By Professor Igor Shparlinski

Journal articles

Shparlinski I, 2005, 'Book Review: Report on global methods for combinatorial isoperimetric problems', Mathematics of Computation, 74, pp. 1033 - 1052, http://dx.doi.org/10.1090/s0025-5718-04-01757-0

Hess F; Shparlinski IE, 2005, 'On the linear complexity and multidimensional distribution of congruential generators over elliptic curves', Designs, Codes, and Cryptography, 35, pp. 111 - 117, http://dx.doi.org/10.1007/s10623-003-6153-0

Shparlinski IE, 2005, 'On the singularity of generalised Vandermonde matrices over finite fields', Finite Fields and their Applications, 11, pp. 193 - 199, http://dx.doi.org/10.1016/j.ffa.2004.11.001

Lange T; Shparlinski I, 2005, 'Collisions in fast generation of ideal classes and points on hyperelliptic and elliptic curves', Applicable Algebra in Engineering, Communications and Computing, 15, pp. 329 - 337, http://dx.doi.org/10.1007/s00200-004-0161-9

Banks WD; Heath-Brown R; Shparlinski IE, 2005, 'On the average value of divisor sums in arithmetic progressions', International Mathematics Research Notices, pp. 1 - 25, http://dx.doi.org/10.1155/imrn.2005.1

Lange T; Shparlinski IE, 2005, 'Certain exponential sums and random walks on elliptic curves', Canadian Journal of Mathematics, 57, pp. 338 - 350, http://dx.doi.org/10.4153/CJM-2005-015-8

Garaev MZ; Luca F; Shparlinski IE, 2005, 'Exponential sums and congruences with factorials', Journal fur die Reine und Angewandte Mathematik, pp. 29 - 44, http://dx.doi.org/10.1515/crll.2005.2005.584.29

Friedlander JB; Pomerance C; Shparlinski IE, 2005, 'Finding the group structure of elliptic curves over finite fields', Bulletin of the Australian Mathematical Society, 72, pp. 251 - 263, http://dx.doi.org/10.1017/s0004972700035048

Contini S; Shparlinski IE, 2005, 'On Stern's attack against secret truncated linear congruential generators', Lecture Notes in Computer Science, 3574, pp. 52 - 60, http://dx.doi.org/10.1007/11506157_5

Luca F; Shparlinski IE, 2005, 'On the largest prime factor of n! + 2ⁿ − 1', Journal de Theorie des Nombres de Bordeaux, 17, pp. 859 - 870, http://dx.doi.org/10.5802/jtnb.524

Shparlinski IE, 2005, 'On the nonlinearity of the sequence of signs of Kloosterman sums', Bulletin of the Australian Mathematical Society, 71, pp. 405 - 409, http://dx.doi.org/10.1017/s0004972700038405

De Koninck JM; Luca F; Shparlinski IE, 2005, 'Powerful numbers in short intervals', Bulletin of the Australian Mathematical Society, 71, pp. 11 - 16, http://dx.doi.org/10.1017/s0004972700037953

Everest G; Shparlinski IE, 2005, 'Prime divisors of sequences associated to elliptic curves', Glasgow Mathematical Journal, 47, pp. 115 - 122, http://dx.doi.org/10.1017/S0017089504002113

Luca F; Shparlinski IE, 2005, 'Prime divisors of shifted factorials', Bulletin of the London Mathematical Society, 37, pp. 809 - 817, http://dx.doi.org/10.1112/S0024609305004923

Hallgren S; Russell A; Shparlinski IE, 2005, 'Quantum noisy rational function reconstruction', Lecture Notes in Computer Science, 3595, pp. 420 - 429, http://dx.doi.org/10.1007/11533719_43

Banks WD; Garaev MZ; Luca F; Shparlinski IE, 2005, 'Uniform Distribution of the Fractional Part of the Average Prime Divisor', Forum Mathematicum, 17, pp. 885 - 901, http://dx.doi.org/10.1515/form.2005.17.6.885

Garaev MZ; Luca F; Shparlinski IE, 2005, 'Waring problem with factorials', Bulletin of the Australian Mathematical Society, 71, pp. 259 - 264, http://dx.doi.org/10.1017/s0004972700038223

Garaev MZ; Luca F; Shparlinski IE, 2004, 'Character sums and congruences with n!', Transactions of the American Mathematical Society, 356, pp. 5089 - 5102, http://dx.doi.org/10.1090/S0002-9947-04-03612-8

Dewar M; Panario D; Shparlinski IE, 2004, 'Distribution of exponential functions with k-full exponent modulo a prime', Indagationes Mathematicae, 15, pp. 497 - 503, http://dx.doi.org/10.1016/S0019-3577(04)80014-4

Vasco MIG; Näslund M; Shparlinski IE, 2004, 'New results on the hardness of diffie-hellman bits', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2947, pp. 159 - 172

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

Banks WD; Harcharras A; Shparlinski IE, 2004, 'Smooth values of shifted primes in arithmetic progressions', Michigan Mathematical Journal, 52, pp. 603 - 618, http://dx.doi.org/10.1307/mmj/1100623415

Shparlinski IE, 2004, 'On the uniformity of distribution of the decryption exponent in fixed encryption exponent RSA', Information Processing Letters, 92, pp. 143 - 147, http://dx.doi.org/10.1016/j.ipl.2004.07.004

Shparlinski IE, 2004, 'Bounds of Gauss sums in finite fields', Proceedings of the American Mathematical Society, 132, pp. 2817 - 2824, http://dx.doi.org/10.1090/S0002-9939-04-07133-3

Luca F; Mireles DJ; Shparlinski IE, 2004, 'Mov attack in various subgroups on elliptic curves', ILLINOIS JOURNAL OF MATHEMATICS, 48, pp. 1041 - 1052, http://dx.doi.org/10.1215/ijm/1258131069

Chou WS; Shparlinski IE, 2004, 'On the cycle structure of repeated exponentiation modulo a prime', Journal of Number Theory, 107, pp. 345 - 356, http://dx.doi.org/10.1016/j.jnt.2004.04.005

Goresky M; Klapper A; Murty R; Shparlinski I, 2004, 'On decimations of ℓ-sequences', SIAM Journal on Discrete Mathematics, 18, pp. 130 - 140, http://dx.doi.org/10.1137/S0895480102403428

Shparlinski IE, 2004, 'Distribution of exponential functions with squarefull exponent in residue rings', Indagationes Mathematicae, 15, pp. 283 - 289, http://dx.doi.org/10.1016/S0019-3577(04)90020-1

Von Zur Gathen J; Shparlinski IE, 2004, 'Polynomial Interpolation from Multiples', Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 15, pp. 1125 - 1130

Conflitti A; Shparlinski IE, 2004, 'On the multidimensional distribution of the subset sum generator of pseudorandom numbers', Mathematics of Computation, 73, pp. 1005 - 1011, http://dx.doi.org/10.1090/S0025-5718-03-01563-1

Frandsen GS; Shparlinski IE, 2004, 'On Reducing a System of Equations to a Single Equation', BRICS Report Series, 11, http://dx.doi.org/10.7146/brics.v11i6.21831

Shparlinski IE; Winterhof A, 2004, 'A nonuniform algorithm for the hidden number problem in subgroups', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2947, pp. 416 - 424, http://dx.doi.org/10.1007/978-3-540-24632-9_30

Banks WD; Shparlinski IE, 2004, 'Arithmetic properties of numbers with restricted digits', Acta Arithmetica, 112, pp. 313 - 332, http://dx.doi.org/10.4064/aa112-4-1

von zur Gathen J; Knopfmacher A; Luca F; Lucht LG; Shparlinski IE, 2004, 'Average order in cyclic groups', Journal de Theorie des Nombres de Bordeaux, 16, pp. 107 - 123, http://dx.doi.org/10.5802/jtnb.436

Mans B; Shparlinski I, 2004, 'Bisecting and gossiping in circulant graphs', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2976, pp. 589 - 598, http://dx.doi.org/10.1007/978-3-540-24698-5_61

Russell A; Shparlinski IE, 2004, 'Classical and quantum function reconstruction via character evaluation', Journal of Complexity, 20, pp. 404 - 422, http://dx.doi.org/10.1016/j.jco.2003.08.019

Shparlinski IE, 2004, 'Exponential function analogue of kloosterman sums', Rocky Mountain Journal of Mathematics, 34, pp. 1497 - 1502, http://dx.doi.org/10.1216/rmjm/1181069811

Banks WD; Conflitti A; Friedlander JB; Shparlinski IE, 2004, 'Exponential sums over Mersenne numbers', Compositio Mathematica, 140, pp. 15 - 30, http://dx.doi.org/10.1112/S0010437X03000022

Luca F; Mireles DJ; Shparlinski IE, 2004, 'Florianptic curves', Illinois Journal of Mathematics, 48, pp. 1041 - 1052, http://dx.doi.org/10.1215/ijm/1258131069

Von Gathen JZ; Shparlinski IE, 2004, 'GCD of random linear forms', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3341, pp. 464 - 469

Shparlinski IE; Steinfield R, 2004, 'Noisy Chinese remaindering in the Lee norm', Journal of Complexity, 20, pp. 423 - 437, http://dx.doi.org/10.1016/j.jco.2003.08.020

Banks WD; Conflitti A; Shparlinski IE, 2004, 'Number theoretic designs for directed regular graphs of small diameter', SIAM Journal on Discrete Mathematics, 17, pp. 377 - 383, http://dx.doi.org/10.1137/S0895480101396676

Frandsen GS; Shparlinski IE, 2004, 'On reducing a system of equations to a single equation', Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, pp. 163 - 166, http://dx.doi.org/10.1145/1005285.1005310

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

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