http://dx.doi.org/10.1017/S000497271000198X

Fouvry E; Luca F; Pappalardi F; Shparlinski IE, 2011, 'Counting dihedral and quaternionic extensions', Transactions of the American Mathematical Society, 363, pp. 3233 - 3253, http://dx.doi.org/10.1090/S0002-9947-2011-05233-5

Shparlinski IE, 2011, 'On small solutions to quadratic congruences', Journal of Number Theory, 131, pp. 1105 - 1111, http://dx.doi.org/10.1016/j.jnt.2010.12.002

Shparlinski IE, 2011, 'Exponential sums with consecutive modular roots of an integer', Quarterly Journal of Mathematics, 62, pp. 207 - 213, http://dx.doi.org/10.1093/qmath/hap023

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, http://arxiv.org/abs/1102.1053v1

Shparlinski IE, 2011, 'On the average distribution of pseudorandom numbers generated by nonlinear permutations', Mathematics of Computation, 80, pp. 1053 - 1061, http://dx.doi.org/10.1090/S0025-5718-2010-02408-1

Křížek M; Luca F; Shparlinski IE; Somer L, 2011, 'On the complexity of testing elite primes', Journal of Integer Sequences, 14, pp. 1 - 5

Konyagin SV; Shparlinski IE, 2011, 'On convex hull of points on modular hyperbolas', Moscow Journal of Combinatorics and Number Theory, 1, pp. 43 - 51

Fouvry E; Shparlinski IE, 2011, 'Smooth shifted monomial products', Publicationes Mathematicae Debrecen, 79, pp. 423 - 432, http://dx.doi.org/10.5486/PMD.2011.5089

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, http://dx.doi.org/10.4064/ba59-3-1

Blackburn SR; Ostafe A; Shparlinski IE, 2011, 'On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves', CoRR, abs/1102.1053

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, http://arxiv.org/abs/1012.1444v2

Ford K; Khan MR; Shparlinski IE, 2010, 'Geometric properties of points on modular hyperbolas', Proceedings of the American Mathematical Society, 138, pp. 4177 - 4185, http://dx.doi.org/10.1090/S0002-9939-2010-10561-0

Farashahi RR; Shparlinski IE, 2010, 'On pseudopoints of algebraic curves', Archiv der Mathematik, 95, pp. 529 - 537, http://dx.doi.org/10.1007/s00013-010-0200-7

Luca F; Shparlinski IE, 2010, 'On the g-Ary Expansions of Apéry, Motzkin, Schröder and Other Combinatorial Numbers', Annals of Combinatorics, 14, pp. 507 - 524, http://dx.doi.org/10.1007/s00026-011-0074-9

Friedlander JB; Gong K; Shparlinskii IE, 2010, 'Character sums over shifted primes', Mathematical Notes, 88, pp. 585 - 598, http://dx.doi.org/10.1134/S0001434610090312

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, http://dx.doi.org/10.1017/S0004972709001270

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


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