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Igor SHPARLINSKI
Igor Shparlinski
MANUSCRIPTS AND PUBLICATIONS
Books

Computational and algorithmic problems in
finite fields, Kluwer AP, 1992.
 (with
A. J. van der Poorten and
H. G. Zimmer, Editors)
Proceedings of The Conference on Number Theoretic and Algebraic Methods in
Computer Science,
World Scientific, 1995.
 Finite fields:
Theory and computation, Kluwer Academic Publishers, 1999.
 Number theoretic
methods in cryptography: Complexity
lower bounds,
Birkhauser, 1999.
 (with S. V. Konyagin)
Character sums with exponential functions and their applications,
Cambridge Univ. Press, Cambridge, 1999.
 (with K.Y. Lam, H. Wang and C. Xing, Editors)
Proc. Workshop on Cryptography and Computational Number Theory
(CCNT'99), Singapore, Birkhauser, 2001.
 (with S.
Boztas, Editors)
Proc. 14th Symp. on Appl. Algebra, Algebraic Algorithms and ErrorCorrecting
Codes, Melbourne, SpringerVerlag, Berlin, 2001.
 Cryptographic
applications of analytic number theory, Birkhauser, 2003.
 (with G. Everest, A. J. van der Poorten and T. Ward )
Recurrence
sequences, Amer. Math. Soc., 2003.
 (with G. L. Mullen and D. Panario, Editors)
Finite fields and applications, Amer. Math. Soc., 2008.
 (with G. McGuire, G. L. Mullen and D. Panario, Editors)
Finite fields: Theory and applications, Amer. Math. Soc., 2010.
 (with J. Borwein and W. Zudilin, Editors)
Number theory and related fields,
Springer Proceedings in Mathematics & Statistics, vol. 43,
SpringerVerlag, Berlin, 2013.

(with D. Kohel, Editors)
Frobenius Distributions: LangTrotter and SatoTate Conjectures,
Amer. Math. Soc., 2016.
Journal and other Refereed Publications
Note:
The following cited journals in Russian have English
translations.
 Avtomatika i Telemechanika = Automatic Remote
Control
 Diskretnaja Matem. = Soviet Discrete Math.
 Izvestija Vyshich Uchebnyh Zavedeniy = Soviet
Math. Izv.
 Matem. Sbornik = Math. USSR Sbornik
 Matem. Zametki = Math. Notes
 Problemy Peredachi Inform. = Problems of
Information Transmission
 Sibirskiy Matem. Zhurnal = Siberian Math. J.
 Uspechi Matem. Nauk = Russian Math.
Surveys
 Zhurnal Vychisl. Matem. i Matem. Fiziki =
USSR Comp. Math. and Math. Phys.
 On the distribution of nonresidues and primitive roots in
recurrence sequences. Matem. Zametki, 1978, v.24, no.6,
603613 (in Russian).
 Bounds for exponential sums for recurrence sequences and their
applications. Izvestija Voronezhskogo Gosudarstvennogo Pedagog.
Inst., 1978, v.197, 7485 (in Russian).
 (with M. B. Levin) On uniform distribution of the fractional
parts of recurrence sequences. Uspechi Matem. Nauk, 1979, v.34,
no.3, 203204 (in Russian).
 On completely uniform distribution. Zhurnal Vychisl. Matem.
i Matem. Fiziki, 1979, v.19, no.5, 13301333 (in Russian).
 On prime divisors of recurrence sequences. Izvestija Vyshich
Uchebnych Zavedenii, 1980, no.4, 100103 (in Russian).
 Distribution of the fractional parts of recurrence sequences.
Zhurnal Vychisl. Matem. i Matem. Fiziki, 1981, v.21, no.6,
15881591 (in Russian).
 A bound for autocorrelation functions of pseudorandom matrices.
Proc. 8th AllUnion Conf. on Coding Theory and Information
Theory, Part 2. Kuibyshev, 1981, 188192 (in Russian).
 (with N. L. Novozhilov and V. V. Romanovcev) On modelling
with Markov chains.
Radioengineering and Electronics, 1982, v.27, no.2,
10411043 (in Russian).
 (with L. L. Kosachevskaja and V. V. Romanovcev) On some
iteration processes in the numerical solution of systems of linear
algebraic equations.
Zhurnal Vychisl. Matem. i Matem. Fiziki, 1982, v.22, no.6,
15041508 (in Russian).
 (with A. N. Vystavkin, L. L. Kosachevskaja and
V. V. Romanovcev) An integral interactive system of experimental data
deconvolution. Avtometrija,
1982, no.5, 35 (in Russian).
 (with A. N. Vystavkin, L. L. Kosachevskaja and
V. V. Romanovcev) A new improved algorithm for the iterative solution
of a system of linear algebraic equations. Computer Physics
Commun., 1982, v.27, 8789.
 On a property of the multiplicative generator of pseudorandom
numbers. Zhurnal Vychisl. Matem. i Matem. Fiziki, 1983, v.23,
no.1, 222223 (in Russian).
 (with A. N. Vystavkin, L. L. Kosachevskaja,
V. V. Romanovcev) On splinebased method for experimental data
deconvolution. Computer Physics Commun., 1983, v.29, 223230.
 On some properties of linear cyclic codes. Problemy Peredachi
Inform., 1983, v.19, no.3,
106110 (in Russian).
 On a bound of some sums with nonlinear recurrence sequences.
Proc. AllUnion Conf. on Transcendental Numbers and their Applications,
Moscow, 1983, 168169 (in Russian).
 (with L. L. Kosachevskaja) On the rate of convergence of some
iteration processes. Zhurnal Vychisl. Matem. i Matem.
Fiziki, 1984, v.24, no.3, 458461 (in Russian).
 On the rate of convergency of the Newton interpolation
process and the size of some codes. Uspechi Matem. Nauk, 1984, v.39, no.2, 205206 (in Russian).
 On the multiplicative generator of pseudorandom numbers.
Zhurnal Vychisl. Matem. i Matem. Fiziki, 1984, v.24, no.9,
14061408 (in Russian).
 (with L. L. Kosachevskaja, V. V. Romanovcev) On some
sequences of iterated parameters. Zhurnal Vychisl. Matem. i
Matem. Fiziki,
1985, v.25, no.1, 136140 (in Russian).
 On the choice of multiplier for the multiplicative generator
of pseudorandom numbers. Proc. 7 AllUnion Conf. on Monte
Carlo Methods in Comp. Math. and Math. Phys., Novosibirsk,
1985, 3134 (in Russian).
 On the number of prime divisors of recurrence sequences.
Matem. Zametki, 1985, v.35, no.1, 2934 (in Russian).
 On prime divisors of denominators of continues fractions.
Proc. AllUnion Conf. on Number Theory and Its Applications,
Tbilisi, 1985, 303305 (in Russian).
 Bounds for some arithmetic sums. Proc. AllUnion Conf. on
Number Theory and Its Applications, Tbilisi, 1985, 305307 (in Russian).
 On the coefficients of primitive polynomials. Matem. Zametki,
1985, v.38, no.6, 810815 (in Russian).
 On weigth enumerators of some codes. Problemy Peredachi
Inform., 1986, v.22, no.2, 4348 (in
Russian).
 On B_s sequences. Combin. Analysis, no.7. Moscow, Moscow
State University, 1986, 4245 (in Russian).
 On primitive polynomials. Problemy Peredachi Inform., 1987, v.23, no.3, 100103 (in Russian).
 On the number of different prime divisors of recurrence sequences.
Matem. Zametki, 1987, v.42, 494507 (in Russian).
 (with S. A. Stepanov) On the structural complexity of normal bases
of a finite field. Proc. Intern. Conf. on Fundamentals of Computation Theory,
Kazan, 1987, Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 1987, v.278,
414416.
 On the degree of the splitting field of a polynomial. Sibirskiy
Matem. Zhurnal, 1987, v.28,
no.5, 222223 (in Russian).
 (with S. A. Stepanov) On construction of a normal basis of a
finite field. Acta Arith., 1987, v.49, no.2, 189192 (in
Russian).
 On polynomials of a given height over finite fields. Matem.
Sbornik, 1988, v.135,
no.2, 253260 (in Russian).
 On residue classes modulo a prime in algebraic number fields.
Matem. Zametki, 1988, v.43, no.4, 433438 (in Russian).
 On a sequence of pseudorandom numbers. Avtomatika i
Telemechanika, 1988, no.8, 185188 (in Russian).
 (with S. A. Stepanov) On the complexity of constructing
a primitive normal basis. Proc. 9th AllUnion Conf. on Coding
Theory and Information Theory, Part 1. Odessa, 1988, 7981 (in
Russian).
 On finding irreducible polynomials over finite fields.
Proc. 9th AllUnion Conf. on Coding Theory and
Information Theory, Part 1. Odessa, 1988, 110113 (in Russian).
 On the distribution of the fractional parts of recurrence
sequences. Developments in Number Theory, no.10. Saratov,
1988, 111120 (in Russian).
 On the dimension of BCH codes. Problemy Peredachi Inform.,
1989, v.25, no.1, 100103 (in Russian).
 On the distribution of primitive and irreducible polynomials
modulo a prime. Diskretnaja Matem., 1989, v.1, no.1, 117124
(in Russian).
 On the distribution of recurrence sequences. Problemy Peredachi
Inform., 1989, v.25, no.2, 4653 (in Russian).
 On arithmetical properties of normform equations. Uspechi
Matem. Nauk, 1989, v.44, no.3,
183184 (in Russian).
 (with S. A. Stepanov) On bounds for exponential sums with
rational and algebraic functions. Automorphic Functions and
Number Theory, Vladivostok, 1989, 518 (in Russian).
 (with S. A. Stepanov) On construction of a primitive normal
basis of a finite field. Mathem. Sbornik, 1989, v.180, no.8,
10671072 (in Russian).
 On some generalisations of Tchebyshev polynomials. Sibirskiy
Matem. Zhurnal, 1990, v.31, no.1, 217218 (in Russian).
 (with G. I. Perel'muter) On the distribution of primitive
roots in finite fields. Uspechi Matem. Nauk, 1990, v.45, no.1,
185186 (in Russian).
 On some arithmetic properties of recurrence sequences. Matem.
Zametki, 1990, v.47, no.6, 134141 (in Russian).
 (with A. N. Skorobogatov) Exponential sums and rational
points on complete intersections. Mathematika, 1990, v.37,
201208.
 (with S. A. Stepanov) Estimates of an incomplete sum of
multiplicative characters of polynomials.
Diskretnaja Matem., 1990, v.2, no.3, 115119
(in Russian).
 On primitive elements in finite fields and on elliptic curves.
Matem. Sbornik, 1990, v.181, no.9, 11961206 (in Russian).
 On polynomial congruences. Acta Arith., 1991, v.58, 153156.
 On the distribution of recurring sequences and Bell numbers
in finite fields. Europ. J. Combin., 1991, v.12, 8187.
 On bounds for Gaussian sums. Matem. Zametki, 1991, v.50,
no.1, 122130 (in Russian).
 (with S. A. Stepanov) On construction of primitive elements and
primitive normal bases in a finite field. Proc. Colloq. on
Computational Number Theory, Debrecen, 1989, Walter de Gruyter, 1991,
124.
 On some problems in the theory of finite fields.
Uspechi Matem. Nauk, 1991, v.46, no.1, 165200 (in Russian).
 (with V. I. Galiev and A. F. Polupanov) On the construction
of solutions of systems of linear ordinary differential equations
in the neighbourhood of a regular singularity. J. of Comp.
and Appl. Math., 1992, v.39, 151163.
 On Gaussian sums for finite fields and elliptic curves.
Proc. SovietFrench Workshop on Algebraic Coding Theory,
Paris, 1991, Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 1992, v.573, 515.
 (with A. J. van der Poorten) On zeros of exponential
polynomials and related questions. Bull. Aust. Math. Soc.,
1992, v.46, 399410.
 (with M. A. Tsfasman and S. G. Vladut) Curves with many
points and multiplication in finite fields (after Chudnovsky &
Chudnovsky). Proc. Intern. Workshop on Coding Theory and Algebraic Geometry,
Luminy, 1991, Lect. Notes in Math., SpringerVerlag, Berlin, 1992, v.1518, 145169.
 A deterministic test for permutation polynomials.
Computational Complexity, 1992, v.2, 129132.
 (with V. I. Galiev and A. F. Polupanov) Distances from the
differences of roots of polynomials to the nearest integers.
Inform. Proc. Letters, 1992, v.43, 143146.
 (with S. A. Stepanov) On normal bases of algebraic number
fields. Proc. Conf. on Analytic and Probabilistic Methods
in Number Theory, Palanga, 1991. Intern. Sci.
Publ., the Netherlands, 1992, 369378.
 On bivariate polynomial factorization over finite fields.
Math. Comp., 1993, v.60, no.202, 787791.
 On parameters of some graphs from finite fields. Europ.
J. Combin., 1993, v.14, 589591.
 (with G. L. Mullen) On values of linear recurring sequences
of vectors over finite fields. Acta Arith., 1993, v.65,
no.1, 221226.
 Finding irreducible and primitive polynomials. Appl.
Algebra in Engin., Commun. and Computing, 1993, v.4, 263268.
 On some applications of finitely generated semigroups.
Proc. Algorithmic Number Theory Symposium, Ithaca, 1994,
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 1994, v.877, 265279.
 On some characteristics of uniformity of
distribution and their applications. Proc. 2nd Conf. on
Computational Algebra and Number Theory. Sydney, 1993, Kluwer Acad. Publ, 1995,
119136.
 (with F. Pappalardi) On Artin's conjecture over function
fields. Finite Fields and Their Appl., 1995, v.1, 399404.
 (with A. J. van der Poorten) On sequences of
polynomials defined by certain recurrence relations.
Acta. Math. Scient., 1995, v.61, 77103.
 (with M. Karpinski) On some approximation problems
concerning sparse polynomials over finite fields.
Theor. Comp. Sci., 1996, v.157, 259266.
 On finding primitive roots in finite fields.
Theor. Comp. Sci., 1996, v.157, 273275.
 (with G. R. Everest) Divisor sums of generalised
exponential polynomials. Canad. Math. Bull., 1996,
v.53, p.3546.
 (with G. L. Mullen)
Open problems in finite fields.
Proc. 3rd Conf. on
Finite Fields and Appl., Glasgow, 1995, London Math. Soc., Lect. Note Series, 1996, v.233, 243268.

Approximate constructions in
finite fields. Proc. 3rd Conf. on
Finite Fields and Appl., Glasgow, 1995, London Math. Soc., Lect. Note Series, 1996,
v.233, 313332.
 (with A. J. van der Poorten) On linear recurrence sequences
with polynomial coefficients. Glasgow Math. J., 1996,
v.38, 147155

On exponential sums with sparse polynomials and rational functions. J.
Number Theory, 1996, v.60, 233244.
 (with J. von zur Gathen and M. Karpinski)
Counting points on
curves over finite fields. Comput.
Complexity, 1996, v.6, 6499. Preliminary version in
Proc. 25th ACM Symp. on Theory of Comput., San Diego, 1993,
ACM Press, 1993, 805812.

On irreducible polynomials of small height in finite fields.
Appl. Algebra in Engin., Commun. and Computing , 1996, v.4,
427431.
 (with J. von zur Gathen)
Orders of Gauss periods in finite
fields. Appl.
Algebra in Engin., Commun. and Computing,
1998, v.9, 1524. Preliminary version in
Proc. 6th Intern. Symp. on Algorithms and Computation, Cairns, 1995
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 1995, v.1004, 208215.
 (with J. von zur Gathen)
Computing components and projections of curves over finite
fields. SIAM J. Comp., 1998, v.28, 822840.
Preliminary version in
Proc. 5th Intern. Symp. on Algorithms and Computation, Beijing, 1994,
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 1994, v.834,
297305.
 (with G. R. Everest) Counting the values taken by
algebraic exponential polynomials. Proc. Amer. Math. Soc., 1999, v.127,
665675.
 (with J. B. Friedlander, M. Larsen and M. Lieman)
On the correlation
of binary M sequences. Designs, Codes and Cryptography,
1999, v.16, 249256.
 (with A. Bernasconi)
Circuit
complexity of testing squarefree numbers. Proc. 16th Annual Symposium on Theoretical Aspects of Comp. Sci., Trier, 1999,
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 1999, v.1563, 4756.
 (with H. Niederreiter) On the distribution and lattice structure of
nonlinear congruential pseudorandom numbers.
Finite Fields and Their Appl.,
1999, v.5, 246253.
 (with J. B. Friedlander and D. Lieman)
On the
distribution of the RSA generator. Proc. Intern. Conf.
on Sequences and Their Applications, (SETA'98), Singapore,
SpringerVerlag, London, 1999, 205212.
 (J.Y. Cai, G. Havas, B. Mans, A. Nerurkar and J.P. Seifert) On routing in
circulant graphs. Proc. 5th Intern. Computing and Combinatorics Conf., Tokyo, 1999,
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 1999, v.1627, 360369.
 (with A. Bernasconi and C. Damm) On the average sensitivity of
testing squarefree numbers. Proc. 5th Intern. Computing and Combinatorics Conf., Tokyo,
1999, Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 1999, v.1627, 291299.
 (with F. Griffin and H. Niederreiter) On the distribution
of nonlinear recursive congruential pseudorandom numbers of higher orders.
Proc. 13th Symp. on Appl. Algebra, Algebraic Algorithms,
and ErrorCorrecting Codes, Hawaii,
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 1999, v.1719, 8793.
 (with J. von zur Gathen) Constructing elements of
large order in finite fields and Gauss
periods. Proc. 13th Symp. on Appl. Algebra, Algebraic Algorithms,
and ErrorCorrecting Codes, Hawaii,
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 1999, v.1719, 404409.
 (with M. Karpinski) On computational hardness of
testing squarefreeness of sparse polynomials. Proc. 13th Symp. on Appl.
Algebra, Algebraic Algorithms, and ErrorCorrecting Codes,
Hawaii,
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 1999, v.1719, 492497.
 (with F. Griffin) On the linear complexity of the
NaorReingold pseudorandom pseudorandom function.
Proc. 2nd Intern. Conf. on Information and Communication Security,
Sydney, 1999, Lect. Notes in
Comp. Sci., SpringerVerlag, Berlin, 1999, v.1726, 301308.
 (with J. von zur Gathen) The CREW PRAM complexity of
modular inversion. SIAM J. Comp., 1999, v.29, 18391857.
Preliminary version in Proc. the 3rd Latin American Theoretical Informatics
Conf., Campinas, 1998, Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 1998, v.1380,
305315.
 (with R. Canetti and J. B. Friedlander) On certain exponential
sums and the distribution of DiffieHellman triples.
J. London Math. Soc., 1999, v.59, 799812.
 (with D. Grant, K. Krastev and D. Lieman)
A public key cryptosystem based on sparse polynomials,
Proc. International
Conf. on Coding Theory, Cryptography and
Related Areas, Guanajuato, 1998, SpringerVerlag, Berlin, 2000, 114121.
 (with J. Gutierrez and H. Niederreiter) On the multidimensional distribution
of nonlinear congruential pseudorandom
numbers in parts of the period, Monatsh. Math., 2000, v.129, 3136.
 (with D. Coppersmith)
On polynomial approximation of the
discrete logarithm and the DiffieHellman mapping.
J. Cryptology, 2000, v.13, 339360.
 (with W. D. Banks and D. Lieman) An identification scheme based on sparse
polynomials. Proc. 2nd Intern. Conf.
on Information and Communication Security, Melbourne, 2000,
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 2000, v.1751, 6874.
 (with H. Niederreiter) Exponential sums
and the distribution of inversive congruential pseudorandom
numbers with primepower modulus. Acta Arith.,
2000, v.92, 8998.
 (with H. Niederreiter) On the distribution of
pseudorandom numbers and vectors generated by
inversive methods, Appl.
Algebra in Engin., Commun. and Computing 2000, v.10, 189202.
 Communication complexity and Fourier coefficients
of the DiffieHellman key. Proc. the 4th Latin American Theoretical
Informatics Conf. Punta del Este, 2000,
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 2000, v.1776, 259268.
 (with W. D. Banks, F. Griffin and D. Lieman)
Nonlinear complexity of the NaorReingold
pseudorandom function. Proc. the 2nd Intern. Conf. on Information
Security and Cryptology, Seoul, 1999,
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 2000, v.1787, 5359.
 Computing Jacobi symbols modulo sparse
integers and polynomials and some
applications. J. Algorithms, 2000, v.36, 241252.
 On the
NaorReingold pseudorandom function from elliptic curves, Appl.
Algebra in Engin., Commun. and Computing, 2000, v.11, 2734.
 (with F. Griffin)
On the linear complexity profile of the power
generator. IEEE Trans. Inform. Theory, 2000, v.46, 21592162.
 (with A. Bernasconi and C. Damm) The average sensitivity
of squarefreeness. Comput. Complexity, 2000, v.9, 3951.
 (with D. Kohel) Exponential sums and
group generators for elliptic curves over finite fields.
Proc. Algorithmic Number Theory Symposium,
Leiden, 2000, Lect. Notes in Comp. Sci.,
SpringerVerlag, Berlin, 2000, v.1838, 395404.
 (with W. D. Banks and D. Lieman) An extremely small
and efficient identification scheme. Proc. 5th Aust. Conf. on Information
Security and Privacy, Brisbane, 2000, Lect. Notes in Comp. Sci.,
SpringerVerlag, Berlin, 2000, v.1841, 378384.
 Linear complexity of the
NaorReingold pseudorandom function.
Inform. Proc. Letters, 2000, v.95, 9599.
 (with R. Canetti, J. B. Friedlander, S. V. Konyagin, M. Larsen and D.
Lieman) On the statistical properties of DiffieHellman
distributions.
Israel J. Math., 2000, v.120, 2346.
 (with M. Karpinski and A. J. van der Poorten) Zero testing of
p adic and modular polynomials.
Theor. Comput. Sci., 1999, v.233, 309317.
 (with J. B. Friedlander and J. Hansen) On character sums with exponential functions.
Mathematika,
2000, v.47, 7585.
 (with J. B. Friedlander and C. Pomerance) Small
values of the Carmichael function and cryptographic
applications. Proc. Workshop on Cryptography and Computational Number Theory
Singapore, 1999, Birkhauser, 2001, 2532.
 (with P. Q. Nguyen and J. Stern)
Distribution of modular sums and the security of the server aided exponentiation.
Proc. Workshop on Cryptography and Computational Number Theory
Singapore, 1999, Birkhauser, 2001, 257268.
 (with M. I. Gonzalez Vasco)
On the security of DiffieHellman
bits. Proc. Workshop on Cryptography and Computational Number Theory
Singapore, 1999, Birkhauser, 2001, 331342.
 (with A. K. Lenstra) On the security of Lenstra's variant of DSA without long
inversions. Proc. Intern. Workshop on Practice and Theory in
Public Key Cryptography, Korea, 2001, Lect. Notes in Comp. Sci.,
SpringerVerlag, Berlin, 2001, v.1992, 6472.
 (with J. B. Friedlander)
Double exponential sums over thin sets.
Proc. Amer. Math. Soc., 2001, v.129, 16171621.
 (with W. D. Banks, D. Lieman and V. T. To)
Cryptographic applications of sparse polynomials over finite rings.
Proc. the 2nd Intern. Conf. on Information
Security and Cryptology, Korea, 2000,
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 2001, v.2015, 206220.
 (with J. B. Friedlander) On the distribution of
DiffieHellman triples with sparse exponents. SIAM J. Discr. Math.,
2001, v.14, 162169.
 (with E. Allender and M. Saks)
A lower bound for primality.
J. of Comp. and Syst. Sci., 2001, v.62, 356366.
Preliminary version in Proc. 14th IEEE Conf. on Comp. Compl.,
Atlanta, 1999, IEEE Press, 1999, 1014.
 (with D. Lieman) On a new exponential sum.
Canad. Math. Bull., 2001, v.44, 8792.
 On the uniformity of distribution of the RSA pairs.
Math. Comp. 2001, v.70, 801808.
 (with J. von zur Gathen) Gauss periods in finite
fields. Proc. 5th Conf. on
Finite Fields and Appl., Augsburg, 1999,
SpringerVerlag, Berlin, 2001, 162177.

On the
linear complexity of the power generator. Designs, Codes and
Cryptography, 2001, v.23, 510.
 On the uniformity of distribution of the
NaorReingold pseudorandom function.
Finite Fields and Their Appl., 2001, v.7, 318326.
 On the multiplicative orders of gamma and gamma +
gamma^{1} over finite fields.
Finite Fields and Their Appl., 2001, v.7, 327331.
 On some properties of the shrinking generator.
Designs, Codes and Cryptography, 2001, v.23, 147156.
 Sparse polynomial approximation in finite fields,
Proc. 33rd ACM Symp. on Theory of Comput., Crete, Greece, July 68, 2001,
209215.
 (with E. El Mahassni) Polynomial representations of
the DiffieHellman mapping, Bull. Aust. Math. Soc., 2001, v.63,
467473.
 (with E. El Mahassni) On some uniformity of
distribution properties of ESIGN. Proc. Intern. Workshop on Coding and
Cryptography, INRIA, Paris 2001, 189196.
 (with H. Niederreiter) On the distribution of inversive congruential
pseudorandom numbers in parts of the period. Math. Comp.,
2001, v.70, 15691574.
 (with J. B. Friedlander)
On the distribution of the power generator.
Math. Comp., 2001, v.70, 15751589.
 (with J. B. Friedlander and C. Pomerance) Period of
the power generator and small values of Carmichael's function.
Math. Comp., 2001, v.70, 15911605.
 (with S. Cohen, H. Niederreiter and M. Zieve) Incomplete character sums and a
special class of permutations. J. Theorie des Nombres Bordeaux, 2001,
v.13, 5363.
 (with A. Bernasconi and C. Damm) Circuit and decision tree complexity of
some number theoretic problems, Information and Computation, 2001,
v.168, 113124.
 (with D. Boneh)
On the unpredictability of bits of the elliptic curve
DiffieHellman scheme. Proc. Crypto'2001,
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin,
2001, v.2139, 201212.
 (with J. H. Silverman)
On the linear complexity of the NaorReingold pseudorandom
function from elliptic curves.
Designs, Codes and Cryptography, 2001, v.243, 279289.
 (with E. El Mahassni and P. Q. Nguyen) The insecurity of
NybergRueppel and other DSAlike
signature schemes with partially known nonces
Proc. Workshop on Lattices and Cryptography, Boston, MA, 2001,
Lect. Notes in Comp. Sci.,
SpringerVerlag, Berlin, 2001, v.2146, 97109.
 On the generalised hidden number problem and
bit security of XTR. Proc. 14th Symp. on Appl. Algebra,
Algebraic Algorithms,
and ErrorCorrecting Codes, Melbourne,
Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 2001, v.2227, 268277.
 (with P. Q. Nguyen) On the insecurity of a
serveraided RSA protocol, Proc. Asiacrypt'2001,
Gold Coast,
Australia, Lect. Notes in Comp. Sci.,
SpringerVerlag, Berlin, 2001, v.2248, 2135.
 (with E. Plaku) On polynomial representations of Boolean functions
related to some number theoretic problems.
Proc. 21st Conf. on Found. of Software Technology
and Theor. Comp. Sci., Bangalore,
India, 2001, Lect. Notes in Comp. Sci.,
SpringerVerlag, Berlin, 2001, v.2245, 305316.
 (with W. D. Banks)
Distribution of inverses in polynomial rings.
Indag. Math., 2001, v.12, 303315.
 (with M. I. Gonzalez Vasco)
Security of the most significant bits of the Shamir message
passing scheme. Math. Comp., 2002, v.71, 333342.
 (with E. El Mahassni) On the uniformity of distribution of congruential
generators over elliptic curves. Proc. Intern. Conf. on Sequences and
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Uniform distribution of the fractional part of the
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Prime divisors of palindromes.
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Some divisibility properties of the Euler function.
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Finding the group structure of
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Prime divisors of shifted factorials,
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Noisy interpolation of sparse
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Complexity of inverting the Euler function.
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Incomplete exponential sums and DiffieHellman triples.
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Double character sums over elliptic curves and finite fields.
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Multiplicative character sums with
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 On the Erdos distance problem over finite fields.
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Catalan and Apery numbers in residue classes.
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Distribution of harmonic sums and Bernoulli polynomials
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Character sums and nonlinear recurrence sequences.
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Distribution of nonlinear
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IEEE Trans. Inform. Theory,
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Short character sums with Beatty sequences.
Math. Res. Letters, 2006, v.13, 539547.
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Nonresidues and primitive roots in Beatty sequences.
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GCD of random linear combinations.
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Congruences and exponential sums with the Euler function.
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Average value of the Euler function on binary palindromes.
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Group structure of elliptic curves over
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Topics in Geometry, Coding Theory and Cryptography,
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Approximating positive reals by ratios of
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Pseudoprime values of the Fibonacci
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Common divisors of the Euler function
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Prime divisors in Beatty sequences.
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Elliptic curves over finite fields:
Number theoretic and cryptographic aspects.
Advances in Applied Mathematics, Modeling, and Computational Science ,
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Experimental Math, (to appear).
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