By Professor Igor Shparlinski

Journal articles

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, http://dx.doi.org/10.1023/A:1011223204345

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, http://dx.doi.org/10.1090/S0025-5718-00-01273-4

Friedlander JB; Shparlinski IE, 2001, 'On the distribution of the power generator', Mathematics of Computation, 70, pp. 1575 - 1589, http://dx.doi.org/10.1090/S0025-5718-00-01283-7

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, http://dx.doi.org/10.1090/S0025-5718-00-01282-5

Bernasconi A; Damm C; Shparlinski I, 2001, 'Circuit and decision tree complexity of some number theoretic problems', Information and Computation, 168, pp. 113 - 124, http://dx.doi.org/10.1006/inco.2000.3017

El Mahassni E; Shparlinski I, 2001, 'On Some Uniformity of Distribution Properties of ESIGN', Electronic Notes in Discrete Mathematics, 6, pp. 132 - 139, http://dx.doi.org/10.1016/S1571-0653(04)00164-7

Shparlinski IE, 2001, 'On the uniformity of distribution of the RSA pairs', Mathematics of Computation, 70, pp. 801 - 808, http://dx.doi.org/10.1090/S0025-5718-00-01274-6

Friedlander JB; Shparlinsk IE, 2001, 'On the distribution of Diffie-Hellman triples with sparse exponents', SIAM Journal on Discrete Mathematics, 14, pp. 162 - 169, http://dx.doi.org/10.1137/S0895480199361740

Friedlander JB; Shparlinski IE, 2001, 'Double exponential sums over thin sets', Proceedings of the American Mathematical Society, 129, pp. 1617 - 1621, http://dx.doi.org/10.1090/s0002-9939-00-05921-9

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, http://dx.doi.org/10.5802/jtnb.303

Lieman D; Shparlinski I, 2001, 'On a new exponential sum', Canadian Mathematical Bulletin, 44, pp. 87 - 92, http://dx.doi.org/10.4153/CMB-2001-010-1

Shparlinski I, 2001, 'On Some Properties of the Shrinking Generator', Designs Codes and Cryptography, 23, pp. 147 - 156, http://dx.doi.org/10.1023/A:1011256430812

Shparlinski I, 2001, 'On the Linear Complexity of the Power Generator', Designs Codes and Cryptography, 23, pp. 5 - 10, http://dx.doi.org/10.1023/A:1011264815860

Shparlinski I, 2001, 'On the Multiplicative Orders of γ and γ+γ-1 over finite fields', Finite Fields and their Applications, 7, pp. 327 - 331, http://dx.doi.org/10.1006/ffta.2000.0292

Shparlinski IE, 2001, 'On the Uniformity of Distribution of the Naor-Reingold Pseudo-Random Function', Finite Fields and their Applications, 7, pp. 318 - 326, http://dx.doi.org/10.1006/ffta.2000.0291

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, http://dx.doi.org/10.1007/3-540-44647-8_12

El Mahassni E; Shparlinski I, 2001, 'Polynomial representations of the Diffie-Hellman mapping', Bulletin of the Australian Mathematical Society, 63, pp. 467 - 473, http://dx.doi.org/10.1017/s0004972700019547

Shparlinski IE, 2001, 'Sparse polynomial approximation in finite fields', Conference Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 209 - 215, http://dx.doi.org/10.1145/380752.380803

Shparlinski IE, 2000, 'Linear complexity of the Naor-Reingold pseudo-random function', Information Processing Letters, 76, pp. 95 - 99, http://dx.doi.org/10.1016/S0020-0190(00)00133-2

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, http://dx.doi.org/10.1007/10719839_27

El Mahassni E; Shparlinski I, 2000, 'On some uniformity of distribution properties of ESIGN', Electronic Notes in Discrete Mathematics, 6, pp. 1 - 8

Griffin F; Shparlinski IE, 2000, 'On the linear complexity profile of the power generator', IEEE Transactions on Information Theory, 46, pp. 2159 - 2162, http://dx.doi.org/10.1109/18.868485

Coppersmith D; Shparlinski I, 2000, 'On polynomial approximation of the discrete logarithm and the Diffie-Hellman mapping', JOURNAL OF CRYPTOLOGY, 13, pp. 339 - 360, http://dx.doi.org/10.1007/s001450010002

Von Zur Gathen J; Shparlinski IE, 2000, 'CREW PRAM complexity of modular inversion', SIAM Journal on Computing, 29, pp. 1839 - 1857, http://dx.doi.org/10.1137/S0097539797328070

Karpinski M; Van Der Poorten A; Shparlinski I, 2000, 'Zero testing of p-adic and modular polynomials', Theoretical Computer Science, 233, pp. 309 - 317, http://dx.doi.org/10.1016/S0304-3975(99)00133-4

Friedlander JB; Hansen J; Shparlinski IE, 2000, 'Character sums with exponential functions', Mathematika, 47, pp. 75 - 85, http://dx.doi.org/10.1112/S0025579300015734

Shparlinski IE, 2000, 'Computing Jacobi Symbols modulo Sparse Integers and Polynomials and Some Applications', Journal of Algorithms, 36, pp. 241 - 252, http://dx.doi.org/10.1006/jagm.2000.1091

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, http://dx.doi.org/10.4064/aa-92-1-89-98

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, http://dx.doi.org/10.1007/s002000050124

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, http://dx.doi.org/10.1007/s006050050004

Shparlinski IE, 2000, 'On the Naor-Reingold pseudo-random function from elliptic curves', Applicable Algebra in Engineering Communications and Computing, 11, pp. 27 - 34, http://dx.doi.org/10.1007/s002000000023

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, http://dx.doi.org/10.1007/s11856-000-1270-1

Bernasconi A; Damm C; Shparlinski I, 2000, 'The average sensitivity of square-freeness', Computational Complexity, 9, pp. 39 - 51, http://dx.doi.org/10.1007/PL00001600

Von Zur Gathen J; Shparlinski I, 1999, 'Computing components and projections of curves over finite fields', SIAM Journal on Computing, 28, pp. 822 - 840, http://dx.doi.org/10.1137/s009753979427741x

Everest GR; Shparlinski IE, 1999, 'Counting the values taken by algebraic exponential polynomials', Proceedings of the American Mathematical Society, 127, pp. 665 - 675, http://dx.doi.org/10.1090/s0002-9939-99-04728-0

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, http://dx.doi.org/10.1112/S002461079900736X

Friedlander J; Larsen M; Lieman D; Shparlinski I, 1999, 'On the Correlation of Binary M-sequences', Designs Codes and Cryptography, 16, pp. 249 - 256, http://dx.doi.org/10.1023/A:1008383811226

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, http://dx.doi.org/10.1006/ffta.1999.0257

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, http://dx.doi.org/10.1007/s002000050093

Shparlinski IE, 1996, 'On irreducible polynomials of small height over finite fields', APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 7, pp. 427 - 431, http://dx.doi.org/10.1007/BF01293260

Shparlinski I, 1996, 'On finding primitive roots in finite fields', Theoretical Computer Science, 157, pp. 273 - 275, http://dx.doi.org/10.1016/0304-3975(95)00164-6

Karpinski M; Shparlinski I, 1996, 'On some approximation problems concerning sparse polynomials over finite fields', Theoretical Computer Science, 157, pp. 259 - 266, http://dx.doi.org/10.1016/0304-3975(95)00162-X

Von Zur Gathen J; Karpinski M; Shparlinski I, 1996, 'Counting curves and their projections', Computational Complexity, 6, pp. 64 - 99, http://dx.doi.org/10.1007/BF01202042

Everest GR; Shparlinski IE, 1996, 'Divisor sums of generalised exponential polynomials', Canadian Mathematical Bulletin, 39, pp. 35 - 46, http://dx.doi.org/10.4153/CMB-1996-005-5

Shparlinski I, 1996, 'On exponential sums with sparse polynomials and rational functions', Journal of Number Theory, 60, pp. 233 - 244, http://dx.doi.org/10.1006/jnth.1996.0121

Shparlinski IE, 1996, 'On irreducible polynomials of small height over finite fields', Applicable Algebra in Engineering Communications and Computing, 7, pp. 427 - 431, http://dx.doi.org/10.1007/BF01293260

Van Der Poorten AJ; Shparlinski IE, 1996, 'On linear recurrence sequences with polynomial coefficients', Glasgow Mathematical Journal, 38, pp. 147 - 155, http://dx.doi.org/10.1017/s0017089500031372

Pappalardi F; Shparlinski I, 1995, 'On artin′s conjecture over function fields', Finite Fields and their Applications, 1, pp. 399 - 404, http://dx.doi.org/10.1006/ffta.1995.1030

Shparlinski IE, 1993, 'Finding irreducible and primitive polynomials', Applicable Algebra in Engineering Communication and Computing, 4, pp. 263 - 268, http://dx.doi.org/10.1007/BF01200150

Shparlinski IE, 1993, 'On bivariate polynomial factorization over finite fields', Mathematics of Computation, 60, pp. 787 - 791, http://dx.doi.org/10.1090/S0025-5718-1993-1176716-3

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