By Professor Igor Shparlinski

Journal articles

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

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

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