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ORCIDIgor E. Shparlinski
Person information
- affiliation: University of New South Wales, Sydney, School of Mathematics and Statistics, Australia
- affiliation: Macquarie University, Sydney, Department of Computing
- award (1996): Humboldt Prize
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2020 – today
- 2024
[j178]Siddharth Iyer
, Igor E. Shparlinski:
Character sums over elements of extensions of finite fields with restricted coordinates. Finite Fields Their Appl. 93: 102335 (2024)- [j177]Moubariz Z. Garaev, Igor E. Shparlinski:
On some congruences and exponential sums. Finite Fields Their Appl. 98: 102451 (2024) - [j176]Bryce Kerr, Ali Mohammadi, Igor E. Shparlinski:
Additive Energy of Polynomial Images. SIAM J. Discret. Math. 38(3): 2163-2180 (2024) - 2023
- [j175]Michael Kaminski, Igor E. Shparlinski, Michel Waldschmidt:
On sets of linear forms of maximal complexity. Comput. Complex. 32(1): 1 (2023) - [j174]Igor E. Shparlinski:
Fixed points of the subset sum pseudorandom number generators. Des. Codes Cryptogr. 91(7): 2473-2479 (2023) - [j173]Igor E. Shparlinski:
On the number of Diophantine m-tuples in finite fields. Finite Fields Their Appl. 90: 102241 (2023) - [j172]Andrzej Dabrowski, Jacek Pomykala, Igor E. Shparlinski:
On oracle factoring of integers. J. Complex. 76: 101741 (2023) - [j171]Bernard Mans, Min Sha, Igor E. Shparlinski, Daniel Sutantyo:
Functional graphs of families of quadratic polynomials. Math. Comput. 92(343): 2307-2331 (2023) - [j170]László Mérai, Igor E. Shparlinski:
Distribution of recursive matrix pseudorandom number generator modulo prime powers. Math. Comput. 93(347): 1355-1370 (2023) - [i46]Riley Baird, Bryce Kerr, Igor E. Shparlinski:
Bohr sets generated by polynomials and Coppersmith's method in many variables. CoRR abs/2310.20342 (2023) - 2022
- [j169]Christian Bagshaw, Igor E. Shparlinski:
Energy bounds, bilinear forms and their applications in function fields. Finite Fields Their Appl. 82: 102048 (2022) - [j168]Igor E. Shparlinski:
Multiplicative Properties of Hilbert Cubes. SIAM J. Discret. Math. 36(2): 1064-1070 (2022) - 2021
- [j167]Marek Karpinski, Igor E. Shparlinski:
Noisy polynomial interpolation modulo prime powers. J. Complex. 64: 101542 (2021) - [j166]Igor E. Shparlinski, Qiang Wang:
Exponential Sums with Sparse Polynomials over Finite Fields. SIAM J. Discret. Math. 35(2): 976-987 (2021) - [c64]Michael Kaminski, Igor E. Shparlinski:
Sets of Linear Forms Which Are Hard to Compute. MFCS 2021: 66:1-66:22 - [i45]Michael Kaminski, Igor E. Shparlinski, Michel Waldschmidt:
On sets of linear forms of maximal complexity. CoRR abs/2110.04657 (2021) - 2020
- [j165]Igor E. Shparlinski:
Geometric progressions in vector sumsets over finite fields. Finite Fields Their Appl. 68: 101747 (2020) - [j164]Domingo Gómez-Pérez, László Mérai, Igor E. Shparlinski:
On the complexity of exact counting of dynamically irreducible polynomials. J. Symb. Comput. 99: 231-241 (2020) - [j163]László Mérai, Igor E. Shparlinski:
Distribution of short subsequences of inversive congruential pseudorandom numbers modulo 2t. Math. Comput. 89(322): 911-922 (2020) - [j162]Simon Macourt, Giorgis Petridis, Ilya D. Shkredov, Igor E. Shparlinski:
Bounds of Trilinear and Trinomial Exponential Sums. SIAM J. Discret. Math. 34(4): 2124-2136 (2020) - [e3]Susanne C. Brenner, Igor E. Shparlinski, Chi-Wang Shu, Daniel B. Szyld:
75 Years of Mathematics of Computation. Contemporary Mathematics 754, American Mathematical Society 2020, ISBN 978-1-4704-5163-9 [contents] - [i44]Marek Karpinski, Igor E. Shparlinski:
Noisy polynomial interpolation modulo prime powers. CoRR abs/2006.05685 (2020)
2010 – 2019
- 2019
- [j161]Igor E. Shparlinski, Arne Winterhof:
Codes correcting restricted errors. Des. Codes Cryptogr. 87(4): 855-863 (2019) - [j160]Bernard Mans, Min Sha, Igor E. Shparlinski, Daniel Sutantyo:
On Functional Graphs of Quadratic Polynomials. Exp. Math. 28(3): 292-300 (2019) - [j159]Simon Macourt, Igor E. Shparlinski:
Double sums of Kloosterman sums in finite fields. Finite Fields Their Appl. 60 (2019) - [i43]Andrzej Dabrowski, Jacek Pomykala, Igor E. Shparlinski:
On oracle factoring of integers. CoRR abs/1912.00345 (2019) - 2018
- [j158]Gábor Ivanyos, Marek Karpinski, Miklos Santha, Nitin Saxena, Igor E. Shparlinski:
Polynomial Interpolation and Identity Testing from High Powers Over Finite Fields. Algorithmica 80(2): 560-575 (2018) - [j157]Domingo Gómez-Pérez, Igor E. Shparlinski:
Arithmetic Properties of Integers in Chains and Reflections of g-ary Expansions. Exp. Math. 27(2): 184-192 (2018) - [j156]Carl Pomerance, Igor E. Shparlinski:
Connected Components of the Graph Generated by Power Maps in Prime Finite Fields. Integers 18A: A16 (2018) - [j155]Marek Karpinski, László Mérai, Igor E. Shparlinski:
Identity testing and interpolation from high powers of polynomials of large degree over finite fields. J. Complex. 49: 74-84 (2018) - [j154]Igor E. Shparlinski:
On Constructing Primitive Roots in Finite Fields With Advice. IEEE Trans. Inf. Theory 64(11): 7132-7136 (2018) - [i42]Igor E. Shparlinski, Arne Winterhof:
Codes correcting restricted errors. CoRR abs/1811.03375 (2018) - 2017
- [j153]Igor E. Shparlinski, Andreas J. Weingartner:
An explicit polynomial analogue of Romanoff's theorem. Finite Fields Their Appl. 44: 22-33 (2017) - [j152]Jason P. Bell, Igor E. Shparlinski:
Power series approximations to Fekete polynomials. J. Approx. Theory 222: 132-142 (2017) - [i41]Domingo Gómez-Pérez, László Mérai, Igor E. Shparlinski:
On the Complexity of Exact Counting of Dynamically Irreducible Polynomials. CoRR abs/1706.04392 (2017) - [i40]Marek Karpinski, Igor E. Shparlinski:
Identity Testing from High Powers of Polynomials of Large Degree over Finite Fields. CoRR abs/1708.09095 (2017) - 2016
- [j151]Igor E. Shparlinski:
On small gaps between the elements of multiplicative subgroups of finite fields. Des. Codes Cryptogr. 80(1): 63-71 (2016) - [j150]Igor E. Shparlinski:
Ratios of Small Integers in Multiplicative Subgroups of Residue Rings. Exp. Math. 25(3): 273-280 (2016) - [j149]Randell Heyman, Igor E. Shparlinski:
Counting irreducible binomials over finite fields. Finite Fields Their Appl. 38: 1-12 (2016) - [j148]Igor E. Shparlinski:
On the additive energy of the distance set in finite fields. Finite Fields Their Appl. 42: 187-199 (2016) - [j147]Sergei V. Konyagin, Florian Luca, Bernard Mans, Luke Mathieson, Min Sha, Igor E. Shparlinski:
Functional graphs of polynomials over finite fields. J. Comb. Theory B 116: 87-122 (2016) - [j146]William D. Banks, Igor E. Shparlinski:
On Gauss sums and the evaluation of Stechkin's constant. Math. Comput. 85(301): 2569-2581 (2016) - [j145]Phong Q. Nguyen, Igor E. Shparlinski:
Counting Co-Cyclic Lattices. SIAM J. Discret. Math. 30(3): 1358-1370 (2016) - [c63]Andrew M. Childs, Wim van Dam, Shih-Han Hung, Igor E. Shparlinski:
Optimal Quantum Algorithm for Polynomial Interpolation. ICALP 2016: 16:1-16:13 - [i39]Igor E. Shparlinski:
Dominating Sets in Circulant Graphs. CoRR abs/1602.01286 (2016) - 2015
- [j144]Igor E. Shparlinski:
Close values of shifted modular inversions and the decisional modular inversion hidden number problem. Adv. Math. Commun. 9(2): 169-176 (2015) - [j143]Joachim von zur Gathen, Igor E. Shparlinski:
Circulant graphs and GCD and LCM of subsets. Inf. Process. Lett. 115(2): 134-138 (2015) - [j142]Igor E. Shparlinski, Andrew V. Sutherland:
On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average. LMS J. Comput. Math. 18(1): 308-322 (2015) - [j141]Jean Bourgain, Sergei V. Konyagin, Igor E. Shparlinski:
Character sums and deterministic polynomial root finding in finite fields. Math. Comput. 84(296): 2969-2977 (2015) - [j140]Igor E. Shparlinski:
Cayley Graphs Generated by Small Degree Polynomials over Finite Fields. SIAM J. Discret. Math. 29(1): 376-381 (2015) - [i38]Gábor Ivanyos, Marek Karpinski, Miklos Santha, Nitin Saxena, Igor E. Shparlinski:
Polynomial Interpolation and Identity Testing from High Powers over Finite Fields. CoRR abs/1502.06631 (2015) - [i37]Phong Q. Nguyen, Igor E. Shparlinski:
Counting Co-Cyclic Lattices. CoRR abs/1505.06429 (2015) - [i36]Andrew M. Childs, Wim van Dam, Shih-Han Hung, Igor E. Shparlinski:
Optimal quantum algorithm for polynomial interpolation. CoRR abs/1509.09271 (2015) - [i35]Oscar García Morchon, Ronald Rietman, Igor E. Shparlinski, Ludo Tolhuizen:
Results on polynomial interpolation with mixed modular operations and unknown moduli. IACR Cryptol. ePrint Arch. 2015: 1003 (2015) - 2014
- [j139]Ian F. Blake, Florian Luca, Igor E. Shparlinski:
VSH and multiplicative modular relations between small primes with polynomial exponents. Appl. Algebra Eng. Commun. Comput. 25(3): 181-188 (2014) - [j138]Bernard Mans, Igor E. Shparlinski:
Random Walks, Bisections and Gossiping in Circulant Graphs. Algorithmica 70(2): 301-325 (2014) - [j137]Oscar García Morchon, Ronald Rietman, Igor E. Shparlinski, Ludo Tolhuizen:
Interpolation and Approximation of Polynomials in Finite Fields over a Short Interval from Noisy Values. Exp. Math. 23(3): 241-260 (2014) - [j136]Igor E. Shparlinski, Andrew V. Sutherland:
On the Distribution of Atkin and Elkies Primes. Found. Comput. Math. 14(2): 285-297 (2014) - [j135]Igor E. Shparlinski:
Products with variables from low-dimensional affine spaces and shifted power identity testing in finite fields. J. Symb. Comput. 64: 35-41 (2014) - [j134]Domingo Gómez-Pérez, Alina Ostafe, Igor E. Shparlinski:
Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators. Math. Comput. 83(287): 1535-1550 (2014) - [j133]San Ling, Igor E. Shparlinski, Huaxiong Wang:
On the Multidimensional Distribution of the Naor-Reingold Pseudo-Random Function. Math. Comput. 83(289): 2429-2434 (2014) - [j132]Randell Heyman, Igor E. Shparlinski:
On shifted Eisenstein polynomials. Period. Math. Hung. 69(2): 170-181 (2014) - [j131]Igor E. Shparlinski:
Evasive properties of sparse graphs and some linear equations in primes. Theor. Comput. Sci. 547: 117-121 (2014) - [j130]Zhixiong Chen, Igor E. Shparlinski, Arne Winterhof:
Covering Sets for Limited-Magnitude Errors. IEEE Trans. Inf. Theory 60(9): 5315-5321 (2014) - [p4]Jonas Kaszian, Pieter Moree, Igor E. Shparlinski:
Periodic structure of the exponential pseudorandom number generator. Applied Algebra and Number Theory 2014: 190-203 - [i34]Oscar García Morchon, Ronald Rietman, Igor E. Shparlinski, Ludo Tolhuizen:
Interpolation and Approximation of Polynomials in Finite Fields over a Short Interval from Noisy Values. CoRR abs/1401.1331 (2014) - [i33]Joachim von zur Gathen, Igor E. Shparlinski:
Circulant graphs and GCD and LCM of Subsets. CoRR abs/1402.5449 (2014) - 2013
- [j129]Randell Heyman, Igor E. Shparlinski:
On the number of Eisenstein polynomials of bounded height. Appl. Algebra Eng. Commun. Comput. 24(2): 149-156 (2013) - [j128]Jaime Gutierrez, Álvar Ibeas, Domingo Gómez-Pérez, Igor E. Shparlinski:
Predicting masked linear pseudorandom number generators over finite fields. Des. Codes Cryptogr. 67(3): 395-402 (2013) - [j127]David Harvey, Igor E. Shparlinski:
Statistics of Different Reduction Types of Fermat Curves. Exp. Math. 22(3): 243-249 (2013) - [j126]Igor E. Shparlinski, Arne Winterhof:
Distribution of values of polynomial Fermat quotients. Finite Fields Their Appl. 19(1): 93-104 (2013) - [j125]Igor E. Shparlinski:
Correcting noisy exponentiation black-boxes modulo a prime. Inf. Process. Lett. 113(12): 414-417 (2013) - [j124]Joachim von zur Gathen, Igor E. Shparlinski:
Generating safe primes. J. Math. Cryptol. 7(4): 333-365 (2013) - [j123]Reza Rezaeian Farashahi, Pierre-Alain Fouque, Igor E. Shparlinski, Mehdi Tibouchi, José Felipe Voloch:
Indifferentiable deterministic hashing to elliptic and hyperelliptic curves. Math. Comput. 82(281): 491-512 (2013) - [j122]Igor E. Shparlinski:
On products of primes and almost primes in arithmetic progressions. Period. Math. Hung. 67(1): 55-61 (2013) - [j121]Igor E. Shparlinski:
Additive Decompositions of Subgroups of Finite Fields. SIAM J. Discret. Math. 27(4): 1870-1879 (2013) - [p3]Igor E. Shparlinski:
Algebraic dynamical systems over finite fields. Handbook of Finite Fields 2013: 337-344 - [p2]Igor E. Shparlinski:
Additive Combinatorics over Finite Fields: New Results and Applications. Finite Fields and Their Applications 2013: 233-272 - [e2]Jonathan M. Borwein, Igor E. Shparlinski, Wadim Zudilin:
Number Theory and Related Fields, In Memory of Alf van der Poorten. Springer 2013, ISBN 978-1-4614-6641-3 [contents] - [i32]Igor E. Shparlinski:
On the Product of Small Elkies Primes. CoRR abs/1301.0035 (2013) - [i31]Igor E. Shparlinski:
Evasive Properties of Sparse Graphs and Some Linear Equations in Primes. CoRR abs/1304.0188 (2013) - [i30]Sergei Konyagin, Florian Luca, Bernard Mans, Luke Mathieson, Igor E. Shparlinski:
Functional Graphs of Polynomials over Finite Fields. CoRR abs/1307.2718 (2013) - [i29]Jean Bourgain, Sergei Konyagin, Igor E. Shparlinski:
Character Sums and Deterministic Polynomial Root Finding in Finite Fields. CoRR abs/1308.4803 (2013) - [i28]Zhixiong Chen, Igor E. Shparlinski, Arne Winterhof:
Covering sets for limited-magnitude errors. CoRR abs/1310.0120 (2013) - [i27]Jonas Kaszian, Pieter Moree, Igor E. Shparlinski:
Periodic Structure of the Exponential Pseudorandom Number Generator. CoRR abs/1312.1311 (2013) - 2012
- [j120]Reza Rezaeian Farashahi, Igor E. Shparlinski:
On Group Structures Realized by Elliptic Curves over a Fixed Finite Field. Exp. Math. 21(1): 1-10 (2012) - [j119]William D. Banks, Francesco Pappalardi, Igor E. Shparlinski:
On Group Structures Realized by Elliptic Curves over Arbitrary Finite Fields. Exp. Math. 21(1): 11-25 (2012) - [j118]Antal Balog, Kevin A. Broughan, Igor E. Shparlinski:
Sum-Products Estimates with Several Sets and Applications. Integers 12: A27 (2012) - [j117]Alina Ostafe, Igor E. Shparlinski:
On the power generator and its multivariate analogue. J. Complex. 28(2): 238-249 (2012) - [j116]San Ling, Igor E. Shparlinski, Ron Steinfeld, Huaxiong Wang:
On the modular inversion hidden number problem. J. Symb. Comput. 47(4): 358-367 (2012) - [j115]Jorge Jiménez Urroz, Florian Luca, Igor E. Shparlinski:
On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves. Math. Comput. 81(278): 1093-1110 (2012) - [j114]Alina Ostafe, Igor E. Shparlinski:
Multiplicative character sums and products of sparse integers in residue classes. Period. Math. Hung. 64(2): 247-255 (2012) - [j113]Jean Bourgain, Moubariz Z. Garaev, Sergei Konyagin, Igor E. Shparlinski:
On the Hidden Shifted Power Problem. SIAM J. Comput. 41(6): 1524-1557 (2012) - [j112]Reza Rezaeian Farashahi, Igor E. Shparlinski:
Pseudorandom Bits From Points on Elliptic Curves. IEEE Trans. Inf. Theory 58(2): 1242-1247 (2012) - [c62]Bernard Mans, Igor E. Shparlinski:
Random Walks and Bisections in Random Circulant Graphs. LATIN 2012: 542-555 - 2011
- [j111]Igor E. Shparlinski:
On the average distribution of pseudorandom numbers generated by nonlinear permutations. Math. Comput. 80(274): 1053-1061 (2011) - [j110]Alina Ostafe, Igor E. Shparlinski:
Pseudorandomness and Dynamics of Fermat Quotients. SIAM J. Discret. Math. 25(1): 50-71 (2011) - [r2]Igor E. Shparlinski:
Computational Diffie-Hellman Problem. Encyclopedia of Cryptography and Security (2nd Ed.) 2011: 240-244 - [i26]Simon R. Blackburn, Alina Ostafe, Igor E. Shparlinski:
On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves. CoRR abs/1102.1053 (2011) - [i25]Jean Bourgain, Sergei Konyagin, Igor E. Shparlinski:
On the Hidden Shifted Power Problem. CoRR abs/1110.0812 (2011) - [i24]Simon R. Blackburn, Alina Ostafe, Igor E. Shparlinski:
On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves. IACR Cryptol. ePrint Arch. 2011: 67 (2011) - 2010
- [j109]Alina Ostafe, Igor E. Shparlinski, Arne Winterhof:
On the generalized joint linear complexity profile of a class of nonlinear pseudorandom multisequences. Adv. Math. Commun. 4(3): 369-379 (2010) - [j108]Alina Ostafe, Igor E. Shparlinski:
Pseudorandom numbers and hash functions from iterations of multivariate polynomials. Cryptogr. Commun. 2(1): 49-67 (2010) - [j107]Reza Rezaeian Farashahi, Igor E. Shparlinski:
On the number of distinct elliptic curves in some families. Des. Codes Cryptogr. 54(1): 83-99 (2010) - [j106]Lev Glebsky, Igor E. Shparlinski:
Short cycles in repeated exponentiation modulo a prime. Des. Codes Cryptogr. 56(1): 35-42 (2010) - [j105]Alina Ostafe, Elena Pelican, Igor E. Shparlinski:
On pseudorandom numbers from multivariate polynomial systems. Finite Fields Their Appl. 16(5): 320-328 (2010) - [j104]Kevin A. Broughan, Florian Luca, Igor E. Shparlinski:
Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem. Integers 10: A41 (2010) - [j103]Koray Karabina, Alfred Menezes, Carl Pomerance, Igor E. Shparlinski:
On the asymptotic effectiveness of Weil descent attacks. J. Math. Cryptol. 4(2): 175-191 (2010) - [j102]Joachim von zur Gathen, Maurice Mignotte, Igor E. Shparlinski:
Approximate polynomial GCD: Small degree and small height perturbations. J. Symb. Comput. 45(8): 879-886 (2010) - [j101]Alina Ostafe, Igor E. Shparlinski:
On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators. Math. Comput. 79(269): 501-511 (2010) - [j100]Igor E. Shparlinski:
On the Distribution of Orbits of PGL2(q) in Fqn and the Klapper Conjecture. SIAM J. Discret. Math. 23(4): 2093-2099 (2010) - [i23]Reza Rezaeian Farashahi, Igor E. Shparlinski:
Pseudorandom Bits From Points on Elliptic Curves. CoRR abs/1005.4771 (2010) - [i22]Reza Rezaeian Farashahi, Pierre-Alain Fouque, Igor E. Shparlinski, Mehdi Tibouchi, José Felipe Voloch:
Indifferentiable Deterministic Hashing to Elliptic and Hyperelliptic Curves. IACR Cryptol. ePrint Arch. 2010: 539 (2010) - [i21]Neal Koblitz, Alfred Menezes, Igor E. Shparlinski:
Discrete Logarithms, Diffie-Hellman, and Reductions. IACR Cryptol. ePrint Arch. 2010: 577 (2010)
2000 – 2009
- 2009
- [j99]Nicholas M. Katz, Igor E. Shparlinski, Maosheng Xiong:
On character sums with distances on the upper half plane over a finite field. Finite Fields Their Appl. 15(6): 738-747 (2009) - [j98]Alina Carmen Cojocaru, Igor E. Shparlinski:
On the embedding degree of reductions of an elliptic curve. Inf. Process. Lett. 109(13): 652-654 (2009) - [j97]Joachim von zur Gathen, Igor E. Shparlinski:
Subset sum pseudorandom numbers: fast generation and distribution. J. Math. Cryptol. 3(2): 149-163 (2009) - [j96]John B. Friedlander, Igor E. Shparlinski:
On the density of some special primes. J. Math. Cryptol. 3(3): 265-271 (2009) - [j95]Reza Rezaeian Farashahi, Igor E. Shparlinski, José Felipe Voloch:
On hashing into elliptic curves. J. Math. Cryptol. 3(4): 353-360 (2009) - [j94]Igor E. Shparlinski:
On the values of Kloosterman sums. IEEE Trans. Inf. Theory 55(6): 2599-2601 (2009)