By Professor Igor Shparlinski

Journal articles

Von Gathen JZ; Shparlinski IE, 2004, 'Predicting Subset Sum Pseudorandom Generators', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 3357, pp. 241 - 251

Galbraith SD; Hopkins HJ; Shparlinski IE, 2004, 'Secure bilinear Diffie-Hellman bits', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 3108, pp. 370 - 378, http://dx.doi.org/10.1007/978-3-540-27800-9_32

Shparlinski IE, 2004, 'Security of polynomial transformations of the Diffie-Hellman key', Finite Fields and their Applications, 10, pp. 123 - 131, http://dx.doi.org/10.1016/S1071-5797(03)00048-0

Von Zur Gathen J; Shparlinski I; Sinclair A, 2003, 'Finding points on curves over finite fields', SIAM Journal on Computing, 32, pp. 1436 - 1448, http://dx.doi.org/10.1137/S0097539799351018

Nguyen PQ; Shparlinski IE, 2003, 'The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces', Designs Codes and Cryptography, 30, pp. 201 - 217, http://dx.doi.org/10.1023/A:1025436905711

Howgrave-Graham NA; Nguyen PQ; Shparlinski IE, 2003, 'Hidden number problem with hidden multipliers, timed-release crypto, and noisy exponentiation', Mathematics of Computation, 72, pp. 1473 - 1485, http://dx.doi.org/10.1090/S0025-5718-03-01495-9

Shparlinski IE, 2003, 'Prime divisors of sparse integers', Periodica Mathematica Hungarica, 46, pp. 215 - 222, http://dx.doi.org/10.1023/A:1025996312037

Nguyen PQ; Shparlinski IE, 2003, 'The insecurity of the digital signature algorithm with partially known nonces', Journal of Cryptology, 15, pp. 151 - 176, http://dx.doi.org/10.1007/s00145-002-0021-3

Konyagin S; Lange T; Shparlinski I, 2003, 'Linear complexity of the discrete logarithm', Designs Codes and Cryptography, 28, pp. 135 - 146, http://dx.doi.org/10.1023/A:1022584306676

Luca F; Shparlinski IE, 2003, 'Average multiplicative orders of elements modulo n', Acta Arithmetica, 109, pp. 387 - 411, http://dx.doi.org/10.4064/aa109-4-7

Allender E; Bernasconi A; Damm C; Von Zur Gathen J; Saks M; Shparlinski I, 2003, 'Complexity of some arithmetic problems for binary polynomials', Computational Complexity, 12, pp. 23 - 47, http://dx.doi.org/10.1007/s00037-003-0176-9

Niederreiter H; Shparlinski IE, 2003, 'Dynamical systems generated by rational functions', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2643, pp. 6 - 17, http://dx.doi.org/10.1007/3-540-44828-4_2

Näslund M; Shparlinski IE; Whyte W, 2003, 'On the bit security of NTRUEncrypt', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2567, pp. 62 - 70, http://dx.doi.org/10.1007/3-540-36288-6_5

Niederreiter H; Shparlinski IE, 2003, 'On the distribution of power residues and primitive elements in some nonlinear recurring sequences', Bulletin of the London Mathematical Society, 35, pp. 522 - 528, http://dx.doi.org/10.1112/S002460930300198X

Gutierrez J; Shparlinski IE; Winterhof A, 2003, 'On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators', IEEE Transactions on Information Theory, 49, pp. 60 - 64, http://dx.doi.org/10.1109/TIT.2002.806144

Khan MR; Shparlinski IE, 2003, 'On the maximal difference between an element and its inverse modulo n', Periodica Mathematica Hungarica, 47, pp. 111 - 117, http://dx.doi.org/10.1023/b:mahu.0000010815.14847.96

Niederreiter H; Shparlinski IE, 2003, 'Periodic sequences with maximal linear complexity and almost maximal k-rrror linear complexity', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2898, pp. 183 - 189, http://dx.doi.org/10.1007/978-3-540-40974-8_15

Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2003, 'Predicting the Inversive Generator', Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 2898, pp. 264 - 275, http://dx.doi.org/10.1007/978-3-540-40974-8_21

Banks WD; Harcharras A; Shparlinski IE, 2003, 'Short Kloosterman sums for polynomials over finite fields', Canadian Journal of Mathematics, 55, pp. 225 - 246, http://dx.doi.org/10.4153/CJM-2003-010-0

Pappalardi F; Saidak F; Shparlinski IE, 2003, 'Square-free values of the Carmichael function', Journal of Number Theory, 103, pp. 122 - 131, http://dx.doi.org/10.1016/S0022-314X(03)00110-0

Guruswami V; Shparlinski I, 2003, 'Unconditional proof of tightness of Johnson bound', Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms, pp. 754 - 755

Codenotti B; Shparlinski IE; Winterhof A, 2002, 'On the hardness of approximating the permanent of structured matrices', Computational Complexity, 11, pp. 158 - 170, http://dx.doi.org/10.1007/s00037-002-0174-3

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 gx(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

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