By Professor Igor Shparlinski

Journal articles

Friedlander JB; Pomerance C; Shparlinski IE, 2002, 'Erratum: Period of the power generator and small values of Carmichael's function (Mathematics of Computation)', Mathematics of Computation, 71, pp. 1803 - 1806, http://dx.doi.org/10.1090/S0025-5718-02-01519-3

Banks WD; Shparlinski IE, 2002, 'On the number of sparse RSA exponents', JOURNAL OF NUMBER THEORY, 95, pp. 340 - 350, http://dx.doi.org/10.1006/jnth.2001.2775

Shparlinski IE, 2002, 'Security of most significant bits of g^x(2)', Information Processing Letters, 83, pp. 109 - 113, http://dx.doi.org/10.1016/S0020-0190(01)00315-5

Mans B; Pappalardi F; Shparlinski I, 2002, 'On the spectral Ádám property for circulant graphs', Discrete Mathematics, 254, pp. 309 - 329, http://dx.doi.org/10.1016/S0012-365X(01)00374-0

Shparlinski IE, 2002, 'On a question of Erdos and Graham', Archiv der Mathematik, 78, pp. 445 - 448, http://dx.doi.org/10.1007/s00013-002-8269-2

Shparlinski IE, 2002, 'On the uniformity of distribution of the EIGamal signature', Applicable Algebra in Engineering, Communications and Computing, 13, pp. 9 - 16, http://dx.doi.org/10.1007/s002000100087

Banks WD; Shparlinski IE, 2002, 'Average normalisations of elliptic curves', Bulletin of the Australian Mathematical Society, 66, pp. 353 - 358, http://dx.doi.org/10.1017/s0004972700040211

Banks WD; Conflitti A; Shparlinski IE, 2002, 'Character sums over integers with restricted g-ary digits', Illinois Journal of Mathematics, 46, pp. 819 - 836, http://dx.doi.org/10.1215/ijm/1258130986

Niederreiter H; Shparlinski IE, 2002, 'On the average distribution of inversive pseudorandom numbers', Finite Fields and their Applications, 8, pp. 491 - 503, http://dx.doi.org/10.1006/ffta.2002.0358

Shparlinski IE, 2002, 'On the distribution of the Diffie-Hellman pairs', Finite Fields and their Applications, 8, pp. 131 - 141, http://dx.doi.org/10.1006/ffta.2000.0321

Banks WD; Shparlinski IE, 2002, 'On the number of sparse RSA exponents', Journal of Number Theory, 95, pp. 340 - 350, http://dx.doi.org/10.1016/S0022-314X(01)92775-1

El Mahassni E; Shparlinski I, 2002, 'On the uniformity of distribution of the elliptic curve ElGamal signature', Finite Fields and their Applications, 8, pp. 589 - 596, http://dx.doi.org/10.1006/ffta.2002.0366

Vasco MIG; Shparlinski IE, 2002, 'Security of the most significant bits of the Shamir message passing scheme', Mathematics of Computation, 71, pp. 333 - 342, http://dx.doi.org/10.1090/S0025-5718-01-01358-8

Friedlander JB; Konyagin S; Shparllnski IE, 2002, 'Some doubly exponential sums over ℤm', Acta Arithmetica, 105, pp. 349 - 370, http://dx.doi.org/10.4064/aa105-4-4

Niederreiter H; Shparlinski IE, 2002, 'On the Average Distribution of Inversive Pseudorandom Numbers', Finite Fields and Their Applications, 8, pp. 491 - 503, http://dx.doi.org/10.1006/ffta.2002.0358

El Mahassni E; Shparlinski I, 2002, 'On the Uniformity of Distribution of the Elliptic Curve ElGamal Signature', Finite Fields and Their Applications, 8, pp. 589 - 596, http://dx.doi.org/10.1006/ffta.2002.0366

Banks WD; Shparlinski IE, 2001, 'Distribution of inverses in polynomial rings', Indagationes Mathematicae, 12, pp. 303 - 315, http://dx.doi.org/10.1016/S0019-3577(01)80012-4

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

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