By Professor Igor Shparlinski

Conference Papers

Lam KY; Sica F, 1999, 'Effective determination of the proportion of split primes in number fields', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 81 - 92, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999

De Bonis A; De Santis A, 1999, 'New results on the randomness of visual cryptography schemes', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 187 - 201, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999

Conflitti A, 1999, 'On elements of high order in finite fields', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 11 - 14, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999

Kohel DR, 1999, 'Rational groups of elliptic curves suitable for cryptography', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 69 - 80, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999

Safavi-Naini R; Wang HX, 1999, 'Robust additive secret sharing schemes over Z_m', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 357 - 368, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999

Silverman RD, 1999, 'RSA public key validation', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 369 - 378, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999

Friedlander JB; Pomerance C; Shparlinski IE, 1999, 'Small values of the Carmichael function and cryptographic applications', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 25 - 32, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999

Nguyen PQ, 1999, 'The dark side of the hidden number problem: Lattice attacks on DSA', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 321 - 330, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999

Hoffstein J; Lieman D, 1999, 'The distribution of the quadratic symbol in function fields and a faster mathematical stream cipher', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 59 - 68, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999

Safavi-Naini R; Susilo W, 1999, 'A general construction for fail-stop signature using authentication codes', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 343 - 356, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800025&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Naslund M; Russell A, 1999, 'Achieving optimal fairness from biased coinflips', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 303 - 319, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800022&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Ding CS; Kohel DR; Ling S, 1999, 'Counting the number of points on affine diagonal curves', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 15 - 24, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Peralta R, 1999, 'Elliptic curve factorization using a "partially oblivious" function', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 123 - 128, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Alonso C; Gutierrez J; Rubio R, 1999, 'On the dimension and the number of parameters of a unirational variety', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 3 - 9, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Hoffstein J; Silverman JH, 1999, 'Polynomial rings and efficient public key authentication II', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 269 - 286, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Mihailescu P, 1999, 'Security of biased sources for cryptographic keys', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 287 - 302, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800021&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Han WB, 1999, 'The distribution of the coefficients of primitive polynomials over finite fields', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 43 - 57, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

van der Poorten A, 1999, 'The Hermite-Serret algorithm and 12(2)+33(2)', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 129 - 136, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800012&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

von zur Gathen J; Shparlinski I, 1999, 'Gauss periods in finite fields', in Jungnickel D; Niederreiter H (ed.), FINITE FIELDS AND APPLICATIONS, SPRINGER-VERLAG BERLIN, GERMANY, UNIV AUGSBURG, DEPT MATH, AUGSBURG, pp. 162 - 177, presented at 5th International Conference on Finite Fields and Applications, GERMANY, UNIV AUGSBURG, DEPT MATH, AUGSBURG, 02 August 1999 - 06 August 1999

Bernasconi A; Shparlinski I, 1999, 'Circuit complexity of testing square-free numbers', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 47 - 56, http://dx.doi.org/10.1007/3-540-49116-3_4

Von Zur Gathen J; Shparlinski I, 1999, 'Constructing elements of large order in finite fields', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 404 - 409, http://dx.doi.org/10.1007/3-540-46796-3_38

Allender E; Saks M; Shparlinski I, 1999, 'Lower bound for primality', in Proceedings of the Annual IEEE Conference on Computational Complexity, pp. 10 - 14

Cai JY; Havas G; Mans B; Nerurkar A; Seifert JP; Shparlinski I, 1999, 'On routing in circulant graphs', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 360 - 369, http://dx.doi.org/10.1007/3-540-48686-0_36

Bernasconi A; Damm C; Shparlinski IE, 1999, 'On the average sensitivity of testing square-free numbers', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 291 - 299, http://dx.doi.org/10.1007/3-540-48686-0_29

Karpinski M; Shparlinski I, 1999, 'On the computational hardness of testing square-freeness of sparse polynomials', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 492 - 497, http://dx.doi.org/10.1007/3-540-46796-3_47

Griffin F; Niederreiter H; Shparlinski IE, 1999, 'On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 87 - 93, http://dx.doi.org/10.1007/3-540-46796-3_9

Griffin F; Shparlinski IE, 1999, 'On the linear complexity of the naor—reingold pseudo-random function', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 301 - 308, http://dx.doi.org/10.1007/978-3-540-47942-0_25

Mans B; Pappalardi F; Shparlinski I, 1998, 'On the ádám conjecture on circulant graphs', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 251 - 260, http://dx.doi.org/10.1007/3-540-68535-9_29

Gathen JVZ; Shparlinski I, 1998, 'The crew pram complexity of modular inversion', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 305 - 315

von zur Gathen J; Shparlinski I, 1995, 'Finding points on curves over finite fields extended abstract', in Annual Symposium on Foundations of Computer Science Proceedings, pp. 284 - 292

von zur Gathen J; Shparlinski I, 1995, 'Finding points on curves over finite fields', in 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, Institute of Electrical and Electronics Engineers (IEEE), pp. 284 - 292, presented at Proceedings of IEEE 36th Annual Foundations of Computer Science, http://dx.doi.org/10.1109/sfcs.1995.492484

von zur Gathen J; Shparlinski I, 1995, 'Orders of gauss periods in finite fields', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 208 - 215, http://dx.doi.org/10.1007/bfb0015425

van der Poorten AJ; Shparlinski I; Zimmer HG, 1995, 'Number Theoretic and Algebraic Methods in Computer Science', in Number Theoretic and Algebraic Methods in Computer Science, WORLD SCIENTIFIC, pp. 1 - 214, presented at International Conference on NTAMCS '93, http://dx.doi.org/10.1142/9789814532532

Von Zur Gathen J; Shparlinski I, 1994, 'Components and projections of curves over finite fields', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 297 - 305, http://dx.doi.org/10.1007/3-540-58325-4_193

Shparlinski IE, 1994, 'On some applications of finitely generated semi-groups', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 265 - 279, http://dx.doi.org/10.1007/3-540-58691-1_66

Von Zur Gathen J; Karpinski M; Shparlinski I, 1993, 'Counting curves and their projections', in Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 805 - 812, http://dx.doi.org/10.1145/167088.167292

Shparlinski IE, 1992, 'On Gaussian sums for finite fields and elliptic curves', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 5 - 15, http://dx.doi.org/10.1007/bfb0034335

STEPANOV SA; SHPARLINSKI IE, 1991, 'ON NORMAL BASES OF ALGEBRAIC NUMBER-FIELDS', in Schweiger F; Manstavicius E (ed.), NEW TRENDS IN PROBABILITY AND STATISTICS, VOL 2, VSP BV, LITHUANIA, PALANGA, pp. 369 - 378, presented at INTERNATIONAL CONF ON ANALYTIC AND PROBABILISTIC METHODS IN NUMBER THEORY, IN HONOUR OF JONAS KUBILIUS ON THE OCCASION OF HIS 70TH BIRTHDAY, LITHUANIA, PALANGA, 24 September 1991 - 28 September 1991, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992BY41L00033&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

SHPARLINSKI IE; TSFASMAN MA; VLADUT SG, 1991, 'CURVES WITH MANY POINTS AND MULTIPLICATION IN FINITE-FIELDS', in Stichtenoth H; Tsfasman MA (ed.), CODING THEORY AND ALGEBRAIC GEOMETRY, SPRINGER-VERLAG BERLIN, FRANCE, CTR INT RENCONTRES MATH, LUMINY, pp. 145 - 169, presented at WORKSHOP ON ALGEBRAIC GEOMETRY AND CODING THEORY - 3 ( AGCT-3 ), FRANCE, CTR INT RENCONTRES MATH, LUMINY, 17 June 1991 - 21 June 1991, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992BX67L00014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Stepanov SA; Shparlinskiy IE, 1987, 'On structure complexity of normal basis of finite field', in Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, pp. 414 - 416, http://dx.doi.org/10.1007/3-540-18740-5_90

Working Papers

Chen C; Shparlinski IE, 2021, Restricted Mean Value Theorems and the Metric Theory of Restricted Weyl Sums, http://dx.doi.org10.1093/qmath/haaa052

Chen C; Shparlinski IE, 2021, On a hybrid version of the Vinogradov mean value theorem, http://dx.doi.org10.1007/s10474-020-01111-9

Munsch M; Shparlinski IE, 2020, On smooth square-free numbers in arithmetic progressions, http://dx.doi.org10.1112/jlms.12297

Kerr B; Shparlinski IE; Yau KH, 2020, A refinement of the burgess bound for character sums, http://dx.doi.org10.1307/mmj/1573700737

Banks WD; Shparlinski IE, 2020, Sums with the Möbius function twisted by characters with powerful moduli, http://dx.doi.org10.1090/tran/7914

Dąbrowski A; Pomykała J; Shparlinski IE, 2019, On oracle factoring of integers, http://dx.doi.org, https://arxiv.org/abs/1912.00345v4

Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2017, On the new bound for the number of solutions of polynomial equations in subgroups and the structure of graphs of Markoff triples, http://dx.doi.org, https://arxiv.org/abs/1711.05335v2

Preprints

Shparlinski I; Sleiman N, 2026, Counting consecutive multiplicatively dependent triples, https://arxiv.org/abs/2609.29408v1

Klurman O; Shparlinski IE; Teräväinen J, 2026, On the generation of multiplicative groups by small primes, https://arxiv.org/abs/2609.25393v1

Shparlinski IE; Xiao Y, 2026, Arithmetic structure of $L_2$-norms of ${\mathrm{SL}}_2(\mathbb{Z})$ matrices, https://arxiv.org/abs/2609.21460v1

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