I. Shparlinski

发表

Distribution of inverses in polynomial rings

W. Banks, I. Shparlinski, 2001 .

Cryptographic Applications of Analytic Number Theory

I. Shparlinski, 2003 .

GROUP STRUCTURE OF ELLIPTIC CURVES OVER FINITE FIELDS AND APPLICATIONS

M. Murty, I. Shparlinski, Ram Murty, 2006 .

GENERATORS OF ELLIPTIC CURVES OVER FINITE FIELDS

I. Shparlinski, J. Voloch, 2011 .

On irreducible divisors of iterated polynomials

I. Shparlinski, Domingo Gómez-Pérez, Alina Ostafe, 2014 .

The Equivalence of Strong RSA and Factoring in the Generic Ring Model of Computation

U. Maurer, I. Shparlinski, Divesh Aggarwal, 2011 .

On two functions arising in the study of the Euler and Carmichael quotients

F. Luca, I. Shparlinski, Min Sha, 2017, 1705.00388.

Exponential Sums over Points of Elliptic Curves

I. Shparlinski, O. Ahmadi, 2013, 1302.4210.

The Equivalence of Strong RSA and Factoring in the Generic Ring Model of Computation

U. Maurer, I. Shparlinski, Divesh Aggarwal, 2011 .

Character Sums with Exponential Functions and their Applications: Introduction

I. Shparlinski, S. Konyagin, 1999 .

Double Character Sums with Intervals and Arbitrary Sets

I. Shparlinski, I. Shkredov, 2018, Proceedings of the Steklov Institute of Mathematics.

On the statistical properties of Diffie-Hellman distributions

R. Canetti, I. Shparlinski, S. Konyagin, 2000 .

On Fully Split Lacunary Polynomials in Finite Fields

I. Shparlinski, Khodakhast Bibak, 2011, 1111.4023.

Exponential Sums and Lattice Reduction: Applications to Cryptography

I. Shparlinski, 2002 .

Character Sums with Exponential Functions and their Applications: Multiplicative Translations of Arbitrary Sets Modulo p

I. Shparlinski, S. Konyagin, 1999 .

Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients

I. Shparlinski, G. Harman, 2014, 1408.4515.

On solutions to some polynomial congruences in small boxes

I. Shparlinski, 2013, 1301.1758.

On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states

A. Klappenecker, M. Roetteler, I. Shparlinski, 2005, quant-ph/0503239.

On the Number of Sparse RSA Exponents

W. Banks, I. Shparlinski, 2002 .

Distribution of Modular Sums and the Security of the Server Aided Exponentiation

Phong Q. Nguyen, J. Stern, I. Shparlinski, 2001 .

Curves with many points and multiplication in finite fileds

I. Shparlinski, M. Tsfasman, S. Vladut, 1992 .

Certain Exponential Sums and Random Walks on Elliptic Curves

T. Lange, I. Shparlinski, 2005, Canadian Journal of Mathematics.

A Nonuniform Algorithm for the Hidden Number Problem in Subgroups

Igor E. Shparlinski, Arne Winterhof, I. Shparlinski, 2004, Public Key Cryptography.

ON THE DISTRIBUTION OF ATKIN AND ELKIES PRIMES FOR REDUCTIONS OF ELLIPTIC CURVES ON AVERAGE

Igor E. Shparlinski, Andrew V. Sutherland, I. Shparlinski, 2015 .

Isomorphism classes of elliptic curves over a finite field in some thin families

Igor E. Shparlinski, Javier Cilleruelo, Ana Zumalacárregui, 2012 .

Distribution of modular inverses and multiples of small integers and the Sato-Tate conjecture on average

I. Shparlinski, I. E. Shparlinski, 2006, math/0608596.

Average normalisations of elliptic curves

Igor E. Shparlinski, William D. Banks, W. Banks, 2002, Bulletin of the Australian Mathematical Society.

Disjointness of the Möbius Transformation and Möbius Function

I. Shparlinski, E. H. EL ABDALAOUI, E. H. el Abdalaoui, 2017, Research in the Mathematical Sciences.

On the dynamical system generated by the Möbius transformation at prime times

I. Shparlinski, L'aszl'o M'erai, 2020, 2009.01089.

Character sums with exponential functions

Igor E. Shparlinski, John B. Friedlander, I. Shparlinski, 2000 .

Exponential sums over Mersenne numbers

W. Banks, I. Shparlinski, J. Friedlander, 2004, Compositio Mathematica.

The large sieve inequality with exponential functions and the distribution of Mersenne numbers modulo primes

I. Shparlinski, M. Garaev, 2005 .

Double character sums over elliptic curves and finite fields

W. Banks, I. Shparlinski, J. Friedlander, 2006 .

EXPONENTIAL SUMS OVER POINTS OF ELLIPTIC CURVES WITH RECIPROCALS OF PRIMES

I. Shparlinski, Alina Ostafe, 2012 .

Number Theory Elementary Number Theory

Jonathan M. Borwein, Igor E. Shparlinski, David H. Bailey, 2016 .

Multiplicative congruences with variables from short intervals

Igor E. Shparlinski, Jean Bourgain, J. Bourgain, 2012, Journal d'Analyse Mathematique.

Character Sums with Exponential Functions and their Applications: Preliminaries

I. Shparlinski, S. Konyagin, 1999 .

Classical and Quantum Polynomial Reconstruction via Legendre Symbol Evaluation

Alexander Russell, Igor Shparlinski, A. Russell, 2002 .

On the largest prime factor of the mersenne numbers

Igor E. Shparlinski, Florian Luca, Kevin Ford, 2007, 0704.1327.

On the largest prime factor of n! + 2 n 1

F. Luca, I. Shparlinski, 2005 .

On some dynamical systems in finite fields and residue rings

Igor E. Shparlinski, I. Shparlinski, 2006, math/0607779.

Character Sums with Exponential Functions and their Applications: Bounds of Short Character Sums

Igor E. Shparlinski, Sergei Konyagin, I. Shparlinski, 1999 .

Bounds of Gauss sums in finite fields

I. Shparlinski, 2004 .

Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions

Igor E. Shparlinski, Bryce Kerr, I. Shparlinski, 2018, Research in Number Theory.

Bilinear Forms with Kloosterman and Gauss Sums

I. Shparlinski, 2016, 1608.06160.

On Certain Exponential Sums and the Distribution of Diffie–Hellman Triples

Igor E. Shparlinski, Ran Canetti, John B. Friedlander, 1999 .

Bilinear forms in Weyl sums for modular square roots and applications

I. Shparlinski, A. Zaharescu, Alexander Dunn, 2019, Advances in Mathematics.

Research Article Distribution of Roots of Polynomial Congruences

I. Shparlinski, 2007 .

On the distribution of rational functions along a curve over Fp and residue races

I. Shparlinski, A. Granville, A. Zaharescu, 2005 .

Incomplete character sums and a special class of permutations

Igor E. Shparlinski, Harald Niederreiter, Stephen D. Cohen, 2001 .

The Sato-Tate distribution in thin families of elliptic curves over high degree extensions of finite fields

I. Shparlinski, 2019, International Journal of Number Theory.

On the Distribution of the Number of Points on Elliptic Curves in a Tower of Extensions of Finite Fields

I. Shparlinski, O. Ahmadi, 2009 .

On distances in lattices from algebraic number fields

I. Shparlinski, Min Sha, A. Dubickas, 2017, 1703.02163.

Bounds on bilinear forms with Kloosterman sums

I. Shparlinski, Xiaosheng Wu, Bryce Kerr, 2022, 2204.05038.

Finding elliptic curves with a prescribed subgroup and rational functions with small image over finite fields

Andrew V. Sutherland, I. Shparlinski, 2014 .

Products in residue classes

I. Shparlinski, P. Kurlberg, J. Friedlander, 2007, 0708.1562.

Irrationality of Power Series for Various Number

F. Luca, W. Banks, I. Shparlinski, 2005 .

SOME SPECIAL CHARACTER SUMS OVER ELLIPTIC CURVES

I. Shparlinski, 2009 .

Mathematisches Forschungsinstitut Oberwolfach Report No . 54 / 2004 Finite Fields : Theory and Applications

I. Shparlinski, 2004 .

Cyclotomic coefficients: gaps and jumps

F. Luca, I. Shparlinski, Oana-Maria Camburu, 2015, 1507.07098.

On the size of the Jacobians of curves over finite fields

I. Shparlinski, 2008 .

Character sums and congruences with n

F. Luca, I. Shparlinski, M. Garaev, 2004, math/0403422.

Distribution of exponential functions with k-full exponent modulo a prime

I. Shparlinski, D. Panario, Michael Dewar, 2004 .

Computational and Algorithmic Problems in Finite Fields

Igor E. Shparlinski, I. Shparlinski, 1992 .

Incomplete exponential sums and Diffie–Hellman triples

W. Banks, I. Shparlinski, S. Konyagin, 2006, Mathematical Proceedings of the Cambridge Philosophical Society.

Congruences with intervals and subgroups modulo a prime

I. Shparlinski, Marc Munsch, 2014, 1412.0440.

Gauß Periods in Finite Fields

J. Gathen, I. Shparlinski, 2001 .

Eecient Approximation Algorithms for Sparse Polynomials over Finite Fields

I. Shparlinski, FieldsMarek Karpinski, 1994 .

On the concentration of points on modular hyperbolas and exponential curves

I. Shparlinski, T. Chan, 2010 .

Bilinear Exponential Sums and Sum-Product Problems on Elliptic Curves

I. Shparlinski, O. Ahmadi, 2008 .

On the Sum-Product Problem on Elliptic Curves

I. Shparlinski, O. Ahmadi, 2008, 0806.0640.

On the exponential sum—product problem

I. Shparlinski, 2008 .

Open problems on exponential and character sums

I. Shparlinski, 2009 .

On the distribution of the Euler function of shifted smooth numbers

Igor E. Shparlinski, I. Shparlinski, Stefanie S. Loiperdinger, 2008, 0810.1093.

On the Structure of Graphs of Markoff Triples

I. Shparlinski, S. Konyagin, I. Vyugin, 2020 .

On the new bound for the number of solutions of polynomial equations in subgroups and the structure of graphs of Markoff triples

I. Shparlinski, S. Konyagin, I. Vyugin, 2017, 1711.05335.

On large values of Weyl sums

I. Shparlinski, Chang-Pao Chen, 2019, Advances in Mathematics.

POWERFUL NUMBERS IN SHORT INTERVALS

F. Luca, I. Shparlinski, J. D. Koninck, 2005 .

On Reducing a System of Equations to a Single Equation

Igor E. Shparlinski, Gudmund Skovbjerg Frandsen, I. Shparlinski, 2004 .

Bounds on short character sums and L-functions with characters to a powerful modulus

W. Banks, I. Shparlinski, 2019, Journal d'Analyse Mathématique.

Multiplicative character sums with the sum of g-ary Digits Function

W. Banks, I. Shparlinski, 2006 .

Open problems and conjectures in finite fields

Igor E. Shparlinski, Gary L. Mullen, G. Mullen, 1996 .

On the density of integer points on generalised Markoff–Hurwitz and Dwork hypersurfaces

I. Shparlinski, Mei-Chu Chang, 2014, 1404.5866.

ON THE DISTRIBUTION OF POINTS ON THE GENERALIZED MARKOFF–HURWITZ AND DWORK HYPERSURFACES

I. Shparlinski, 2014 .

Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields

I. Shparlinski, I. Shkredov, Simon Macourt, 2017, Canadian Journal of Mathematics.

N T ] 2 9 O ct 2 02 0 NOISY POLYNOMIAL INTERPOLATION MODULO PRIME POWERS

M. Karpinski, I. Shparlinski, Marek Karpinski, 2020 .

Sets with integral distances in finite fields

I. Shparlinski, Maosheng Xiong, A. Iosevich, 2009 .

On the number of distances between the coordinates of points on modular hyperbolas

I. Shparlinski, Arne Winterhof, 2008 .

Distribution of short subsequences of inversive congruential pseudorandom number generator

I. Shparlinski, L. Mérai, 2018, 1812.08837.

On Bilinear Exponential and Character Sums with Reciprocals of Polynomials

I. Shparlinski, 2015, 1504.03192.

Double character sums over subgroups and intervals

I. Shparlinski, Mei-Chu Chang, 2014, 1401.6611.

On the size of the Gelfond exponent

I. Shparlinski, 2010 .

On the distribution of arguments of Gauss sums

I. Shparlinski, 2009 .

Exponential Function Analogue of Kloosterman Sums

I. Shparlinski, 2004 .

On the Distribution of the Diffie-Hellman Pairs

I. Shparlinski, 2002 .

ON FINDING SOLUTIONS TO EXPONENTIAL CONGRUENCES

I. Shparlinski, 2018, Bulletin of the Australian Mathematical Society.

Some doubly exponential sums over Z

I. Shparlinski, S. Konyagin, J. Friedlander, 2022 .

Discrete Logarithms, Diffie-Hellman, and Reductions

Igor E. Shparlinski, Alfred Menezes, Neal Koblitz, 2010, IACR Cryptol. ePrint Arch..

Pseudorandom number generators from elliptic curves

Igor E. Shparlinski, I. Shparlinski, 2009 .

On the Average Sensitivity of Testing Square-Free Numbers

Igor E. Shparlinski, Carsten Damm, Anna Bernasconi, 1999, COCOON.

On the Complexity of Some Arithmetic Problems over IF 2 [ T ]

E. Allender, M. Saks, I. Shparlinski, 2022 .

On Gaussian Sums for Finite Fields and Elliptic Curves

Igor E. Shparlinski, I. Shparlinski, 1991, Algebraic Coding.

On bounds of Gaussian sums

I. Shparlinski, 1991 .

On the Linear Complexity of the Naor-Reingold Pseudo-Random Function

Igor E. Shparlinski, Frances Griffin, I. Shparlinski, 1999, ICICS.

On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators

Igor E. Shparlinski, Alina Ostafe, I. Shparlinski, 2009, Math. Comput..

Reductions Modulo Primes of Systems of Polynomial Equations and Algebraic Dynamical Systems

C. D'Andrea, I. Shparlinski, Alina Ostafe, 2015, 1505.05814.

Modular Reduction of Systems of Polynomial Equations and Algebraic Dynamical Systems

C. D'Andrea, I. Shparlinski, Alina Ostafe, 2015 .

On Group Structures Realized by Elliptic Curves over Arbitrary Finite Fields

Igor E. Shparlinski, Francesco Pappalardi, William D. Banks, 2010, Exp. Math..

Recurrence Sequences

Igor E. Shparlinski, Alfred J. van der Poorten, Graham Everest, 2003, Mathematical surveys and monographs.

On the Convex Closure of the Graph of Modular Inversions

Igor E. Shparlinski, Mizan R. Khan, Christian L. Yankov, 2007, Exp. Math..

On the Convex Hull of the Points on Modular Hyperbolas

I. Shparlinski, S. Konyagin, 2010, 1012.1444.

On the maximal difference between an element and its inverse in residue rings

Christian L. Yankov, I. Shparlinski, K. Ford, 2005 .

Non-approximability of the Permanent of Structured Matrices over Finite Fields

Igor E. Shparlinski, Bruno Codenotti, B. Codenotti, 2002, Electron. Colloquium Comput. Complex..

Linear complexity of the Naor-Reingold pseudo-random function

Igor E. Shparlinski, I. Shparlinski, 2000, Inf. Process. Lett..

On the Linear Complexity of the Naor-Reingold Pseudo-Random Number Generator

I. Shparlinski, F. Griffin, 1999 .

On some applications of finitely generated semi-groups

Igor E. Shparlinski, I. Shparlinski, 1994, ANTS.

On sparsity of representations of polynomials as linear combinations of exponential functions

Igor E. Shparlinski, Alina Ostafe, Dragos Ghioca, 2021, Journal of the London Mathematical Society.

On quadratic fields generated by the Shanks sequence

F. Luca, I. Shparlinski, 2009, Proceedings of the Edinburgh Mathematical Society.

A SPARSITY RESULT FOR THE DYNAMICAL MORDELL–LANG CONJECTURE IN POSITIVE CHARACTERISTIC

I. Shparlinski, Alina Ostafe, D. Ghioca, 2021, Bulletin of the Australian Mathematical Society.

On Coincidences Among Quadratic Fields Generated by the Shanks Sequence

W. Banks, I. Shparlinski, 2016 .

Exponential Sums with Sparse Polynomials over Finite Fields

Igor E. Shparlinski, Qiang Wang, I. Shparlinski, 2020, SIAM J. Discret. Math..

Bounds on bilinear sums of Kloosterman sums

Igor E. Shparlinski, Nilanjan Bag, I. Shparlinski, 2021, 2111.07311.

Congruences with intervals and arbitrary sets

W. Banks, I. Shparlinski, 2019, Archiv der Mathematik.

Bounds of some double exponential sums

Igor E. Shparlinski, Nilanjan Bag, I. Shparlinski, 2021 .

DISTRIBUTION OF POINTS ON MODULAR HYPERBOLAS

Igor E. Shparlinski, I. Shparlinski, 2007 .

Close values of shifted modular inversions and the decisional modular inversion hidden number problem

Igor E. Shparlinski, I. Shparlinski, 2015, Adv. Math. Commun..

On the Lower Bound of the Linear Complexity Over of

Igor E. Shparlinski, Arne Winterhof, Florian Luca, 2006 .

On squares in polynomial products

F. Luca, I. Shparlinski, J. Cilleruelo, 2010 .

On the set of distances between two sets over finite fields

Igor E. Shparlinski, I. Shparlinski, 2006, Int. J. Math. Math. Sci..

Approximate constructions in finite fields

Igor E. Shparlinski, I. Shparlinski, 1996 .

Elements of large order on varieties over prime finite fields

I. Shparlinski, Mei-Chu Chang, U. Zannier, 2014 .

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface

Hsinchun Chen, Daniel Zeng, David Madigan, 2007, KDD 2013.

On Some Characteristics of Uniformity of Distribution and Their Applications

Igor E. Shparlinski, I. Shparlinski, 1995 .

Number Theoretic Methods in Cryptography

Igor E. Shparlinski, I. Shparlinski, 1999 .

Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields

I. Shparlinski, L'aszl'o M'erai, 2018, Acta Arithmetica.

C C ] 1 M ar 2 01 8 IDENTITY TESTING AND INTERPOLATION FROM HIGH POWERS OF POLYNOMIALS OF LARGE DEGREE OVER FINITE FIELDS

M. Karpinski, I. Shparlinski, L. Mérai, 2018 .

Points on curves in small boxes en applications

I. Shparlinski, Mei-Chu Chang, J. Cilleruelo, 2011, 1111.1543.

On the Distribution of Power Residues and Primitive Elements in Some Nonlinear Recurring Sequences

Igor E. Shparlinski, Harald Niederreiter, H. Niederreiter, 2003 .

Unlikely intersections over finite fields: Polynomial orbits in small subgroups

I. Shparlinski, L'aszl'o M'erai, 2019, Discrete & Continuous Dynamical Systems - A.

Groups generated by iterations of polynomials over finite fields

I. Shparlinski, 2015, Proceedings of the Edinburgh Mathematical Society.

Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus

Igor E. Shparlinski, Harald Niederreiter, H. Niederreiter, 2000 .

Noisy Chinese remaindering in the Lee norm

Igor E. Shparlinski, Ron Steinfeld, Ron Steinfeld, 2004, J. Complex..

An effective local--global principle for algebraic varieties and the sum product problem in finite fields

I. Shparlinski, Bryce Kerr, Jorge Mello, 2020, 2005.02923.

Congruences and Exponential Sums with the Euler Function

W. Banks, I. Shparlinski, 2004 .

Divisor problem in arithmetic progressions modulo a prime power

I. Shparlinski, Kui Liu, Tianping Zhang, 2016, 1602.03583.

Orders of points in families of elliptic curves

I. Shparlinski, 2020 .

Pseudolinearly Dependent Points on Elliptic Curves

I. Shparlinski, Min Sha, M. Sha, 2014 .

Effective results on linear dependence for elliptic curves

I. Shparlinski, Min Sha, M. Sha, 2014, 1410.1596.

Finding Points on Curves over Nite Elds Extended Abstract

J. Gathen, I. Shparlinski, 2007 .

Efficient Arithmetic in Finite Fields of Small Odd Characteristic with applications in elliptic curve cryptography

I. Shparlinski, 2004 .

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface

Stefan Katzenbeisser, L. Jean Camp, Michael K. Reiter, 2007, Knowledge Discovery and Data Mining.

COUNTING INTEGERS WITH A SMOOTH TOTIENT

C. Pomerance, W. Banks, I. Shparlinski, 2018, The Quarterly Journal of Mathematics.

Smooth values of shifted primes in arithmetic progressions

W. Banks, I. Shparlinski, A. Harcharras, 2004 .

Complexity of inverting the Euler function

I. Shparlinski, S. Contini, Ernie Croot, 2004, Math. Comput..

Functional graphs of families of quadratic polynomials

I. Shparlinski, B. Mans, Min Sha, 2022, 2208.01885.

Classical and Quantum Polynomial Reconstruction via Legendre Symbol Evaluation

A. Russell, I. Shparlinski, 2002, quant-ph/0212016.

On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states

A. Klappenecker, M. Roetteler, I. Shparlinski, 2005, quant-ph/0503239.

Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height

W. Banks, I. Shparlinski, 2006, math/0609144.

On the Distribution of Kloosterman Sums

I. Shparlinski, 2006, math/0608595.

Exponential sums with polynomial values of the discrete logarithm

W. Banks, I. Shparlinski, 2007 .

On some exponential sums with exponential and rational functions

I. Shparlinski, 2013 .

On the singularity of the Demjanenko matrix of quotients of Fermat curves

I. Shparlinski, F. Fité, 2014, 1404.5178.

Finding elliptic curves with a subgroup of prescribed size

Andrew V. Sutherland, I. Shparlinski, 2014, 1403.7887.

Finding the group structure of elliptic curves over finite fields

C. Pomerance, I. Shparlinski, J. Friedlander, 2005, Bulletin of the Australian Mathematical Society.

Frobenius Distributions: Lang-Trotter and Sato-Tate Conjectures

I. Shparlinski, D. Kohel, 2016 .

Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups

J. Silverman, I. Shparlinski, Alina Ostafe, 2018, International Mathematics Research Notices.

Orbits of polynomial dynamical systems modulo primes

C. D'Andrea, I. Shparlinski, Alina Ostafe, 2017, 1702.01976.

ORBITS LENGTHS OF MODULAR REDUCTIONS OF PAIRS OF POLYNOMIAL DYNAMICAL SYSTEMS

C. D'Andrea, I. Shparlinski, Alina Ostafe, 2016 .

MULTIPLICATIVE ORDERS IN ORBITS OF POLYNOMIALS OVER FINITE FIELDS

I. Shparlinski, 2017, Glasgow Mathematical Journal.

LOWER BOUNDS FOR PERIODS OF DUCCI SEQUENCES

I. Shparlinski, Florian Breuer, 2019, Bulletin of the Australian Mathematical Society.

On the Distribution of Pseudopowers

C. Pomerance, I. Shparlinski, S. Konyagin, 2007, Canadian Journal of Mathematics.

Parameters of Integral Circulant Graphs and Periodic Quantum Dynamics

Nitin Saxena, S. Severini, I. Shparlinski, 2007, quant-ph/0703236.

Character sums with exponential functions over smooth numbers

W. Banks, I. Shparlinski, J. Friedlander, 2006 .

Common Divisors of the Euler Function at Related Arguments

F. Luca, W. Banks, I. Shparlinski, 2011 .

ON THE CONSECUTIVE POWERS OF A PRIMITIVE ROOT: GAPS AND EXPONENTIAL SUMS

I. Shparlinski, S. Konyagin, 2012 .

Disjointness of the M\"obius Transformation and M\"obius Function

I. Shparlinski, E. Abdalaoui, 2017, 1711.11062.

On the greatest common divisor of integer parts of polynomials

W. Banks, I. Shparlinski, 2022, 2205.00253.

Bounds on bilinear forms with Kloosterman sums

I. Shparlinski, Xiaosheng Wu, Bryce Kerr, 2022, 2204.05038.

On a hybrid version of the Vinogradov mean value theorem

I. Shparlinski, Chang-Pao Chen, 2019, Acta Mathematica Hungarica.

Analogues of the Balog–Wooley Decomposition for Subsets of Finite Fields and Character Sums with Convolutions

I. Shparlinski, Arne Winterhof, O. Roche-Newton, 2017, Annals of Combinatorics.

Double exponential sums with exponential functions

I. Shparlinski, K. Yau, 2017 .

Character sums with smooth numbers

I. Shparlinski, 2017, 1705.10148.

Bounds of double multiplicative character sums and gaps between residues of exponential functions

I. Shparlinski, K. Yau, 2016 .

Bounds on short character sums and L-functions for characters with a smooth modulus

W. Banks, I. Shparlinski, 2016, 1605.07553.

On the number of distinct quadratic fields generated by the Shanks sequence

W. Banks, I. Shparlinski, 2016, 1602.06473.

SYSTEMS OF CONGRUENCES WITH PRODUCTS OF VARIABLES FROM SHORT INTERVALS

I. Shparlinski, 2015, Bulletin of the Australian Mathematical Society.

Counting Additive Decompositions of Quadratic Residues in Finite Fields

S. Blackburn, I. Shparlinski, S. Konyagin, 2014, 1403.2589.

ON THE DENSITY OF INTEGER POINTS ON GENERALISED MARKOFF-HURWITZ HYPERSURFACES

I. Shparlinski, Mei-Chu Chang, 2014 .

Character Sums with Division Polynomials

Katherine E. Stange, I. Shparlinski, 2009, Canadian Mathematical Bulletin.

Smooth shifted monomial products

I. Shparlinski, É. Fouvry, 2011 .

On the Distribution of Irreducible Trinomials

I. Shparlinski, 2011, Canadian Mathematical Bulletin.

Twisted exponential sums over points of elliptic curves

I. Shparlinski, Alina Ostafe, 2011 .

On the Complexity of Testing Elite Primes

F. Luca, I. Shparlinski, L. Somer, 2011 .

Partitions into two Lehmer numbers

I. Shparlinski, Arne Winterhof, 2010 .

Sums with convolutions of Dirichlet characters

W. Banks, I. Shparlinski, 2010 .

On pseudopoints of algebraic curves

I. Shparlinski, R. R. Farashahi, 2010, 1005.4775.

ON POINT SETS IN VECTOR SPACES OVER FINITE FIELDS THAT DETERMINE ONLY ACUTE ANGLE TRIANGLES

I. Shparlinski, 2009, Bulletin of the Australian Mathematical Society.

INTEGERS 9 Supplement ( 2009 ) ON PSEUDOSQUARES AND PSEUDOPOWERS

C. Pomerance, I. Shparlinski, 2009 .

On quadratic fields generated by polynomials

F. Luca, I. Shparlinski, 2008, Bulletin of the Australian Mathematical Society.

On the distribution of rational functions on consecutive powers

I. Shparlinski, J. Gutierrez, 2008 .

Distribution of consecutive modular roots of an integer

J. Bourgain, I. Shparlinski, 2008 .

On Pseudosquares and Pseudopowers

C. Pomerance, I. Shparlinski, 2007, 0712.1081.

TATE–SHAFAREVICH GROUPS AND FROBENIUS FIELDS OF REDUCTIONS OF ELLIPTIC CURVES

I. Shparlinski, 2007, 0707.2976.

Coincidences in the values of the Euler and Carmichael functions

F. Luca, W. Banks, I. Shparlinski, 2006 .

Small exponent point groups on elliptic curves

F. Luca, I. Shparlinski, J. McKee, 2006 .

Small exponent point groups on elliptic curves par

F. Luca, I. Shparlinski, J. McKee, 2006 .

Square-free values of the Carmichael function

I. Shparlinski, F. Pappalardi, F. Saidak, 2003 .

N ov 2 01 8 CODES CORRECTING RESTRICTED ERRORS

I. Shparlinski, Arne Winterhof, 2022 .

Character sums with Beatty sequences on Burgess-type intervals

W. Banks, I. Shparlinski, 2006, math/0608042.

Density of non‐residues in Burgess‐type intervals and applications

D. R. Heath-Brown, W. Banks, I. Shparlinski, 2006, math/0607692.

New estimates for exponential sums over multiplicative subgroups and intervals in prime fields

I. Shparlinski, C. Trujillo, M. Garaev, 2020, Journal of Number Theory.

Polynomial Values in Subfields and Affine Subspaces of Finite Fields

I. Shparlinski, O. Roche-Newton, 2014, 1407.2273.

Value Sets of Sparse Polynomials

I. Shparlinski, J. Voloch, 2018, Canadian Mathematical Bulletin.

Arithmetic properties of quadratic exponential polynomials

I. Shparlinski, U. Zannier, 2019 .

Bounds on bilinear forms with Kloosterman sums

I. Shparlinski, Xiaosheng Wu, Bryce Kerr, 2022, 2204.05038.

Average order in cyclic groups

Arnold Knopfmacher, Igor E. Shparlinski, Joachim von zur Gathen, 2004 .

Bounds on average values of double incomplete Kloosterman sums

I. Shparlinski, 2019, Journal of Number Theory.

On a question of Erdös and Graham

I. Shparlinski, 2002 .

On character sums with determinants

I. Shparlinski, 'Etienne Fouvry, 2022, 2210.15761.

Elliptic divisibility sequences

Igor E. Shparlinski, Graham Everest, Thomas Ward, 2003 .

ON THE NONLINEARITY OF THE SEQUENCE OF SIGNS OF KLOOSTERMAN SUMS

I. Shparlinski, 2005 .

ON CURVES OVER FINITE FIELDS WITH JACOBIANS OF SMALL EXPONENT

I. Shparlinski, Kevin Ford, 2006, math/0607474.

Distribution of polynomial discriminants modulo a prime

I. Shparlinski, 2015, Archiv der Mathematik.

Subgroups generated by rational functions in finite fields

I. Shparlinski, Domingo Gómez-Pérez, 2014, Monatshefte für Mathematik.

Weil Sums over Small Subgroups

I. Shparlinski, J. Voloch, Alina Ostafe, 2022, Mathematical Proceedings of the Cambridge Philosophical Society.

The Sato–Tate distribution in thin parametric families of elliptic curves

I. Shparlinski, J. Voloch, Régis de la Bretèche, 2018, Mathematische Zeitschrift.

Modular hyperbolas

I. Shparlinski, 2012, Japanese Journal of Mathematics.

On the concentration of points of polynomial maps and applications

I. Shparlinski, Alina Ostafe, J. Cilleruelo, 2011, Mathematische Zeitschrift.

Analogues of the Balog–Wooley Decomposition for Subsets of Finite Fields and Character Sums with Convolutions

I. Shparlinski, Arne Winterhof, O. Roche-Newton, 2019, Annals of Combinatorics.

On the Győry-Sárközy-Stewart conjecture in function fields

I. Shparlinski, 2018 .

On the density of integer points on generalised Markoff–Hurwitz and Dwork hypersurfaces

I. Shparlinski, Mei-Chu Chang, 2015, Mathematische Zeitschrift.

Congruences with intervals and arbitrary sets

W. Banks, I. Shparlinski, 2019, Archiv der Mathematik.

Character sums with smooth numbers

I. Shparlinski, 2018, Archiv der Mathematik.

On the Distribution and Lattice Structure of Nonlinear Congruential Pseudorandom Numbers

Igor E. Shparlinski, Harald Niederreiter, H. Niederreiter, 1999 .

Functional graphs of polynomials over finite fields pdf

Bernard Mans, Luke Mathieson, Florian Luca, 2013, J. Comb. Theory B.

On the asymptotic effectiveness of Weil descent attacks

Igor E. Shparlinski, Alfred Menezes, Carl Pomerance, 2010, J. Math. Cryptol..

Elliptic curves over finite fields : number theoretic and cryptographic aspects

Igor E. Shparlinski, I. Shparlinski, 2013 .

On the Insecurity of a Server-Aided RSA Protocol

Igor E. Shparlinski, Phong Q. Nguyen, I. Shparlinski, 2001, ASIACRYPT.

Recent Advances in the Theory of Nonlinear Pseudorandom Number Generators

Igor E. Shparlinski, Harald Niederreiter, H. Niederreiter, 2002 .

Reconstructing noisy polynomial evaluation in residue rings

Igor E. Shparlinski, Simon R. Blackburn, Domingo Gómez-Pérez, 2006, J. Algorithms.

Computational Diffie-Hellman Problem

Igor E. Shparlinski, I. Shparlinski, 2011, Encyclopedia of Cryptography and Security.

Diffie-Hellman Problem

Igor E. Shparlinski, I. Shparlinski, 2005, Encyclopedia of Cryptography and Security.

An Extremely Small and Efficient Identification Scheme

Igor E. Shparlinski, William D. Banks, Daniel Lieman, 2000, ACISP.

On the Value Set of n! Modulo a Prime

F. Luca, H. Stichtenoth, W. Banks, 2005 .

On the number of Eisenstein polynomials of bounded height

Igor E. Shparlinski, Randell Heyman, I. Shparlinski, 2013, Applicable Algebra in Engineering, Communication and Computing.

ON STABLE QUADRATIC POLYNOMIALS

F. Luca, I. Shparlinski, Alina Ostafe, 2012, Glasgow Mathematical Journal.

EXPONENTIAL AND CHARACTER SUMS WITH MERSENNE NUMBERS

W. Banks, I. Shparlinski, J. Friedlander, 2012, Journal of the Australian Mathematical Society.

SUM–PRODUCT ESTIMATES AND MULTIPLICATIVE ORDERS OF γ AND γ+γ−1 IN FINITE FIELDS

I. Shparlinski, 2011, Bulletin of the Australian Mathematical Society.

Bounds of multiplicative character sums with Fermat quotients of primes

Igor E. Shparlinski, I. Shparlinski, 2011 .

Fermat quotients: exponential sums, value set and primitive roots

Igor E. Shparlinski, I. Shparlinski, 2011, 1104.3909.

On Small Solutions to Quadratic Congruences

I. Shparlinski, 2010, 1004.0715.

Bilinear character sums and sum-product problems on elliptic curves

I. Shparlinski, O. Ahmadi, 2010, Proceedings of the Edinburgh Mathematical Society.

ON SOME WEIGHTED AVERAGE VALUES OF L-FUNCTIONS

Igor Shparlinski, I. Shparlinski, 2008, Bulletin of the Australian Mathematical Society.

ON THE NUMBER OF SIGN CHANGES OF HECKE EIGENVALUES OF NEWFORMS

I. Shparlinski, W. Kohnen, Y. Lau, 2008, Journal of the Australian Mathematical Society.

Arithmetic properties of the Ramanujan function

F. Luca, I. Shparlinski, 2006, math/0607591.

Dynamical Systems Generated by Rational Functions

Igor E. Shparlinski, Harald Niederreiter, H. Niederreiter, 2003, AAECC.

Covering Sets for Limited-Magnitude Errors

Zhixiong Chen, Igor E. Shparlinski, Arne Winterhof, 2013, IEEE Transactions on Information Theory.

On shifted Eisenstein polynomials

Igor E. Shparlinski, Randell Heyman, I. Shparlinski, 2013, Period. Math. Hung..

On the typical size and cancellations among the coefficients of some modular forms

F. Luca, I. Shparlinski, Maksym Radziwiłł, 2013, Mathematical Proceedings of the Cambridge Philosophical Society.

PSEUDOPRIME CULLEN AND WOODALL NUMBERS

F. Luca, I. Shparlinski, 2007 .

New Bounds of Weyl Sums

I. Shparlinski, Chang-Pao Chen, 2019, International Mathematics Research Notices.

The Insecurity of the Digital Signature Algorithm with Partially Known Nonces

Igor E. Shparlinski, Phong Q. Nguyen, I. Shparlinski, 2002, Journal of Cryptology.

On numbers n dividing the nth term of a linear recurrence

C. Pomerance, F. Luca, I. Shparlinski, 2010, Proceedings of the Edinburgh Mathematical Society.

Noisy interpolation of sparse polynomials in finite fields

Igor E. Shparlinski, Arne Winterhof, I. Shparlinski, 2005, Applicable Algebra in Engineering, Communication and Computing.

A hidden number problem in small subgroups

Igor E. Shparlinski, Arne Winterhof, I. Shparlinski, 2005, Math. Comput..

The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces

Igor E. Shparlinski, Phong Q. Nguyen, I. Shparlinski, 2003, Des. Codes Cryptogr..

Hidden Number Problem with the Trace and Bit Security of XTR and LUC

Igor E. Shparlinski, Mats Näslund, Wen-Ching Winnie Li, 2002, CRYPTO.

Security of most significant bits of gx2

Igor E. Shparlinski, I. Shparlinski, 2002, Inf. Process. Lett..

On the Generalised Hidden Number Problem and Bit Security of XTR

Igor E. Shparlinski, I. Shparlinski, 2001, AAECC.

Sparse polynomial approximation in finite fields

Igor E. Shparlinski, I. Shparlinski, 2001, STOC '01.

The Insecurity of Nyberg-Rueppel and Other DSA-Like Signature Schemes with Partially Known Nonces

Igor E. Shparlinski, Phong Q. Nguyen, Edwin El Mahassni, 2001, CaLC.

Security of the most significant bits of the Shamir message passing scheme

Igor E. Shparlinski, María Isabel González Vasco, Maria Isabel Gonzalez Vasco, 2000, Math. Comput..

Conceptual Modeling

Paolo Atzeni, Adam J. Lee, F. L. Bauer, 2012, Lecture Notes in Computer Science.

On the Divisibility of Fermat Quotients

Igor E. Shparlinski, Kevin Ford, Jean Bourgain, 2010 .

Bounds of Trilinear and Quadrilinear Exponential Sums

Igor E. Shparlinski, Giorgis Petridis, I. Shparlinski, 2016, Journal d'Analyse Mathématique.

Periodic structure of the exponential pseudorandom number generator pdf

Igor E. Shparlinski, Pieter Moree, Jonas Kaszian, 2013, Applied Algebra and Number Theory.

Sum-Products Estimates with Several Sets and Applications

Igor E. Shparlinski, Kevin A. Broughan, Antal Balog, 2012, Integers.

On character sums with distances on the upper half plane over a finite field

Igor E. Shparlinski, Nicholas M. Katz, Maosheng Xiong, 2009, Finite Fields Their Appl..

On the elliptic curve analogue of the sum-product problem

Igor E. Shparlinski, I. Shparlinski, 2008, Finite Fields Their Appl..

ON THE SOLVABILITY OF BILINEAR EQUATIONS IN FINITE FIELDS

I. Shparlinski, 2007, Glasgow Mathematical Journal.

On the value set of the Ramanujan function

I. Shparlinski, 2005 .

On the additive energy of the distance set in finite fields

Igor E. Shparlinski, I. Shparlinski, 2016, Finite Fields Their Appl..

REVIEWS AND DESCRIPTIONS OF TABLES AND BOOKS

Igor Shparlinski, I. Shparlinski, David S. Watkins, 1997 .

On the spectral Ádám property for circulant graphs

Bernard Mans, Igor Shparlinski, Francesco Pappalardi, 2002, Discret. Math..

On the Ádám Conjecture on Circulant Graphs

Bernard Mans, Igor E. Shparlinski, Francesco Pappalardi, 1998, COCOON.

Graphs with integral spectrum

Noga Alon, Igor E. Shparlinski, Ian F. Blake, 2009 .

Counting curves and their projections

Marek Karpinski, Igor E. Shparlinski, Joachim von zur Gathen, 1993, computational complexity.

On shifted Eisenstein polynomials

I. Shparlinski, Randell Heyman, 2014, Periodica Mathematica Hungarica.

Explicit Form of Cassels’ p-adic Embedding Theorem for Number Fields

I. Shparlinski, A. Dubickas, M. Sha, 2014, Canadian Journal of Mathematics.

Counting dihedral and quaternionic extensions

F. Luca, I. Shparlinski, É. Fouvry, 2011 .

Numbers at work and play

Igor E. Shparlinski, I. Shparlinski, 2010 .

On the distribution of solutions to polynomial congruences

I. Shparlinski, 2012 .

Ju l 2 00 6 On a Generalisation of a Lehmer Problem

I. Shparlinski, 2008 .

On Routing in Circulant Graphs

Bernard Mans, Jean-Pierre Seifert, Igor E. Shparlinski, 1999, COCOON.

Averaging Operators Over Homogeneous Varieties Over Finite Fields

I. Shparlinski, Chun-Yen Shen, D. Koh, 2015, The Journal of Geometric Analysis.

On the Linear Complexity and Multidimensional Distribution of Congruential Generators over Elliptic Curves

Igor E. Shparlinski, Florian Hess, F. Hess, 2005, Des. Codes Cryptogr..

Collisions in Fast Generation of Ideal Classes and Points on Hyperelliptic and Elliptic Curves

Tanja Lange, Igor E. Shparlinski, T. Lange, 2005, Applicable Algebra in Engineering, Communication and Computing.

On Exponential Sums and Group Generators for Elliptic Curves over Finite Fields

Igor E. Shparlinski, David R. Kohel, I. Shparlinski, 2000, ANTS.

On the Uniformity of Distribution of Congruential Generators over Elliptic Curves

Igor E. Shparlinski, Edwin El Mahassni, I. Shparlinski, 2001, SETA.

On Finding Primitive Roots in Finite Fields

Igor E. Shparlinski, I. Shparlinski, 1996, Theor. Comput. Sci..

Indifferentiable deterministic hashing to elliptic and hyperelliptic curves

Igor E. Shparlinski, Mehdi Tibouchi, Reza Rezaeian Farashahi, 2012, Math. Comput..

Concentration of points on curves in finite fields

Igor E. Shparlinski, Javier Cilleruelo, I. Shparlinski, 2013 .

Averaging Operators Over Homogeneous Varieties Over Finite Fields

I. Shparlinski, Chun-Yen Shen, D. Koh, 2013, 1304.1990.

On the Skolem problem and some related questions for parametric families of linear recurrence sequences

I. Shparlinski, Alina Ostafe, 2020, Canadian Journal of Mathematics.

On the Győry-Sárközy-Stewart conjecture in function fields

I. Shparlinski, 2018, Czechoslovak Mathematical Journal.

On abelian multiplicatively dependent points on a curve in a torus

I. Shparlinski, Alina Ostafe, U. Zannier, 2017, 1704.04694.

Some additive combinatorics problems in matrix rings

Corneliu G. Hoffman, F. Luca, I. Shparlinski, 2009, 0902.3482.

Distribution of matrices with restricted entries over finite fields

I. Shparlinski, O. Ahmadi, 2007 .

On the exponent of the group of points on elliptic curves in extension fields

Igor E. Shparlinski, Florian Luca, F. Luca, 2005 .

Level curves of rational functions and unimodular points on rational curves

I. Shparlinski, F. Pakovich, 2018, Proceedings of the American Mathematical Society.

Finite Field Experiments

I. Shparlinski, Hans-Christian Graf v. Bothmer, 2008 .

Geometric progressions in vector sumsets over finite fields

Igor E. Shparlinski, I. Shparlinski, 2020, Finite Fields Their Appl..

Identity testing and interpolation from high powers of polynomials of large degree over finite fields

Marek Karpinski, Igor E. Shparlinski, László Mérai, 2017, J. Complex..

An explicit polynomial analogue of Romanoff's theorem

Igor E. Shparlinski, Andreas J. Weingartner, I. Shparlinski, 2015, Finite Fields Their Appl..

Distribution of polynomial discriminants modulo a prime

I. Shparlinski, 2015 .

Counting irreducible binomials over finite fields

Igor E. Shparlinski, Randell Heyman, I. Shparlinski, 2015, Finite Fields Their Appl..

Cayley Graphs Generated by Small Degree Polynomials over Finite Fields

Igor E. Shparlinski, I. Shparlinski, 2014, SIAM J. Discret. Math..

Interpolation and Approximation of Polynomials in Finite Fields over a Short Interval from Noisy Values

Óscar García-Morchón, Igor E. Shparlinski, Ronald Rietman, 2014, Exp. Math..

On Gauss sums and the evaluation of Stechkin's constant

Igor E. Shparlinski, William D. Banks, W. Banks, 2013, Math. Comput..

Predicting masked linear pseudorandom number generators over finite fields

Igor E. Shparlinski, Domingo Gómez-Pérez, Jaime Gutierrez, 2013, Des. Codes Cryptogr..

On the concentration of points of polynomial maps and applications

Igor E. Shparlinski, Alina Ostafe, Javier Cilleruelo, 2012 .

On Gaps Between Primitive Roots in the Hamming Metric

I. Shparlinski, C. Elsholtz, R. Dietmann, 2012, 1207.0842.

On the Distribution of Atkin and Elkies Primes

Igor E. Shparlinski, Andrew V. Sutherland, I. Shparlinski, 2011, Foundations of Computational Mathematics.

Degree Growth, Linear Independence and Periods of a Class of Rational Dynamical Systems

Alina Ostafe, Igor Shparlinski, I. Shparlinski, 2011, 1109.0575.

On the average distribution of pseudorandom numbers generated by nonlinear permutations

Igor E. Shparlinski, I. Shparlinski, 2011, Math. Comput..

On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves pdf

Igor E. Shparlinski, Alina Ostafe, Simon R. Blackburn, 2011, IACR Cryptol. ePrint Arch..

On pseudorandom numbers from multivariate polynomial systems

Igor E. Shparlinski, Alina Ostafe, Elena Pelican, 2010, Finite Fields Their Appl..

On the Distribution of Orbits of PGL2(q) in Fqn and the Klapper Conjecture

IGOR E. SHPARLINSKI, I. Shparlinski, 2009, SIAM J. Discret. Math..

Pseudorandom numbers and hash functions from iterations of multivariate polynomials

Igor E. Shparlinski, Alina Ostafe, I. Shparlinski, 2009, Cryptography and Communications.

On quadratic fields generated by discriminants of irreducible trinomials

I. Shparlinski, 2008, 0811.1300.

Visible points on multidimensional modular hyperbolas

I. Shparlinski, Arne Winterhof, 2008 .

Classical and Quantum Algorithms for Exponential Congruences

Igor E. Shparlinski, Wim van Dam, I. Shparlinski, 2008, TQC.

Bounds of incomplete multiple Kloosterman sums

I. Shparlinski, 2007 .

Quantum period reconstruction of approximate sequences

Igor E. Shparlinski, Arne Winterhof, I. Shparlinski, 2007, Inf. Process. Lett..

Multiplicative order of Gauss periods

Igor E. Shparlinski, Jose Felipe Voloch, Omran Ahmadi, 2007, 0707.4034.

Geometric progressions in sumsets over finite fields

I. Shparlinski, O. Ahmadi, 2007 .

Character sums over shifted smooth numbers

Igor E. Shparlinski, I. Shparlinski, 2007 .

On the distribution of angles of the Salié sums

I. Shparlinski, 2007, Bulletin of the Australian Mathematical Society.

On the distribution of points on multidimensional modular hyperbolas

I. Shparlinski, 2007 .

Some divisibilities amongst the terms of linear recurrences

F. Luca, I. Shparlinski, 2006 .

On a generalisation of a Lehmer problem

I. Shparlinski, 2006, math/0607414.

Catalan and Apéry numbers in residue classes

Igor E. Shparlinski, Florian Luca, Moubariz Z. Garaev, 2006, J. Comb. Theory, Ser. A.

NON-RESIDUES AND PRIMITIVE ROOTS IN BEATTY SEQUENCES

W. Banks, I. Shparlinski, 2006 .

Character sums and nonlinear recurrence sequences

Igor E. Shparlinski, Simon R. Blackburn, S. Blackburn, 2006, Discret. Math..

On the energy of some circulant graphs

Igor E. Shparlinski, I. Shparlinski, 2006 .

On some generalisations of the Erdős distance problem over finite fields

Igor E. Shparlinski, I. Shparlinski, 2006 .

On the nonlinearity of linear recurrence sequences

Igor E. Shparlinski, Arne Winterhof, I. Shparlinski, 2006, Appl. Math. Lett..

Distribution of harmonic sums and Bernoulli polynomials modulo a prime

F. Luca, I. Shparlinski, M. Garaev, 2006 .

Distribution of Nonlinear Congruential Pseudorandom Numbers Modulo Almost Squarefree Integers

Igor E. Shparlinski, Arne Winterhof, I. Shparlinski, 2006 .

Prime divisors of palindromes

Igor E. Shparlinski, William D. Banks, W. Banks, 2005, Period. Math. Hung..

Quantum Noisy Rational Function Reconstruction

Igor E. Shparlinski, Alexander Russell, Sean Hallgren, 2005, COCOON.

Irrationality of Power Series for Various Number Theoretic Functions

Igor E. Shparlinski, Florian Luca, William D. Banks, 2005 .

Uniform Distribution of Fractional Parts Related to Pseudoprimes

F. Luca, W. Banks, I. Shparlinski, 2005, Canadian Journal of Mathematics.

On the singularity of generalised Vandermonde matrices over finite fields

Igor E. Shparlinski, I. Shparlinski, 2005, Finite Fields Their Appl..

Polynomial Gauss sums

Igor E. Shparlinski, Daniel Panario, Stephen D. Cohen, 2005 .

Predicting Subset Sum Pseudorandom Generators

Igor E. Shparlinski, Joachim von zur Gathen, J. Gathen, 2004, Selected Areas in Cryptography.

Secure Bilinear Diffie-Hellman Bits

Igor E. Shparlinski, Steven D. Galbraith, Herbie J. Hopkins, 2004, ACISP.

Classical and quantum function reconstruction via character evaluation

Alexander Russell, Igor E. Shparlinski, A. Russell, 2004, J. Complex..

Exponential sums and congruences with factorials

F. Luca, I. Shparlinski, M. Garaev, 2004, math/0403424.

On the multidimensional distribution of the subset sum generator of pseudorandom numbers

Igor E. Shparlinski, Alessandro Conflitti, I. Shparlinski, 2003, Math. Comput..

On the hardness of approximating the permanent of structured matrices

Igor E. Shparlinski, Bruno Codenotti, Arne Winterhof, 2003, computational complexity.

A Variant of NTRU with Non-invertible Polynomials

Igor E. Shparlinski, William D. Banks, W. Banks, 2002, INDOCRYPT.

The Hidden Number Problem in Extension Fields and Its Applications

Igor E. Shparlinski, Mats Näslund, María Isabel González Vasco, 2002, LATIN.

On the Linear Complexity of the Naor–Reingold Pseudo-random Function from Elliptic Curves

Igor E. Shparlinski, Joseph H. Silverman, J. Silverman, 2001, Des. Codes Cryptogr..

On the distribution of the power generator

Igor E. Shparlinski, John B. Friedlander, I. Shparlinski, 2001, Math. Comput..

On the distribution of inversive congruential pseudorandom numbers in parts of the period

Igor E. Shparlinski, Harald Niederreiter, H. Niederreiter, 2001, Math. Comput..

On Some Properties of the Shrinking Generator

Igor E. Shparlinski, I. Shparlinski, 2001, Des. Codes Cryptogr..

Polynomial representations of the Diffie-Hellman mapping

Igor E. Shparlinski, Edwin El Mahassni, I. Shparlinski, 2001, Bulletin of the Australian Mathematical Society.

On the Linear Complexity of the Power Generator

Igor E. Shparlinski, I. Shparlinski, 2001, Des. Codes Cryptogr..

On the Multiplicative Orders of γ and γ+γ -1 over finite fields

I. Shparlinski, 2001 .

On the Security of Lenstra's Variant of DSA without Long Inversions

Igor E. Shparlinski, Arjen K. Lenstra, A. K. Lenstra, 2001, Public Key Cryptography.

On the Multidimensional Distribution of Inversive Congruential Pseudorandom Numbers in Parts of the Period

Igor E. Shparlinski, Harald Niederreiter, Jaime Gutierrez, 2000 .

On the Distribution of Nonlinear Recursive Congruential Pseudorandom Numbers of Higher Orders

Igor E. Shparlinski, Harald Niederreiter, Frances Griffin, 1999, AAECC.

On The Correlation Of Binary M-sequences

Igor E. Shparlinski, Michael Larsen, John B. Friedlander, 1999, Des. Codes Cryptogr..

Computing components and projections of curves over finite fields

Igor E. Shparlinski, Joachim von zur Gathen, J. Gathen, 1999, SIAM J. Comput..

The CREW PRAM Complexity of Modular Inversion

Igor E. Shparlinski, Joachim von zur Gathen, J. Gathen, 1998, SIAM J. Comput..

On Exponential Sums with Sparse Polynomials and Rational Functions

Igor E. Shparlinski, I. Shparlinski, 1996 .

Components and Projections of Curves over Finite Fields

Igor E. Shparlinski, Joachim von zur Gathen, J. Gathen, 1994, ISAAC.

Finding irreducible and primitive polynomials

Igor E. Shparlinski, I. Shparlinski, 1993, Applicable Algebra in Engineering, Communication and Computing.

On bivariate polynomial factorization over finite fields

Igor E. Shparlinski, I. Shparlinski, 1993 .

On Structure Complexity of Normal Basis of Finite Field

Igor E. Shparlinski, S. A. Stepanov, I. Shparlinski, 1987, FCT.

On Polynomial Approximation of the Discrete Logarithm and the Diffie—Hellman Mapping

Igor E. Shparlinski, Don Coppersmith, D. Coppersmith, 2015, Journal of Cryptology.

On the number of distinct elliptic curves in some families

Igor E. Shparlinski, Reza Rezaeian Farashahi, I. Shparlinski, 2010, Des. Codes Cryptogr..

Exponential sums with Dickson polynomials

Igor E. Shparlinski, Domingo Gómez-Pérez, Jaime Gutierrez, 2006, Finite Fields Their Appl..

Short character sums with Beatty sequences

W. Banks, I. Shparlinski, 2006 .

On the number of zero trace elements in polynomial bases for F

I. Shparlinski, 2005 .

A SPARSITY RESULT FOR THE DYNAMICAL MORDELL–LANG CONJECTURE IN POSITIVE CHARACTERISTIC

I. Shparlinski, Alina Ostafe, D. Ghioca, 2016, Bulletin of the Australian Mathematical Society.

On the Product of Small Elkies Primes pdf

Igor E. Shparlinski, I. Shparlinski, 2012, ArXiv.

On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves

Igor E. Shparlinski, Jorge Jiménez Urroz, Florian Luca, 2011, Math. Comput..

On the embedding degree of reductions of an elliptic curve

Igor E. Shparlinski, Alina Carmen Cojocaru, I. Shparlinski, 2009, Inf. Process. Lett..

On oracle factoring of integers pdf

Jacek Pomykala, Igor E. Shparlinski, Andrzej Dabrowski, 2019, J. Complex..

Codes correcting restricted errors

I. Shparlinski, Arne Winterhof, 2018, Designs, Codes and Cryptography.

Codes correcting restricted errors

Igor E. Shparlinski, Arne Winterhof, I. Shparlinski, 2018, Des. Codes Cryptogr..

Polynomial Interpolation and Identity Testing from High Powers Over Finite Fields

Marek Karpinski, Igor E. Shparlinski, Miklos Santha, 2015, Algorithmica.

On the fixed points of the map $x \mapsto x^x$ modulo a prime, II

F. Luca, I. Shparlinski, P. Kurlberg, 2014, 1607.04948.

On the Fixed Points of the Map x -> x^x Modulo a Prime

F. Luca, I. Shparlinski, P. Kurlberg, 2014 .

Generating safe primes

Igor E. Shparlinski, Joachim von zur Gathen, J. Gathen, 2013, J. Math. Cryptol..

On the Hidden Shifted Power Problem pdf

Igor E. Shparlinski, Moubariz Z. Garaev, Jean Bourgain, 2011, SIAM J. Comput..

On Group Structures Realized by Elliptic Curves over a Fixed Finite Field

Igor E. Shparlinski, Reza Rezaeian Farashahi, I. Shparlinski, 2010, Exp. Math..

On the length of critical orbits of stable quadratic polynomials

Igor E. Shparlinski, Alina Ostafe, I. Shparlinski, 2009, 0909.3972.

Pseudoprime reductions of elliptic curves

Igor E. Shparlinski, Florian Luca, Alina Carmen Cojocaru, 2009, Mathematical Proceedings of the Cambridge Philosophical Society.

Divisibility, Smoothness and Cryptographic Applications pdf

Igor E. Shparlinski, David Naccache, D. Naccache, 2008, Algebraic Aspects of Digital Communications.

On RSA Moduli with Prescribed Bit Patterns

Igor E. Shparlinski, I. Shparlinski, 2006, Des. Codes Cryptogr..

Distributional Properties of the Largest Prime Factor

W. Banks, I. Shparlinski, G. Harman, 2005 .

Smooth Orders and Cryptographic Applications

Igor E. Shparlinski, Carl Pomerance, C. Pomerance, 2002, ANTS.

Statistical distribution and collisions of VSH

Igor E. Shparlinski, Ian F. Blake, I. Blake, 2007, J. Math. Cryptol..

Constructing Dominating Sets in Circulant Graphs

I. Shparlinski, 2018, Annals of Combinatorics.

Identity Testing from High Powers of Polynomials of Large Degree over Finite Fields pdf

Marek Karpinski, Igor E. Shparlinski, M. Karpinski, 2017, ArXiv.

Constructing Dominating Sets in Circulant Graphs

Igor E. Shparlinski, I. Shparlinski, 2016, 1602.01286.

Character sums and deterministic polynomial root finding in finite fields pdf

Igor E. Shparlinski, Jean Bourgain, Sergei Konyagin, 2013, Math. Comput..

Statistics of Different Reduction Types of Fermat Curves

Igor E. Shparlinski, David Harvey, David Harvey, 2012, Exp. Math..

On congruences with products of variables from short intervals and applications

Igor Shparlinski, Jean Bourgain, Sergei Konyagin, 2012, 1203.0017.

GCD of Random Linear Combinations

Igor E. Shparlinski, Joachim von zur Gathen, J. Gathen, 2006, Algorithmica.

Cryptographic Applications of Sparse Polynomials over Finite Rings

Igor E. Shparlinski, William D. Banks, Daniel Lieman, 2000, ICISC.

An Identification Scheme Based on Sparse Polynomials

Igor E. Shparlinski, William D. Banks, Daniel Lieman, 2000, Public Key Cryptography.

On the $g$-ary expansions of middle binomial coefficients and Catalan numbers

F. Luca, I. Shparlinski, 2011 .

On the g-Ary Expansions of Apéry, Motzkin, Schröder and Other Combinatorial Numbers

F. Luca, I. Shparlinski, 2010 .

Möbius Randomness Law for Frobenius Traces of Ordinary Curves

I. Shparlinski, M. Sha, 2020, Canadian Mathematical Bulletin.

Möbius Randomness Law for Frobenius Traces

I. Shparlinski, M. Sha, 2019, 1909.00969.

Arithmetic properties of Apéry numbers

F. Luca, I. Shparlinski, 2008 .

Counting solvable $S$-unit equations

I. Shparlinski, C. Stewart, 2020, 2007.15170.

Squarefree parts of discriminants of trinomials

I. Shparlinski, 2014, Archiv der Mathematik.

On multiplicatively dependent vectors of algebraic numbers

Igor E. Shparlinski, Min Sha, Francesco Pappalardi, 2016, 1606.02874.

ON THE SQUARE-FREE PARTS OF ⌊en!⌋

F. Luca, I. Shparlinski, 2007, Glasgow Mathematical Journal.

Perfect powers in value sets and orbits of polynomials

I. Shparlinski, Alina Ostafe, Lukas Pottmeyer, 2019, 1907.12057.

On Multiplicative Dependence of Values of Rational Functions and a Generalization of the Northcott Theorem

I. Shparlinski, Alina Ostafe, U. Zannier, 2017, Michigan Mathematical Journal.

Orbits of Algebraic Dynamical Systems in Subgroups and Subfields

I. Shparlinski, Alina Ostafe, 2017 .

Optimal Quantum Algorithm for Polynomial Interpolation

Igor E. Shparlinski, Shih-Han Hung, Andrew M. Childs, 2015, ICALP.

Some arithmetic properties of numbers of the form $\lfloor p^c\rfloor$

Victor Z. Guo, W. Banks, I. Shparlinski, 2015, 1508.03281.

Density of non-residues in short intervals

D. R. Heath-Brown, W. Banks, I. Shparlinski, 2006 .

Counting Co-Cyclic Lattices pdf

Igor E. Shparlinski, Phong Q. Nguyen, I. Shparlinski, 2015, SIAM J. Discret. Math..

Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices

I. Shparlinski, Alina Ostafe, 2022, 2203.03880.

Counting the values taken by algebraic exponential polynomials

I. Shparlinski, G. Everest, 1999 .

On a sum involving the Euler function

I. Shparlinski, O. Bordellès, Li-Xia Dai, 2018, Journal of Number Theory.

Euclidean minima of algebraic number fields

I. Shparlinski, A. Dubickas, M. Sha, 2023, 2307.10880.

Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers

I. Shparlinski, Ray Li, 2020, 2001.09721.

Discriminants of fields generated by polynomials of given height

I. Shparlinski, Alina Ostafe, R. Dietmann, 2019, Israel Journal of Mathematics.

On the Number of Products Which Form Perfect Powers and Discriminants of Multiquadratic Extensions

I. Shparlinski, P. Kurlberg, R. Bretèche, 2019, International Mathematics Research Notices.

INFINITE HILBERT CLASS FIELD TOWERS OVER CYCLOTOMIC FIELDS

I. Shparlinski, 2008, Glasgow Mathematical Journal.

Sets of Linear Forms Which Are Hard to Compute

Igor E. Shparlinski, Michael Kaminski, I. Shparlinski, 2021, MFCS.

New books and journals

Huaxiong Wang, I. Shparlinski, K. Lam, 2003 .

Local mean value estimates for Weyl sums

I. Shparlinski, Chang-Pao Chen, J. Brandes, 2023, 2303.11913.

Character sums over sparse elements of finite fields

I. Shparlinski, Arne Winterhof, L'aszl'o M'erai, 2022, 2211.08452.

Functional graphs of families of quadratic polynomials

I. Shparlinski, B. Mans, Daniel Sutantyo, 2022, Math. Comput..

On the Glasner property for matrices with polynomial entries

Igor E. Shparlinski, I. Shparlinski, 2021, Journal of Number Theory.

Bounds on the Norms of Maximal Operators on Weyl Sums

Igor E. Shparlinski, Roger C. Baker, Changhao Chen, 2021, Journal of Number Theory.

Cancellations Amongst Kloosterman Sums

I. Shparlinski, T. P. Zhang, Tianping Zhang, 2016, 1601.05123.

Predicting masked linear pseudorandom number generators over finite fields

I. Shparlinski, Domingo Gómez-Pérez, J. Gutierrez, 2012, Designs, Codes and Cryptography.

On the lower bound of the linear complexity over F/sub p/ of Sidelnikov sequences

Igor E. Shparlinski, Arne Winterhof, Florian Luca, 2006, IEEE Transactions on Information Theory.

2 4 A ug 2 00 6 On the Distribution of Kloosterman Sums

I. Shparlinski, 2008 .

Distribution of Inverses and Multiples of Small Integers and the Sato – Tate Conjecture on Average

I. Shparlinski, 2008 .

Quadratic Non-Residues Versus Primitive Roots Modulo p

F. Luca, I. Shparlinski, 2008 .

Character sums with Beatty sequences

W. Banks, I. Shparlinski, 2005 .

Additive energy of polynomial images

I. Shparlinski, Bryce Kerr, A. Mohammadi, 2023, 2306.10677.

Equations and Character Sums with Matrix Powers, Kloosterman Sums over Small Subgroups, and Quantum Ergodicity

Igor E. Shparlinski, Alina Ostafe, Jos'e Felipe Voloch, 2021, International Mathematics Research Notices.

Additive energy of cyclic matrix groups and character sums with matrix exponential functions

Igor E. Shparlinski, Alina Ostafe, I. Shparlinski, 2021, 2108.13146.

Energy bounds for modular roots and their applications

Ilya D. Shkredov, Igor E. Shparlinski, Alexandru Zaharescu, 2021, 2103.09405.

Points on curves in small boxes en applications

Igor E. Shparlinski, Javier Cilleruelo, I. Shparlinski, 2011, 1111.1543.

On the Sato–Tate conjecture on average for some families of elliptic curves

I. Shparlinski, 2011 .

ARITHMETIC AND GEOMETRIC PROGRESSIONS IN PRODUCT SETS OVER FINITE FIELDS

I. Shparlinski, 2007, Bulletin of the Australian Mathematical Society.

On some matrix counting problems

I. Shparlinski, Alina Ostafe, Ali Mohammadi, 2023, 2310.05038.

Moments and non-vanishing of $L$-functions over subgroups

I. Shparlinski, Marc Munsch, 2023, 2309.10207.

On Nonzero Coefficients of Binary Cyclotomic Polynomials

I. Shparlinski, L. P. Wijaya, 2023, 2307.07229.

Square-free values of random polynomials

I. Shparlinski, T. Browning, 2023, 2305.15493.

On some congruences and exponential sums

I. Shparlinski, M. Garaev, 2023, 2304.08689.

On the distribution of modular inverses from short intervals

I. Shparlinski, M. Garaev, 2023, Mathematika.

Distribution of recursive matrix pseudorandom number generator modulo prime powers

I. Shparlinski, L'aszl'o M'erai, 2023, Mathematics of Computation.

On the number of Diophantine m-tuples in finite fields

I. Shparlinski, 2023, Finite Fields Their Appl..

Chowla and Sarnak conjectures for Kloosterman sums

I. Shparlinski, E. Abdalaoui, R. Steiner, 2022, Mathematische Nachrichten.

On character sums with determinants

I. Shparlinski, 'Etienne Fouvry, 2022, Science China Mathematics.

On the greatest common divisor of integer parts of polynomials

W. Banks, I. Shparlinski, 2022, 2205.00253.

Bounds on bilinear forms with Kloosterman sums

I. Shparlinski, Xiaosheng Wu, Bryce Kerr, 2022, Journal of the London Mathematical Society.

Multiplicative Properties of Hilbert Cubes

I. Shparlinski, 2022, SIAM J. Discret. Math..

Large Weyl sums and Hausdorff dimension

Igor E. Shparlinski, Roger C. Baker, Changhao Chen, 2021, Journal of Mathematical Analysis and Applications.

Bounds of trilinear sums with Kloosterman fractions

Igor E. Shparlinski, I. Shparlinski, 2021, Archiv der Mathematik.

Additive energy and a large sieve inequality for sparse sequences

Igor E. Shparlinski, Roger C. Baker, Marc Munsch, 2021, Mathematika.

On the dynamical system generated by the Möbius transformation at prime times

I. Shparlinski, L. Mérai, 2021, Research in the Mathematical Sciences.

Metric theory of Weyl sums

Igor Shparlinski, Changhao Chen, James Maynard, 2020, Mathematische Annalen.

On a conjecture of Soundararajan

W. Banks, I. Shparlinski, 2020, Bulletin of the London Mathematical Society.

On the distribution of modular square roots of primes

I. Shparlinski, I. Shkredov, A. Zaharescu, 2020, Mathematische Zeitschrift.

Hybrid bounds on two-parametric family Weyl sums along smooth curves

I. Shparlinski, Chang-Pao Chen, 2020, 2003.02419.

Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions

I. Shparlinski, Bryce Kerr, 2020, Research in Number Theory.

On digits of Mersenne numbers

I. Shparlinski, L'aszl'o M'erai, Bryce Kerr, 2020, Revista Matemática Iberoamericana.

Restricted mean value theorems and the metric theory of restricted Weyl sums

I. Shparlinski, Chang-Pao Chen, 2019, The Quarterly Journal of Mathematics.

Large and small values of quadratic Weyl sums

I. Shparlinski, Chang-Pao Chen, 2019 .

Small values of Weyl sums

I. Shparlinski, Chang-Pao Chen, 2019, Journal of Mathematical Analysis and Applications.

Dynamical irreducibility of polynomials modulo primes

I. Shparlinski, Alina Ostafe, L'aszl'o M'erai, 2019, Mathematische Zeitschrift.

Dynamical irreducibility of polynomials in reduction modulo primes

I. Shparlinski, Alina Ostafe, L. Mérai, 2019 .

Hausdorff dimension of the large values of Weyl sums

I. Shparlinski, Chang-Pao Chen, 2019, Journal of Number Theory.

Double sums of Kloosterman sums in finite fields

Igor E. Shparlinski, Simon Macourt, I. Shparlinski, 2019, Finite Fields Their Appl..

Disjointness of the Möbius Transformation and Möbius Function

I. Shparlinski, E. H. el Abdalaoui, 2019, Research in the Mathematical Sciences.

Double Character Sums with Intervals and Arbitrary Sets

I. Shparlinski, I. Shkredov, 2018, Proceedings of the Steklov Institute of Mathematics.

SMOOTH SQUAREFREE AND SQUAREFULL INTEGERS IN ARITHMETIC PROGRESSIONS

I. Shparlinski, Marc Munsch, K. Yau, 2018, Mathematika.

Sums with the Möbius function twisted by characters with powerful moduli

W. Banks, I. Shparlinski, 2018, Transactions of the American Mathematical Society.

On sums of Kloosterman and Gauss sums

I. Shparlinski, 2018, Transactions of the American Mathematical Society.

A Refinement of the Burgess Bound for Character Sums

I. Shparlinski, Bryce Kerr, K. Yau, 2017, Michigan Mathematical Journal.

On smooth square‐free numbers in arithmetic progressions

I. Shparlinski, Marc Munsch, 2017, Journal of the London Mathematical Society.

Trilinear forms with double Kloosterman sums

I. Shparlinski, 2017, International Journal of Number Theory.

Denominators of Bernoulli polynomials

F. Luca, I. Shparlinski, P. Moree, 2017, 1706.09804.

On the exponential large sieve inequality for sparse sequences modulo primes

I. Shparlinski, Mei-Chu Chang, Bryce Kerr, 2017, 1706.04776.

On the Complexity of Exact Counting of Dynamically Irreducible Polynomials

Igor E. Shparlinski, Domingo Gómez-Pérez, László Mérai, 2017, J. Symb. Comput..

On the error term of a lattice counting problem

F. Luca, I. Shparlinski, 2017, 1705.08714.

On the convex hull of the points on multivariate modular hyperbolas

I. Shparlinski, 2017 .

CANCELLATIONS BETWEEN KLOOSTERMAN SUMS MODULO A PRIME POWER WITH PRIME ARGUMENTS

I. Shparlinski, Kui Liu, Tianping Zhang, 2016, Mathematika.

Bilinear forms with exponential sums with binomials

I. Shparlinski, Kui Liu, Tianping Zhang, 2016, Journal of Number Theory.

Elliptic curves in isogeny classes

I. Shparlinski, Liangyi Zhao, 2016, Journal of Number Theory.

Power series approximations to Fekete polynomials

Igor E. Shparlinski, Jason Bell, J. Bell, 2016, J. Approx. Theory.

On squares in Piatetski–Shapiro sequences

I. Shparlinski, Kui Liu, Tianping Zhang, 2016, Functiones et Approximatio Commentarii Mathematici.

On Some Multiple Character Sums

I. Shparlinski, I. Shkredov, 2016, 1610.01061.

Arithmetic Properties of Integers in Chains and Reflections of g-ary Expansions

Igor E. Shparlinski, Domingo Gómez-Pérez, I. Shparlinski, 2016, Exp. Math..

On small gaps between the elements of multiplicative subgroups of finite fields

Igor E. Shparlinski, I. Shparlinski, 2016, Des. Codes Cryptogr..

Ratios of Small Integers in Multiplicative Subgroups of Residue Rings

Igor E. Shparlinski, I. Shparlinski, 2016, Exp. Math..

Dominating Sets in Circulant Graphs pdf

Igor E. Shparlinski, I. Shparlinski, 2016, ArXiv.

Prescribing the binary digits of squarefree numbers and quadratic residues

I. Shparlinski, C. Elsholtz, R. Dietmann, 2016, 1601.04754.

The Sato--Tate Distribution in Families of Elliptic Curves with a Rational Parameter of Bounded Height

I. Shparlinski, M. Sha, 2015, 1512.07301.

The Sato–Tate distribution in thin parametric families of elliptic curves

I. Shparlinski, J. Voloch, R. Bretèche, 2015, 1509.03009.

Upper and lower bounds for higher moments of theta functions

I. Shparlinski, Marc Munsch, 2015, 1506.01999.

Small discriminants of complex multiplication fields of elliptic curves over finite fields

I. Shparlinski, 2015, Czechoslovak Mathematical Journal.

On small gaps between the elements of multiplicative subgroups of finite fields

I. Shparlinski, 2015, Designs, Codes and Cryptography.

Linear Congruences with Ratios

I. Shparlinski, 2015, 1503.03196.

Fractional parts of Dedekind sums

W. Banks, I. Shparlinski, 2014, 1411.1820.

Random Walks, Bisections and Gossiping in Circulant Graphs

Bernard Mans, Igor E. Shparlinski, I. Shparlinski, 2014, Algorithmica.

Products with variables from low-dimensional affine spaces and shifted power identity testing in finite fields

Igor E. Shparlinski, I. Shparlinski, 2014, J. Symb. Comput..

Enumeration of certain varieties over a finite field

I. Shparlinski, J. Friedlander, 2014 .

Lang-Trotter and Sato-Tate Distributions in Single and Double Parametric Families of Elliptic Curves

I. Shparlinski, M. Sha, 2014, 1404.0182.

Distribution of elliptic twin primes in isogeny and isomorphism classes

Igor E. Shparlinski, Daniel Sutantyo, I. Shparlinski, 2014 .

Quadratic non-residues in short intervals

I. Shparlinski, S. Konyagin, 2013, 1311.7016.

On gaps between quadratic non-residues in the Euclidean and Hamming metrics

I. Shparlinski, C. Elsholtz, R. Dietmann, 2013 .

MULTIPLE EXPONENTIAL AND CHARACTER SUMS WITH MONOMIALS

I. Shparlinski, 2013, 1309.0324.

On the fractional parts of an/n

F. Luca, I. Shparlinski, J. Cilleruelo, 2013 .

Evasive properties of sparse graphs and some linear equations in primes pdf

Igor E. Shparlinski, I. Shparlinski, 2013, Theor. Comput. Sci..

Additive Decompositions of Subgroups of Finite Fields

Igor E. Shparlinski, I. Shparlinski, 2013, SIAM J. Discret. Math..

On digit patterns in expansions of rational numbers with prime denominator

W. Steiner, I. Shparlinski, 2012, 1205.5673.

Indifferentiable deterministic hashing to elliptic and hyperelliptic curves

Mehdi Tibouchi, Pierre-Alain Fouque, I. Shparlinski, 2012, Math. Comput..

Random Walks and Bisections in Random Circulant Graphs

Bernard Mans, Igor E. Shparlinski, I. Shparlinski, 2012, LATIN.

On the power generator and its multivariate analogue

Igor E. Shparlinski, Alina Ostafe, I. Shparlinski, 2012, J. Complex..

On the Lang-Trotter and Sato-Tate Conjectures on Average for Polynomial Families of Elliptic Curves

I. Shparlinski, 2012, 1203.6500.

Concentration of points and isomorphism classes of hyperelliptic curves over a finite field in some thin families

I. Shparlinski, Mei-Chu Chang, J. Cilleruelo, 2011 .

On vanishing Fermat quotients and a bound of the Ihara sum

Igor E. Shparlinski, I. Shparlinski, 2011, 1104.3910.

Modular hyperbolas

Igor E. Shparlinski, I. Shparlinski, 2011, 1103.2879.

Pseudorandom Bits From Points on Elliptic Curves

Igor E. Shparlinski, Reza Rezaeian Farashahi, I. Shparlinski, 2010, IEEE Transactions on Information Theory.

On the Restricted Divisor Function in Arithmetic Progressions

I. Shparlinski, 2010, 1003.5347.

Pseudorandomness and Dynamics of Fermat Quotients

Igor E. Shparlinski, Alina Ostafe, I. Shparlinski, 2010, SIAM J. Discret. Math..

Multiplicative character sums with twice-differentiable functions

W. Banks, I. Shparlinski, 2009 .

On the distribution of the number of points on algebraic curves in extensions of finite fields

I. Shparlinski, O. Ahmadi, 2009, 0907.3664.

On the Values of Kloosterman Sums

Igor E. Shparlinski, I. Shparlinski, 2009, IEEE Transactions on Information Theory.

ON THE DISTRIBUTION OF SOLUTIONS TO LINEAR EQUATIONS

I. Shparlinski, 2009 .

Some additive combinatorics problems in matrix rings

Corneliu G. Hoffman, F. Luca, I. Shparlinski, 2009, 0902.3482.

Average distribution of prime ideals in families of number fields

I. Shparlinski, J. Voloch, 2008 .

Least totient in a residue class

I. Shparlinski, J. Friedlander, 2008 .

Pseudorandom Graphs from Elliptic Curves

Igor E. Shparlinski, I. Shparlinski, 2008, LATIN.

On a Generalised Lehmer Problem for Arbitrary Powers

I. Shparlinski, 2008, 0803.3487.

Character sums with subsequence sums

Igor E. Shparlinski, Sanka Balasuriya, I. Shparlinski, 2007, Period. Math. Hung..

Estimates for Wieferich numbers

Igor E. Shparlinski, Florian Luca, William D. Banks, 2007 .

On RSA moduli with almost half of the bits prescribed

Igor E. Shparlinski, Sidney W. Graham, I. Shparlinski, 2007, Discret. Appl. Math..

Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields

F. Luca, I. Shparlinski, 2007, Canadian Mathematical Bulletin.

Distribution of Roots of Polynomial Congruences

Igor E. Shparlinski, I. Shparlinski, 2007, Int. J. Math. Math. Sci..

Least totient in a residue class

I. Shparlinski, J. Friedlander, 2007 .

On values taken by the largest prime factor of shifted primes

Igor E. Shparlinski, William D. Banks, W. Banks, 2007, Journal of the Australian Mathematical Society.

JOINT DISTRIBUTION OF DISCRETE LOGARITHMS

I. Shparlinski, 2013 .

Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem

Igor E. Shparlinski, Kevin A. Broughan, Florian Luca, 2010, Integers.

On the smallest pseudopower

Igor E. Shparlinski, Carl Pomerance, Jean Bourgain, 2009 .

On the density of some special primes

Igor E. Shparlinski, John B. Friedlander, I. Shparlinski, 2009, J. Math. Cryptol..

Exponential Sums with Farey Fractions

I. Shparlinski, 2009 .

On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas

I. Shparlinski, 2008 .

Primitive points on a modular hyperbola

I. Shparlinski, 2006 .

Multiplicative Structure of Values of the Euler Function

Igor E. Shparlinski, Carl Pomerance, William D. Banks, 2004 .

On Stern's Attack Against Secret Truncated Linear Congruential Generators

Igor E. Shparlinski, Scott Contini, I. Shparlinski, 2005, ACISP.

Elliptic Curves with Low Embedding Degree

Igor E. Shparlinski, Florian Luca, F. Luca, 2006, Journal of Cryptology.

On the Unpredictability of Bits of the Elliptic Curve Diffie--Hellman Scheme

Igor E. Shparlinski, Dan Boneh, D. Boneh, 2001, CRYPTO.

On the bit security of the Diffie-Hellman key

Igor E. Shparlinski, Ian F. Blake, Theodoulos Garefalakis, 2005, Applicable Algebra in Engineering, Communication and Computing.

Pseudoprime reductions of elliptic curves

I. Shparlinski, A. Cojocaru, Florian Luca, 2009, Mathematical Proceedings of the Cambridge Philosophical Society.

On the number of polynomial maps into Z_n

F. Luca, I. Shparlinski, 2006 .

Metric theory of lower bounds on Weyl sums

I. Shparlinski, Bryce Kerr, Chang-Pao Chen, 2020, 2004.02539.

Noisy polynomial interpolation modulo prime powers pdf

Marek Karpinski, Igor Shparlinski, I. Shparlinski, 2020, J. Complex..

Correcting noisy exponentiation black-boxes modulo a prime

Igor E. Shparlinski, I. Shparlinski, 2013, Inf. Process. Lett..

Chinese Remaindering with Multiplicative Noise

Igor E. Shparlinski, Ron Steinfeld, Ron Steinfeld, 2007, Theory of Computing Systems.

Predicting nonlinear pseudorandom number generators

Igor E. Shparlinski, Simon R. Blackburn, Domingo Gómez-Pérez, 2004, Math. Comput..

Bisecting and Gossiping in Circulant Graphs

Bernard Mans, Igor E. Shparlinski, I. Shparlinski, 2004, LATIN.

Polynomial interpolation from multiples

Igor E. Shparlinski, Joachim von zur Gathen, J. Gathen, 2004, SODA '04.

Predicting the Inversive Generator

Igor E. Shparlinski, Simon R. Blackburn, Domingo Gómez-Pérez, 2003, IMACC.

Hidden number problem with hidden multipliers, timed-release crypto, and noisy exponentiation

Igor E. Shparlinski, Phong Q. Nguyen, Nick Howgrave-Graham, 2003, Math. Comput..

Exponential sums in coding theory, cryptology and algorithms

Igor E. Shparlinski, I. Shparlinski, 2002 .

Security of the most significant bits of the Shamir message passing scheme

María Isabel González Vasco, I. Shparlinski, 2002, Math. Comput..

On the Security of Diffie-Hellman Bits

Igor E. Shparlinski, María Isabel González Vasco, Maria Isabel Gonzalez Vasco, 2000, Electron. Colloquium Comput. Complex..

Sums of algebraic trace functions twisted by arithmetic functions

I. Shparlinski, M. Korolev, 2018 .

Arithmetic properties of φ(n)/λ(n) and the structure of the multiplicative group modulo n

F. Luca, W. Banks, I. Shparlinski, 2006 .

Prime divisors of sparse integers

Igor E. Shparlinski, I. Shparlinski, 2003, Period. Math. Hung..

On a ternary quadratic form over primes

I. Shparlinski, É. Fouvry, 2011 .

Almost primes of the form ⌊pc⌋

Victor Z. Guo, W. Banks, I. Shparlinski, 2016 .

Piatetski-Shapiro sequences

W. Banks, I. Shparlinski, R. Baker, 2012, 1203.5884.

Constructions of Approximately Mutually Unbiased Bases

Igor E. Shparlinski, Arne Winterhof, I. Shparlinski, 2006, LATIN.

On the Multidimensional Distribution of the Naor-Reingold Pseudo-Random Function

Igor E. Shparlinski, Huaxiong Wang, San Ling, 2014, Math. Comput..

Cryptographic applications of analytic number theory - complexity lower bounds and pseudorandomness

Igor E. Shparlinski, I. Shparlinski, 2003, Progress in computer science and applied logic.

On the Naor–Reingold Pseudo-Random Function from Elliptic Curves

Igor E. Shparlinski, I. Shparlinski, 2000, Applicable Algebra in Engineering, Communication and Computing.

Non-linear Complexity of the Naor-Reingold Pseudo-random Function

Igor E. Shparlinski, William D. Banks, Daniel Lieman, 1999, ICISC.

On the distribution of values and zeros of polynomial systems over arbitrary sets

I. Shparlinski, Bryce Kerr, 2012, 1210.6721.

On Polynomial Representations of Boolean Functions Related to Some Number Theoretic Problems

Erion Plaku, Igor Shparlinski, E. Plaku, 2001, FSTTCS.

Energy bounds, bilinear forms and their applications in function fields

I. Shparlinski, Christopher d. Bagshaw, 2022, Finite Fields Their Appl..

On the average value of divisor sums in arithmetic progressions

W. Banks, I. Shparlinski, Roger Heath-Brown, 2005 .

On multiplicatively dependent vectors of algebraic numbers

I. Shparlinski, C. Stewart, F. Pappalardi, 2016, 1606.02874.

Zero testing of p-adic and modular polynomials

Marek Karpinski, Igor E. Shparlinski, Alfred J. van der Poorten, 2000, Theor. Comput. Sci..

Pointwise and correlation bounds on Dedekind sums over small subgroups

I. Shparlinski, Marc Munsch, Bence Borda, 2023, 2305.04304.

On the value set of Fermat quotients

Igor E. Shparlinski, I. Shparlinski, 2012 .

Character sums with fermat quotients

Igor E. Shparlinski, I. Shparlinski, 2011 .

On reducing a system of equations to a single equation

Igor E. Shparlinski, Gudmund Skovbjerg Frandsen, I. Shparlinski, 2004, ISSAC '04.

SOME DIVISIBILITY PROPERTIES OF THE EULER FUNCTION

F. Luca, W. Banks, I. Shparlinski, 2005, Glasgow Mathematical Journal.

On Some Approximation Problems Concerning Sparse Polynomials over Finite Fields

Marek Karpinski, Igor E. Shparlinski, I. Shparlinski, 1996, Theor. Comput. Sci..

Distribution of Elements of Cosets of Small Subgroups and Applications

Igor E. Shparlinski, Jean Bourgain, J. Bourgain, 2011, 1103.0567.

EXPANSION OF ORBITS OF SOME DYNAMICAL SYSTEMS OVER FINITE FIELDS

I. Shparlinski, J. Gutierrez, 2010, Bulletin of the Australian Mathematical Society.

Bounds on the Fourier coefficients of the weighted sum function

Igor E. Shparlinski, I. Shparlinski, 2007, Inf. Process. Lett..

New Results on the Hardness of Diffie-Hellman Bits

Igor E. Shparlinski, Mats Näslund, María Isabel González Vasco, 2004, Public Key Cryptography.

On the Uniformity of Distribution of the Naor-Reingold Pseudo-Random Function

Igor E. Shparlinski, I. Shparlinski, 2001 .

On a New Exponential Sum

Igor E. Shparlinski, Daniel Lieman, I. Shparlinski, 2001, Canadian Mathematical Bulletin.

On the Distribution of Diffie-Hellman Triples with Sparse Exponents

Igor E. Shparlinski, John B. Friedlander, I. Shparlinski, 2001, SIAM J. Discret. Math..

Double exponential sums over thin sets

Igor E. Shparlinski, John B. Friedlander, I. Shparlinski, 2000 .

Order of torsion for reduction of linearly independent points for a family of Drinfeld modules

Igor Shparlinski, Dragos Ghioca, I. Shparlinski, 2021, Journal of Number Theory.

Geometric properties of points on modular hyperbolas

I. Shparlinski, Mizan R. Khan, Kevin Ford, 2010 .

Sums of inverses in thin sets of finite fields

I. Shparlinski, Ana Zumalac'arregui, 2016, 1611.07647.

Polynomial Values in Small Subgroups of Finite Fields

Igor E. Shparlinski, I. Shparlinski, 2014, 1401.0964.

Subgroups generated by rational functions in finite fields

Igor E. Shparlinski, Domingo Gómez-Pérez, I. Shparlinski, 2013, 1309.7378.

INTEGERS WITH A LARGE SMOOTH DIVISOR

W. Banks, I. Shparlinski, 2006, math/0601460.

Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators

DOMINGO GÓMEZ-PÉREZ, ALINA OSTAFE, IGOR SHPARLINSKI, 2013, Math. Comput..

On the Average Distribution of Inversive Pseudorandom Numbers

Igor E. Shparlinski, Harald Niederreiter, H. Niederreiter, 2002 .

Statistics of ranks, determinants and characteristic polynomials of rational matrices

I. Shparlinski, Alina Ostafe, Vivian Kuperberg, 2024, 2401.10086.