By Professor Igor Shparlinski

Journal articles

Shparlinski IE, 2014, 'On solutions to some polynomial congruences in small boxes', Bulletin of the Australian Mathematical Society, 89, pp. 300 - 307, http://dx.doi.org/10.1017/S0004972713000671

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, http://dx.doi.org/10.1090/S0025-5718-2014-02794-4

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, http://dx.doi.org/10.1016/j.jsc.2013.12.005

Mans B; Shparlinski I, 2014, 'Random walks, bisections and gossiping in circulant graphs', Algorithmica, 70, pp. 301 - 325

Shparlinski IE, 2014, 'Squarefree parts of discriminants of trinomials', Archiv Der Mathematik, 102, pp. 545 - 554, http://dx.doi.org/10.1007/s00013-014-0654-0

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, http://dx.doi.org/10.1007/s00200-014-0219-2

Shparlinski IE; Sutherland AV, 2014, 'On the Distribution of Atkin and Elkies Primes', Foundations of Computational Mathematics, pp. 1 - 13, http://dx.doi.org/10.1007/s10208-013-9181-9

Shparlinski IE, 2013, 'Additive decompositions of subgroups of finite fields', SIAM Journal on Discrete Mathematics, 27, pp. 1870 - 1879, http://dx.doi.org/10.1137/130924470

Von Zur Gathen J; Shparlinski IE, 2013, 'Generating safe primes', Journal of Mathematical Cryptology, 7, pp. 333 - 365, http://dx.doi.org/10.1515/jmc-2013-5011

Shparlinski IE; Steiner W, 2013, 'On digit patterns in expansions of rational numbers with prime denominator', Quarterly Journal of Mathematics, 64, pp. 1231 - 1238, http://dx.doi.org/10.1093/qmath/has027

Dietmann R; Elsholtz C; Shparlinski IE, 2013, 'On gaps between primitive roots in the hamming metric', Quarterly Journal of Mathematics, 64, pp. 1043 - 1055, http://dx.doi.org/10.1093/qmath/has022

Shparlinski IE, 2013, 'On the average number of square-free values of polynomials', Canadian Mathematical Bulletin, 56, pp. 844 - 849, http://dx.doi.org/10.4153/CMB-2012-021-8

Harvey D; Shparlinski IE, 2013, 'Statistics of different reduction types of fermat curves', Experimental Mathematics, 22, pp. 243 - 249, http://dx.doi.org/10.1080/10586458.2013.790201

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, http://dx.doi.org/10.1016/j.indag.2013.02.005

Cilleruelo J; Shparlinski I, 2013, 'Concentration of points on curves in finite fields', Monatshefte Fur Mathematik, 171, pp. 315 - 327, http://dx.doi.org/10.1007/s00605-013-0498-x

Shparlinski IE, 2013, 'On products of primes and almost primes in arithmetic progressions', Periodica Mathematica Hungarica, 67, pp. 55 - 61, http://dx.doi.org/10.1007/s10998-013-2736-3

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, http://dx.doi.org/10.1016/j.jnt.2013.02.012

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, http://dx.doi.org/10.1307/mmj/1378757885

Shparlinski IE, 2013, 'On some exponential sums with exponential and rational functions', Rocky Mountain Journal of Mathematics, 43, pp. 361 - 371, http://dx.doi.org/10.1216/RMJ-2013-43-1-361

Shparlinski I, 2013, 'Erratum: Sum-product estimates and multiplicative orders ofΓ and Γ + Γ-1 in finite fields (Bulletin of the Australian Mathematical Society)', Bulletin of the Australian Mathematical Society, 87, pp. 527 - 528, http://dx.doi.org/10.1017/S0004972712001062

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, http://dx.doi.org/10.1007/s00200-013-0187-y

Gutierrez J; Ibeas A; Gómez-Pérez D; Shparlinski IE, 2013, 'Predicting masked linear pseudorandom number generators over finite fields', Designs Codes and Cryptography, 67, pp. 395 - 402, http://dx.doi.org/10.1007/s10623-012-9615-4

Shparlinski IE, 2013, 'On the Sato-Tate conjecture on average for some families of elliptic curves', Forum Mathematicum, 25, pp. 647 - 664, http://dx.doi.org/10.1515/FORM.2011.141

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, http://dx.doi.org/10.1134/S0081543813010057

Shparlinski IE, 2013, 'On vanishing Fermat quotients and a bound of the Ihara sum', Kodai Mathematical Journal, 36, pp. 99 - 108, http://dx.doi.org/10.2996/kmj/1364562722

Shparlinski IE, 2013, 'Correcting noisy exponentiation black-boxes modulo a prime', Information Processing Letters, 113, pp. 414 - 417, http://dx.doi.org/10.1016/j.ipl.2013.03.016

Shparlinski IE, 2013, 'Elliptic curves over finite fields: Number theoretic and cryptographic aspects', Fields Institute Communications, 66, pp. 65 - 90, http://dx.doi.org/10.1007/978-1-4614-5389-5_4

Baker RC; Banks WD; Brüdern J; Shparlinski IE; Weingartner AJ, 2013, 'Piatetski-Shapiro sequences', Acta Arithmetica, 157, pp. 37 - 68, http://dx.doi.org/10.4064/aa157-1-3

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, http://dx.doi.org/10.1090/S0025-5718-2012-02606-8

Shparlinski IE; Winterhof A, 2013, 'Distribution of values of polynomial Fermat quotients', Finite Fields and their Applications, 19, pp. 93 - 104, http://dx.doi.org/10.1016/j.ffa.2012.10.004

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

Cilleruelo J; Kumchev A; Luca F; Rué J; Shparlinski IE, 2013, 'On the fractional parts of an/n', Bulletin of the London Mathematical Society, 45, pp. 249 - 256, http://dx.doi.org/10.1112/blms/bds084

Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2012, 'On the hidden shifted power problem', SIAM Journal on Computing, 41, pp. 1524 - 1557, http://dx.doi.org/10.1137/110850414

Shparlinski IE; Stange KE, 2012, 'Character sums with division polynomials', Canadian Mathematical Bulletin, 55, pp. 850 - 857, http://dx.doi.org/10.4153/CMB-2011-126-x

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, http://dx.doi.org/10.1007/s00209-011-0959-7

Shparlinski IE, 2012, 'Modular hyperbolas', Japanese Journal of Mathematics, 7, pp. 235 - 294, http://dx.doi.org/10.1007/s11537-012-1140-8

Shparlinski IE, 2012, 'On the distribution of solutions to polynomial congruences', Archiv Der Mathematik, 99, pp. 345 - 351, http://dx.doi.org/10.1007/s00013-012-0436-5

Balog A; Broughan KA; Shparlinski IE, 2012, 'Sum-Products Estimates with Several Sets and Applications', Integers, 12, pp. 895 - 906, http://dx.doi.org/10.1515/integers-2012-0012

Ostafe A; Shparlinski IE, 2012, 'Multiplicative character sums and products of sparse integers in residue classes', Periodica Mathematica Hungarica, 64, pp. 247 - 255, http://dx.doi.org/10.1007/s10998-012-6771-2

González 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, http://dx.doi.org/10.1017/S0013091510001355

Shparlinski I, 2012, 'Sum-product estimates and multiplicative orders of γ and γ+γ -1 in finite fields', Bulletin of the Australian Mathematical Society, 85, pp. 505 - 508, http://dx.doi.org/10.1017/S0004972711002887

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, http://dx.doi.org/10.1007/978-3-642-29344-3_46

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, http://dx.doi.org/10.1093/imrn/rnr097

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, http://dx.doi.org/10.1017/S0305004111000399

Ahmadi O; Luca F; Ostafe A; Shparlinski IE, 2012, 'On stable quadratic polynomials', Glasgow Mathematical Journal, 54, pp. 359 - 369, http://dx.doi.org/10.1017/S001708951200002X

Ling S; Shparlinski IE; Steinfeld R; Wang H, 2012, 'On the modular inversion hidden number problem', Journal of Symbolic Computation, 47, pp. 358 - 367, http://dx.doi.org/10.1016/j.jsc.2011.09.002

Shparlinski IE, 2012, 'On the value set of fermat quotients', Proceedings of the American Mathematical Society, 140, pp. 1199 - 1206, http://dx.doi.org/10.1090/S0002-9939-2011-11203-6

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, http://dx.doi.org/10.1090/S0025-5718-2011-02543-3

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, http://dx.doi.org/10.1017/S1446788712000109

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

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