# Igor Shparlinski MANUSCRIPTS AND PUBLICATIONS

## Books

1. Computational and algorithmic problems in finite fields, Kluwer AP, 1992.
2. (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.
3. Finite fields: Theory and computation, Kluwer Academic Publishers, 1999.
4. Number theoretic methods in cryptography: Complexity lower bounds, Birkhauser, 1999.
5. (with S. V. Konyagin) Character sums with exponential functions and their applications, Cambridge Univ. Press, Cambridge, 1999.
6. (with K.-Y. Lam, H. Wang and C. Xing, Editors) Proc. Workshop on Cryptography and Computational Number Theory (CCNT'99), Singapore, Birkhauser, 2001.
7. (with S. Boztas, Editors) Proc. 14th Symp. on Appl. Algebra, Algebraic Algorithms and Error-Correcting Codes, Melbourne, Springer-Verlag, Berlin, 2001.
8. Cryptographic applications of analytic number theory, Birkhauser, 2003.
9. (with G. Everest, A. J. van der Poorten and T. Ward ) Recurrence sequences, Amer. Math. Soc., 2003.
10. (with G. L. Mullen and D. Panario, Editors) Finite fields and applications, Amer. Math. Soc., 2008.
11. (with G. McGuire, G. L. Mullen and D. Panario, Editors) Finite fields: Theory and applications, Amer. Math. Soc., 2010.
12. (with J. Borwein and W. Zudilin, Editors) Number theory and related fields, Springer Proceedings in Mathematics \& Statistics, vol. 43, Springer-Verlag, Berlin, 2013.

## 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.
1. On the distribution of nonresidues and primitive roots in recurrence sequences. Matem. Zametki, 1978, v.24, no.6, 603-613 (in Russian).
2. Bounds for exponential sums for recurrence sequences and their applications. Izvestija Voronezhskogo Gosudarstvennogo Pedagog. Inst., 1978, v.197, 74-85 (in Russian).
3. (with M. B. Levin) On uniform distribution of the fractional parts of recurrence sequences. Uspechi Matem. Nauk, 1979, v.34, no.3, 203-204 (in Russian).
4. On completely uniform distribution. Zhurnal Vychisl. Matem. i Matem. Fiziki, 1979, v.19, no.5, 1330-1333 (in Russian).
5. On prime divisors of recurrence sequences. Izvestija Vyshich Uchebnych Zavedenii, 1980, no.4, 100-103 (in Russian).
6. Distribution of the fractional parts of recurrence sequences. Zhurnal Vychisl. Matem. i Matem. Fiziki, 1981, v.21, no.6, 1588-1591 (in Russian).
7. A bound for autocorrelation functions of pseudorandom matrices. Proc. 8th All-Union Conf. on Coding Theory and Information Theory, Part 2. Kuibyshev, 1981, 188-192 (in Russian).
8. (with N. L. Novozhilov and V. V. Romanovcev) On modelling with Markov chains. Radioengineering and Electronics, 1982, v.27, no.2, 1041-1043 (in Russian).
9. (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, 1504-1508 (in Russian).
10. (with A. N. Vystavkin, L. L. Kosachevskaja and V. V. Romanovcev) An integral interactive system of experimental data deconvolution. Avtometrija, 1982, no.5, 3-5 (in Russian).
11. (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, 87-89.
12. On a property of the multiplicative generator of pseudorandom numbers. Zhurnal Vychisl. Matem. i Matem. Fiziki, 1983, v.23, no.1, 222-223 (in Russian).
13. (with A. N. Vystavkin, L. L. Kosachevskaja, V. V. Romanovcev) On spline-based method for experimental data deconvolution. Computer Physics Commun., 1983, v.29, 223-230.
14. On some properties of linear cyclic codes. Problemy Peredachi Inform., 1983, v.19, no.3, 106-110 (in Russian).
15. On a bound of some sums with nonlinear recurrence sequences. Proc. All-Union Conf. on Transcendental Numbers and their Applications, Moscow, 1983, 168-169 (in Russian).
16. (with L. L. Kosachevskaja) On the rate of convergence of some iteration processes. Zhurnal Vychisl. Matem. i Matem. Fiziki, 1984, v.24, no.3, 458-461 (in Russian).
17. On the rate of convergency of the Newton interpolation process and the size of some codes. Uspechi Matem. Nauk, 1984, v.39, no.2, 205-206 (in Russian).
18. On the multiplicative generator of pseudorandom numbers. Zhurnal Vychisl. Matem. i Matem. Fiziki, 1984, v.24, no.9, 1406-1408 (in Russian).
19. (with L. L. Kosachevskaja, V. V. Romanovcev) On some sequences of iterated parameters. Zhurnal Vychisl. Matem. i Matem. Fiziki, 1985, v.25, no.1, 136-140 (in Russian).
20. On the choice of multiplier for the multiplicative generator of pseudorandom numbers. Proc. 7 All-Union Conf. on Monte Carlo Methods in Comp. Math. and Math. Phys., Novosibirsk, 1985, 31-34 (in Russian).
21. On the number of prime divisors of recurrence sequences. Matem. Zametki, 1985, 35, no.1, 29-34 (in Russian).
22. On prime divisors of denominators of continues fractions. Proc. All-Union Conf. on Number Theory and Its Applications, Tbilisi, 1985, 303-305 (in Russian).
23. Bounds for some arithmetic sums. Proc. All-Union Conf. on Number Theory and Its Applications, Tbilisi, 1985, 305-307.
24. On the coefficients of primitive polynomials. Matem. Zametki, 1985, v.38, no.6, 810-815 (in Russian).
25. On weigth enumerators of some codes. Problemy Peredachi Inform., 1986, v.22, no.2, 43-48 (in Russian).
26. On B_s sequences. Combin. Analysis, no.7. Moscow, Moscow State University, 1986, 42-45 (in Russian).
27. On primitive polynomials. Problemy Peredachi Inform., 1987, v.23, no.3, 100-103 (in Russian).
28. On the number of different prime divisors of recurrence sequences. Matem. Zametki, 1987, v.42, 494-507 (in Russian).
29. (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., Springer-Verlag, Berlin, 1987, v.278, 414-416.
30. On the degree of the splitting field of a polynomial. Sibirskiy Matem. Zhurnal, 1987, v.28, no.5, 222-223 (in Russian).
31. (with S. A. Stepanov) On construction of a normal basis of a finite field. Acta Arith., 1987, v.49, no.2, 189-192 (in Russian).
32. On polynomials of a given height over finite fields. Matem. Sbornik, 1988, v.135, no.2, 253-260 (in Russian).
33. On residue classes modulo a prime in algebraic number fields. Matem. Zametki, 1988, v.43, no.4, 433-438 (in Russian).
34. On a sequence of pseudorandom numbers. Avtomatika i Telemechanika, 1988, no.8, 185-188 (in Russian).
35. (with S. A. Stepanov) On the complexity of constructing a primitive normal basis. Proc. 9th All-Union Conf. on Coding Theory and Information Theory, Part 1. Odessa, 1988, 79-81 (in Russian).
36. On finding irreducible polynomials over finite fields. Proc. 9th All-Union Conf. on Coding Theory and Information Theory, Part 1. Odessa, 1988, 110-113 (in Russian).
37. On the distribution of the fractional parts of recurrence sequences. Developments in Number Theory, no.10. Saratov, 1988, 111-120 (in Russian).
38. On the dimension of BCH codes. Problemy Peredachi Inform., 1989, v.25, no.1, 100-103 (in Russian).
39. On the distribution of primitive and irreducible polynomials modulo a prime. Diskretnaja Matem., 1989, v.1, no.1, 117-124 (in Russian).
40. On the distribution of recurrence sequences. Problemy Peredachi Inform., 1989, v.25, no.2, 46-53 (in Russian).
41. On arithmetical properties of norm-form equations. Uspechi Matem. Nauk, 1989, v.44, no.3, 183-184 (in Russian).
42. (with S. A. Stepanov) On bounds for exponential sums with rational and algebraic functions. Automorphic Functions and Number Theory, Vladivostok, 1989, 5-18 (in Russian).
43. (with S. A. Stepanov) On construction of a primitive normal basis of a finite field. Mathem. Sbornik, 1989, v.180, no.8, 1067-1072 (in Russian).
44. On some generalisations of Tchebyshev polynomials. Sibirskiy Matem. Zhurnal, 1990, v.31, no.1, 217-218 (in Russian).
45. (with G. I. Perel'muter) On the distribution of primitive roots in finite fields. Uspechi Matem. Nauk, 1990, v.45, no.1, 185-186 (in Russian).
46. On some arithmetic properties of recurrence sequences. Matem. Zametki, 1990, v.47, no.6, 134-141 (in Russian).
47. (with A. N. Skorobogatov) Exponential sums and rational points on complete intersections. Mathematika, 1990, v.37, 201-208.
48. (with S. A. Stepanov) Estimates of an incomplete sum of multiplicative characters of polynomials. Diskretnaja Matem., 1990, v.2, no.3, 115-119 (in Russian).
49. On primitive elements in finite fields and on elliptic curves. Matem. Sbornik, 1990, v.181, no.9, 1196-1206 (in Russian).
50. On polynomial congruences. Acta Arith., 1991, v.58, 153-156.
51. On the distribution of recurring sequences and Bell numbers in finite fields. Europ. J. Combin., 1991, v.12, 81-87.
52. On bounds for Gaussian sums. Matem. Zametki, 1991, v.50, no.1, 122-130 (in Russian).
53. (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, 1-24.
54. On some problems in the theory of finite fields. Uspechi Matem. Nauk, 1991, v.46, no.1, 165-200 (in Russian).
55. (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, 151-163.
56. On Gaussian sums for finite fields and elliptic curves. Proc. Soviet-French Workshop on Algebraic Coding Theory, Paris, 1991, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1992, v.573, 5-15.
57. (with A. J. van der Poorten) On zeros of exponential polynomials and related questions. Bull. Aust. Math. Soc., 1992, v.46, 399-410.
58. (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., Springer-Verlag, Berlin, 1992, v.1518, 145-169.
59. A deterministic test for permutation polynomials. Computational Complexity, 1992, v.2, 129-132.
60. (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, 143-146.
61. (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, 369-378.
62. On bivariate polynomial factorization over finite fields. Math. Comp., 1993, v.60, no.202, 787-791.
63. On parameters of some graphs from finite fields. Europ. J. Combin., 1993, v.14, 589-591.
64. (with G. L. Mullen) On values of linear recurring sequences of vectors over finite fields. Acta Arith., 1993, v.65, no.1, 221-226.
65. Finding irreducible and primitive polynomials. Appl. Algebra in Engin., Commun. and Computing, 1993, v.4, 263-268.
66. On some applications of finitely generated semigroups. Proc. Algorithmic Number Theory Symposium, Ithaca, 1994, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1994, v.877, 265-279.
67. On some characteristics of uniformity of distribution and their applications. Proc. 2-nd Conf. on Computational Algebra and Number Theory. Sydney, 1993, Kluwer Acad. Publ, 1995, 119-136.
68. (with F. Pappalardi) On Artin's conjecture over function fields. Finite Fields and Their Appl., 1995, v.1, 399-404.
69. (with A. J. van der Poorten) On sequences of polynomials defined by certain recurrence relations. Acta. Math. Scient., 1995, v.61, 77-103.
70. (with M. Karpinski) On some approximation problems concerning sparse polynomials over finite fields. Theor. Comp. Sci., 1996, v.157, 259-266.
71. On finding primitive roots in finite fields. Theor. Comp. Sci., 1996, v.157, 273-275.
72. (with G. R. Everest) Divisor sums of generalised exponential polynomials. Canad. Math. Bull., 1996, v.53, p.35-46.
73. (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, 243-268.
74. Approximate constructions in finite fields. Proc. 3rd Conf. on Finite Fields and Appl., Glasgow, 1995, London Math. Soc., Lect. Note Series, 1996, v.233, 313-332.
75. (with A. J. van der Poorten) On linear recurrence sequences with polynomial coefficients. Glasgow Math. J., 1996, v.38, 147-155
76. On exponential sums with sparse polynomials and rational functions. J. Number Theory, 1996, v.60, 233-244.
77. (with J. von zur Gathen and M. Karpinski) Counting points on curves over finite fields. Comput. Complexity, 1996, v.6, 64-99. Preliminary version in Proc. 25th ACM Symp. on Theory of Comput., San Diego, 1993, ACM Press, 1993, 805-812.
78. On irreducible polynomials of small height in finite fields. Appl. Algebra in Engin., Commun. and Computing , 1996, v.4, 427-431.
79. (with J. von zur Gathen) Orders of Gauss periods in finite fields. Appl. Algebra in Engin., Commun. and Computing, 1998, v.9, 15-24. Preliminary version in Proc. 6th Intern. Symp. on Algorithms and Computation, Cairns, 1995 Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1995, v.1004, 208-215.
80. (with J. von zur Gathen) Computing components and projections of curves over finite fields. SIAM J. Comp., 1998, v.28, 822-840. Preliminary version in Proc. 5th Intern. Symp. on Algorithms and Computation, Beijing, 1994, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1994, v.834, 297-305.
81. (with G. R. Everest) Counting the values taken by algebraic exponential polynomials. Proc. Amer. Math. Soc., 1999, v.127, 665-675.
82. (with J. B. Friedlander, M. Larsen and M. Lieman) On the correlation of binary M -sequences. Designs, Codes and Cryptography, 1999, v.16, 249-256.
83. (with A. Bernasconi) Circuit complexity of testing square-free numbers. Proc. 16th Annual Symposium on Theoretical Aspects of Comp. Sci., Trier, 1999, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1999, v.1563, 47-56.
84. (with H. Niederreiter) On the distribution and lattice structure of nonlinear congruential pseudorandom numbers. Finite Fields and Their Appl., 1999, v.5, 246-253.
85. (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, Springer-Verlag, London, 1999, 205-212.
86. (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., Springer-Verlag, Berlin, 1999, v.1627, 360-369.
87. (with A. Bernasconi and C. Damm) On the average sensitivity of testing square-free numbers. Proc. 5th Intern. Computing and Combinatorics Conf., Tokyo, 1999, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1999, v.1627, 291-299.
88. (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 Error-Correcting Codes, Hawaii, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1999, v.1719, 87-93.
89. (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 Error-Correcting Codes, Hawaii, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1999, v.1719, 404-409.
90. (with M. Karpinski) On computational hardness of testing square-freeness of sparse polynomials. Proc. 13th Symp. on Appl. Algebra, Algebraic Algorithms, and Error-Correcting Codes, Hawaii, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1999, v.1719, 492-497.
91. (with F. Griffin) On the linear complexity of the Naor-Reingold pseudo-random pseudo-random function. Proc. 2nd Intern. Conf. on Information and Communication Security, Sydney, 1999, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1999, v.1726, 301-308.
92. (with J. von zur Gathen) The CREW PRAM complexity of modular inversion. SIAM J. Comp., 1999, v.29, 1839-1857. Preliminary version in Proc. the 3rd Latin American Theoretical Informatics Conference, Campinas, 1998, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1998, v.1380, 305-315.
93. (with R. Canetti and J. B. Friedlander) On certain exponential sums and the distribution of Diffie-Hellman triples. J. London Math. Soc., 1999, v.59, 799-812.
94. (with D. Grant, K. Krastev and D. Lieman) A public key cryptosystem based on sparse polynomials, Proc. International Conference on Coding Theory, Cryptography and Related Areas, Guanajuato, 1998, Springer-Verlag, Berlin, 2000, 114-121.
95. (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, 31-36.
96. (with D. Coppersmith) On polynomial approximation of the discrete logarithm and the Diffie-Hellman mapping. J. Cryptology, 2000, v.13, 339-360.
97. (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., Springer-Verlag, Berlin, 2000, v.1751, 68-74.
98. (with H. Niederreiter) Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus. Acta Arith., 2000, v.92, 89-98.
99. (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, 189-202.
100. Communication complexity and Fourier coefficients of the Diffie-Hellman key. Proc. the 4th Latin American Theoretical Informatics Conf. Punta del Este, 2000, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2000, v.1776, 259-268.
101. (with W. D. Banks, F. Griffin and D. Lieman) Non-linear complexity of the Naor-Reingold pseudo-random function. Proc. the 2nd Intern. Conf. on Information Security and Cryptology, Seoul, 1999, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2000, v.1787, 53-59.
102. Computing Jacobi symbols modulo sparse integers and polynomials and some applications. J. Algorithms, 2000, v.36, 241-252.
103. On the Naor-Reingold pseudo-random function from elliptic curves, Appl. Algebra in Engin., Commun. and Computing, 2000, v.11, 27-34.
104. (with F. Griffin) On the linear complexity profile of the power generator. IEEE Trans. Inform. Theory, 2000, v.46, 2159-2162.
105. (with A. Bernasconi and C. Damm) The average sensitivity of square-freeness. Comput. Complexity, 2000, v.9, 39-51.
106. (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., Springer-Verlag, Berlin, 2000, v.1838, 395-404.
107. (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., Springer-Verlag, Berlin, 2000, v.1841, 378-384.
108. Linear complexity of the Naor-Reingold pseudo-random function. Inform. Proc. Letters, 2000, v.95, 95-99.
109. (with R. Canetti, J. B. Friedlander, S. V. Konyagin, M. Larsen and D. Lieman) On the statistical properties of Diffie-Hellman distributions. Israel J. Math., 2000, v.120, 23-46.
110. (with M. Karpinski and A. J. van der Poorten) Zero testing of p -adic and modular polynomials. Theor. Comput. Sci., 1999, v.233, 309-317.
111. (with J. B. Friedlander and J. Hansen) On character sums with exponential functions. Mathematika, 2000, v.47, 75-85.
112. (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, 25-32.
113. (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, 257-268.
114. (with M. I. Gonzalez Vasco) On the security of Diffie-Hellman bits. Proc. Workshop on Cryptography and Computational Number Theory Singapore, 1999, Birkhauser, 2001, 331-342.
115. (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., Springer-Verlag, Berlin, 2001, v.1992, 64-72.
116. (with J. B. Friedlander) Double exponential sums over thin sets. Proc. Amer. Math. Soc., 2001, v.129, 1617-1621.
117. (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., Springer-Verlag, Berlin, 2001, v.2015, 206-220.
118. (with J. B. Friedlander) On the distribution of Diffie-Hellman triples with sparse exponents. SIAM J. Discr. Math., 2001, v.14, 162-169.
119. (with E. Allender and M. Saks) A lower bound for primality. J. of Comp. and Syst. Sci., 2001, v.62, 356-366. Preliminary version in Proc. 14th IEEE Conf. on Comp. Compl., Atlanta, 1999, IEEE Press, 1999, 10-14.
120. (with D. Lieman) On a new exponential sum. Canad. Math. Bull., 2001, v.44, 87-92.
121. On the uniformity of distribution of the RSA pairs. Math. Comp. 2001, v.70, 801-808.
122. (with J. von zur Gathen) Gauss periods in finite fields. Proc. 5th Conf. on Finite Fields and Appl., Augsburg, 1999, Springer-Verlag, Berlin, 2001, 162-177.
123. On the linear complexity of the power generator. Designs, Codes and Cryptography, 2001, v.23, 5-10.
124. On the uniformity of distribution of the Naor-Reingold pseudo-random function. Finite Fields and Their Appl., 2001, v.7, 318-326.
125. On the multiplicative orders of gamma and gamma + gamma^{-1} over finite fields. Finite Fields and Their Appl., 2001, v.7, 327-331.
126. On some properties of the shrinking generator. Designs, Codes and Cryptography, 2001, v.23, 147-156.
127. Sparse polynomial approximation in finite fields, Proc. 33rd ACM Symp. on Theory of Comput., Crete, Greece, July 6-8, 2001, 209-215.
128. (with E. El Mahassni) Polynomial representations of the Diffie-Hellman mapping, Bull. Aust. Math. Soc., 2001, v.63, 467-473.
129. (with E. El Mahassni) On some uniformity of distribution properties of ESIGN. Proc. Intern. Workshop on Coding and Cryptography, INRIA, Paris 2001, 189-196.
130. (with H. Niederreiter) On the distribution of inversive congruential pseudorandom numbers in parts of the period. Math. Comp., 2001, v.70, 1569-1574.
131. (with J. B. Friedlander) On the distribution of the power generator. Math. Comp., 2001, v.70, 1575-1589.
132. (with J. B. Friedlander and C. Pomerance) Period of the power generator and small values of Carmichael's function. Math. Comp., 2001, v.70, 1591-1605.
133. (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, 53-63.
134. (with A. Bernasconi and C. Damm) Circuit and decision tree complexity of some number theoretic problems, Information and Computation, 2001, v.168, 113-124.
135. (with D. Boneh) On the unpredictability of bits of the elliptic curve Diffie-Hellman scheme. Proc. Crypto'2001, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2001, v.2139, 201-212.
136. (with J. H. Silverman) On the linear complexity of the Naor-Reingold pseudo-random function from elliptic curves. Designs, Codes and Cryptography, 2001, v.243, 279-289.
137. (with E. El Mahassni and P. Q. Nguyen) The insecurity of Nyberg-Rueppel and other DSA-like signature schemes with partially known nonces Proc. Workshop on Lattices and Cryptography, Boston, MA, 2001, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2001, v.2146, 97-109.
138. On the generalised hidden number problem and bit security of XTR. Proc. 14th Symp. on Appl. Algebra, Algebraic Algorithms, and Error-Correcting Codes, Melbourne, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2001, v.2227, 268-277.
139. (with P. Q. Nguyen) On the insecurity of a server-aided RSA protocol, Proc. Asiacrypt'2001, Gold Coast, Australia, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2001, v.2248, 21-35.
140. (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., Springer-Verlag, Berlin, 2001, v.2245, 305-316.
141. (with W. D. Banks) Distribution of inverses in polynomial rings. Indag. Math., 2001, v.12, 303-315.
142. (with M. I. Gonzalez Vasco) Security of the most significant bits of the Shamir message passing scheme. Math. Comp., 2002, v.71, 333-342.
143. (with E. El Mahassni) On the uniformity of distribution of congruential generators over elliptic curves. Proc. Intern. Conf. on Sequences and their Applications (SETA'01), Bergen, Springer-Verlag, London, 2002, 257-264.
144. (with A. K. Lenstra) Selective forgery of RSA signatures with fixed-pattern padding. Proc. Intern. Workshop on Practice and Theory in Public Key Cryptography, Paris, 2002, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2002, v.2274, 228-236.
145. (with H. Niederreiter) Recent advances in the theory of nonlinear pseudorandom number generators. Proc. Conf. on Monte Carlo and Quasi-Monte Carlo Methods, 2000, Springer, Berlin., 2002, 86-102.
146. (with M. I. Gonzalez Vasco and M. Naslund) The hidden number problem in extension fields and its applications. Proc. the 5th Latin American Theoretical Informatics Conference, Cancun, 2002, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2002, v.2286, 105-117.
147. On the uniformity of distribution of the ElGamal signature. Appl. Algebra in Engin., Commun. and Computing, 2002, v.13, 9-16.
148. On the distribution of the Diffie-Hellman pairs. Finite Fields and Their Appl., 2002, v.8, 131-141.
149. Security of most significant bits of g^{x^2}, Inform. Proc. Letters, 2002, v.83, 109-113
150. (with B. Mans and F. Pappalardi) On the Adam conjecture on circulant graphs. Discrete Mathematics, 2002, v.254, 309-329. Preliminary version in Proc. of the 4th Annual International Computing and Combinatorics Conference, Taipei, 1998, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1998, v.1449, 251-260.
151. (with C. Pomerance) Smooth orders and cryptographic applications. Proc. Algorithmic Number Theory Symposium, Sydney, 2002, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2002, v.2369, 338-348.
152. (with R. Steinfeld) Chinese remaindering for algebraic numbers in a hidden field. Proc. Algorithmic Number Theory Symposium, Sydney, 2002, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2002, v.2369, 349-356.
153. (with P. Q. Nguyen) The insecurity of the Digital Signature Algorithm with partially known nonces. J. Cryptology, 2002, v.15, 151-176.
154. On a question of Erdos and Graham. Archiv Math., 2002, v.78, 445-448.
155. (with with W.-C. W. Li and M. Naslund) The hidden number problem with the trace and bit security of XTR and LUC. Proc. Crypto'2002, Santa Barbara, 2002, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2002, v.2442, 433-448.
156. Playing Hide-and-Seek'' in finite fields: Hidden number problem and its applications, Proc. 7th Spanish Meeting on Cryptology and Information Security, Univ. of Oviedo, 2002, 49-72.
157. (with W. D. Banks) On the number of sparse RSA exponents. J. Number Theory, 2002, v.95, 340-350.
158. (with H. Niederreiter) On the average distribution of inversive pseudorandom numbers. Finite Fields and Their Appl., 2002, v.8, 491-503.
159. (with E. El Mahassni) On the uniformity of distribution of the elliptic curve ElGamal signature. Finite Fields and Their Appl., 2002, v.8, 589-596.
160. Exponential sums and lattice reduction: Applications to cryptography, Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, Proc. 6th Conf. on Finite Fields and Appl., Oaxaca, 2001, Springer-Verlag, Berlin, 2002, 286-298.
161. (with J. B. Friedlander and S. V. Konyagin) Some doubly exponential sums over Z_m. Acta Arith., 2002, v.105, 349-370.
162. (with W. D. Banks) A variant of NTRU with non-invertible polynomials. Proc. Indocrypt'02, Hyderabad, India, 2002, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2002, v.2551, 62-70.
163. Exponential sums in coding theory, cryptology and algorithms. Coding Theory and Cryptology, World Scientific, 2002, 323-383.
164. (with W. D. Banks and A. Conflitti) Character sums over integers with restricted g-ary digits digits. Illinois J. Math., 2002, v.46, 819-836.
165. (with W. D. Banks) Average normalizations of elliptic curves. Bull. Aust. Math. Soc., 2002, v.66, 353-358.
166. (with B. Codenotti and A. Winterhof) Non-approximability of the permanent of structured matrices over finite fields, Comp. Compl., 2002, v.11, 158-170.
167. (with M. Naslund and W. Whyte) On the bit security of NTRU. Proc. Intern. Workshop on Public Key Cryptography, PKC'03, Miami, USA, 2003, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2003, v.2567, 62-70.
168. (with J. Gutierrez and A. Winterhof) On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators. IEEE Trans. Inform. Theory, 2003, v.49, 60-64.
169. (with V. Guruswami) Unconditional proof of tightness of Johnson bound. Proc. 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'03), Baltimore, MD, SIAM, 2003, 754-755.
170. (with T. Lange and S. V. Konyagin) Linear complexity of the discrete logarithm, Designs, Codes and Cryptography, 2003, v.28, 135-146.
171. (with J. von zur Gathen and A. Shokrollahi) An autentication scheme based on sparse polynomials. Proc. IEEE Inform. Theory Workshop, Paris, IEEE, 2003, 159-162.
172. (with H. Niederreiter) Dynamical systems generated by rational functions, Proc. 15th Symp. on Appl. Algebra, Algebraic Algorithms and Error-Correcting Codes, Toulouse, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2003, v.2643, 6-17.
173. (with N. A. Howgrave-Graham and P. Q. Nguyen) Hidden number problem with hidden multipliers, timed-release crypto and noisy exponentiation. Math. Comp., 2003, v.72, 1473-1485.
174. (with W. D. Banks and A. Harcharras) Short Kloosterman sums for polynomials over finite fields. Canad. J. Math., 2003, v.55, 225-246.
175. (with F. Luca) Average multiplicative orders of elements modulo n. Acta Arith., 2003, v.109, 387-411.
176. (with H. Niederreiter) On the distribution of power residues and primitive elements in some nonlinear recurring sequences. Bull. London Math. Soc., 2003, v.35, 522-528.
177. (with P. Q. Nguyen) The insecurity of the elliptic curve Digital Signature Algorithm with partially known nonces. Designs, Codes and Cryptography, 2003, v.30, 201-217.
178. (with J. von zur Gathen and A. Sinclair) Finding points on curves over finite fields. SIAM J. Comp., 2003, v.32, 1436-1448. Preliminary version in Proc. 36 IEEE Symposium on Foundations of Computer Science, Milwaulkee, 1995, IEEE Press, 1995, 284-292.
179. Prime divisors of sparse integers. Period. Math. Hungarica, 2003, v.46, 215-222.
180. (with F. Pappalardi and F. Saidak) Squarefree values of the Carmichael function. J. Number Theory, 2003, v.103, 122-131.
181. (with H. Niederreiter) Periodic sequences with maximal linear complexity and almost maximal k-error linear complexity. Proc. 9th IMA Intern. Conf on Cryptography and Coding, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2003, v.2898, 183-189.
182. (with S. R. Blackburn, D. Gomez-Perez and J. Gutierrez) Predicting the inversive generator. Proc. 9th IMA Intern. Conf on Cryptography and Coding, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2003, v.2898, 264-275.
183. (with M. Khan) On the maximal difference between an element and its inverse modulo n. Period. Math. Hungarica, 2003, v.47, 111-117.
184. (with E. Allender, A. Bernasconi, C. Damm, J. von zur Gathen and M. Saks) Complexity of some arithmetic problems for binary polynomials. Comp. Compl., 2003, v.12, 23-47.
185. Security of polynomial transformations of the Diffie-Hellman key. Finite Fields and Their Appl., 2004, v.10, 123-131.
186. (with W. D. Banks and A. Conflitti) Number theoretic designs for directed regular graphs of small diameter. SIAM J. Discr. Math., 2004, v.17, 377-383.
187. (with J. von zur Gathen) Polynomial interpolation from multiples, Proc. 15th ACM-SIAM Symposium on Discrete Algorithms, (SODA'04) New Orleans, LA, SIAM, 2004, 1125-1130.
188. (with W. D. Banks, A. Conflitti and J. B. Friedlander) Exponential sums with Mersenne numbers. Compos. Math., 2004, v.140, 15-30.
189. (with A. Conflitti) On the multidimensional distribution of the subset sum generator of pseudorandom numbers. Math. Comp., 2004, v.73, 1005-1011.
190. (with M. I. Gonzalez Vasco and M. N\"aslund) New results on the hardness of Diffie-Hellman bits. Proc. Intern. Workshop on Public Key Cryptography, Singapore, 2004, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, v.2947, 2004, 159-172.
191. (with A. Winterhof) A nonuniform algorithm for the hidden number problem in subgroups. Proc. Intern. Workshop on Public Key Cryptography, Singapore, 2004, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, v.2947, 2004, 416-424.
192. (with W. D. Banks) Arithmetic properties of numbers with restricted digits. Acta Arith., 2004, v.112, 313-332.
193. (with B. Mans) Bisecting and gossiping in circulant graphs. Proc. the 6th Latin American Theoretical Informatics Conference, Buenos Aires, 2004, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, v.2976, 2004, 589-598.
194. (with W. D. Banks, J. B. Friedlander and C. Pomerance) Multiplicative structure of values of the Euler function. High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams, Fields Institute Communications, v.41, Amer. Math. Soc., 2004, 29-48.
195. (with W. D. Banks) Congruences and exponential sums with the Euler function. High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams, Fields Institute Communications, v.41, Amer. Math. Soc., 2004, 49-60.
196. (with A. Russell) Classical and quantum algorithms for function reconstruction via character evaluation. J. Compl., 2004, v.20, 404-422.
197. (with R. Steinfeld) Noisy Chinese remaindering in the Lee norm. J. Compl., 2004, v.20, 423-437.
198. (with J. B. Friedlander and J. Hansen) On the distribution of the power generator modulo a prime power. Proc. DIMACS Workshop on Unusual Applications of Number Theory, 2000 Amer. Math. Soc., 2004, 71-79.
199. Bounds of Gauss sums in finite fields. Proc. Amer. Math. Soc., 2004, v.132, 2817-2824.
200. Exponential function analogue of Kloosterman sums. Rocky Mountain J. Math., 2004, v.34, 1497-1502.
201. (with S. D. Galbraith and H. J. Hopkins) Secure bilinear Diffie-Hellman bits. Proc. 9th Australasian Conference on Information Security and Privacy, Sydney, 2004, Springer-Verlag, Berlin, 2004, v.3108, 370-378.
202. (with G. S. Frandsen) On reducing systems of p -adic equations to one equation. Proc. Intern. Symp. on Symbolic and Algebraic Comp., Santander, 2004, 163-166.
203. (with W.-S. Chou) On the cycle structure of repeated exponentiation modulo a prime, J. Number Theory, 2004, v.107, 345-356.
204. Distribution of exponential functions with squarefull exponent in residue rings. Indag. Math., 2004, v.15, 283-289.
205. (with M. Goresky, A. Klapper and M. R. Murty) On decimations of l-sequences. SIAM J. Discr. Math., 2004, v.18, 130-140.
206. (with M. Z. Garaev and F. Luca) Character sums and congruences with n!. Trans. Amer. Math. Soc., 2004, v.356, 5089-5102.
207. On the uniformity of distribution of the decryption exponent in the fixed encryption exponent RSA. Inform. Proc. Letters, 2004, v.92, 143-147.
208. (with J. von zur Gathen, A. Knopfmacher, F. Luca and L. Lucht) Average order in cyclic groups. J. Theorie des Nombres Bordeaux, 2004, v.16, 107-123.
209. (with J. von zur Gathen) GCD of random linear forms, Proc. 15th Annual Symposium on Algorithms and Computation, Hong Kong, 2004, Hong Kong, 2004, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2004, v.3341, 455-460.
210. (with W. D. Banks and A. Harcharras) Smooth values of shifted primes in arithmetic progressions. Michigan Math. J., 2004, v.52, 603-618.
211. (with F. Luca and D. J. Mireles) MOV attack in various subgroups on elliptic curves. Illinois J. Math., 2004, v.48, 1041-1052.
212. (with M. Dewar and D. Panario) Distribution of exponential functions with k -full exponent modulo a prime, Indag. Math., 2004, v.15, 497-503.
213. (with J. von zur Gathen) Predicting subset sum pseudorandom number generators. Proc. 11th Workshop on Selected Areas in Cryptography, Waterloo, 2004, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2005, v.3357, 241-251.
214. (with W. D. Banks and R. Heath-Brown) On the average value of divisor sums in arithmetic progressions. Intern. Math. Research Notices, 2005, no.1, 1-25.
215. (with G. R. Everest) Prime divisors of sequences associated to elliptic curves. Glasgow Math. J., 2005, v.47, 115-122.
216. (with T. Lange) Collisions in fast generation of ideal classes and points on hyperelliptic and elliptic curves. Appl. Algebra in Engin., Commun. and Computing, 2005, v.15, 329-337.
217. (with F. Hess) On the linear complexity and multidimensional distribution of congruential generators over elliptic curves. Designs, Codes and Cryptography, 2005, v.35, 111-117.
218. On the singularity of generalised Vandermonde matrices over finite fields. Finite Fields and Their Appl., 2005, v.11, 193-199.
219. Orders of points on elliptic curves, Affine Algebraic Geometry, Amer. Math. Soc, 2005, 245-252.
220. (with J.-M. De Koninck and F. Luca) Powerful numbers in short intervals. Bull. Aust. Math. Soc., 2005, v.71, 11-16.
221. (with S. R. Blackburn, D. Gomez-Perez and J. Gutierrez) Predicting nonlinear pseudorandom number generators, Math. Comp., 2005, v.74, 1471-1494.
222. (with S. Cohen, M. Dewar, J. B. Friedlander and D. Panario) Polynomial Gauss sums. Proc. Amer. Math. Soc., 2005, v.133, 2193-2199.
223. (with W. D. Banks, F. Luca and H. Stichtenoth) On the value set of n! modulo a prime. Turkish. Math. J., 2005, v.29, 169-174.
224. (with M. Z. Garaev and F. Luca) Waring problem with factorials. Bull. Aust. Math. Soc., 2005, v.71, 259-264.
225. (with T. Lange) Certain exponential sums and random walks on elliptic curves, Canad. J. Math., 2005, v.57, 338-350.
226. (with F. Luca) On the exponent of the group of points on elliptic curves in extension fields. Intern. Math. Research Notices, 2005, no.23, 1391-1411.
227. (with A. Granville and A. Zaharescu) On the distribution of rational functions along a curve over F_p and residue races. J. Number Theory, 2005, v.112, 216-237.
228. (with W. D. Banks and F. Luca) Irrationality of power series for various number theoretic functions. Manuscr. Math., 2005, v.117, 183-197.
229. On the number of zero trace elements in polynomial bases for F_{2^n}. Revista Matematica Complutense, 2005, v.18, 177-180.
230. (with W. D. Banks, F. Luca and F. Saidak) Values of arithmetical functions equal to a sum of two squares. Quart. J. Math., 2005, v.56, 123-139.
231. (with S. Hallgren and A. Russell) Quantum noisy rational function reconstruction. Proc. of the 11th Annual International Computing and Combinatorics Conference, Kunming, 2005, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2005, v.3595, 420-429.
232. (with S. Contini) On Stern's attack agra inst secret truncated linear congruential generators. Proc. 10th Aust. Conf. on Information Security and Privacy, Brisbane, 2005, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2005, v.3574, 52-60.
233. On the nonlinearity of the sequence of signs of Kloosterman sums. Bull. Aust. Math. Soc., 2005, v.71, 405-409.
234. (with A. Winterhof) A hidden number problem in small subgroups. Math. Comp., 2005, v.74, 2073-2080.
235. (with A. Klappenecker, M. R{\"o}tteler and A. Winterhof) On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states. J. Math. Physics, 2005, v.46, 082101, 1-17.
236. (with K. Ford, M. Khan and C. L. Yankov) On the maximal difference between an element and its inverse in residue rings. Proc. Amer. Math. Soc., 2005, v.133, 3463-3468.
237. (with W. D. Banks, K. Ford, F. Luca and F. Pappalardi) Values of the Euler function in various sequences. Monatsh. Math., 2005, v.146, 1-19.
238. (with M. Z. Garaev) The large sieve inequality with exponential functions and the distribution of Mersenne numbers modulo primes. Intern. Math. Research Notices, 2005, no.39, 2391-2408.
239. (with M. Z. Garaev and F. Luca) Exponential sums and congruences with factorials. J. Reine Angew. Math., 2005, v.584, 29-44.
240. with A. Winterhof) On the linear complexity of bounded integer sequences over different moduli. Inform. Proc. Letters, 2005, v.96, 178-184.
241. (with W. D. Banks, M. Z. Garaev and F. Luca) Uniform distribution of the fractional part of the average prime divisor. Forum Math., 2005, v.17, 885-901.
242. (with W. D. Banks) Prime divisors of palindromes. Period. Math. Hungarica, 2005, v.51, 1-10.
243. (with W. D. Banks and F. Luca) Some divisibility properties of the Euler function. Glasgow Math. J., 2005, v.47, 517-528.
244. (with J. B. Friedlander and C. Pomerance) Finding the group structure of elliptic curves over finite fields. Bull. Aust. Math. Soc., 2005, v.72, 251-263.
245. (with F. Luca) Prime divisors of shifted factorials, Bull. London Math. Soc., 2005, v.37, 809-817.
246. (with E. Levieil and F. Luca) Prime divisors of some shifted products. Intern. J. Math. and Math. Sci., 2005, no.19, 3057-3073.
247. Playing Hide-and-Seek'' with numbers: The hidden number problem, lattices and exponential sums. Public-Key Cryptography, Proc. Symp. in Appl. Math., v,62, Amer. Math. Soc., 2005, 153-177.
248. (with E. Levieil and F. Luca) Bounding the number of solutions of some congruences. Bol. Soc. Matem. Mexicana, 2005, v.11, 3057-3073.
249. (with W. D. Banks and G. Harman) Distributional properties of the largest prime factor. Michigan Math. J., 2005, v.53, 665-681.
250. On the value set of the Ramanujan function. Archiv Math., 2005, v.85, 508-513.
251. (with F. Luca) On the largest prime divisor of n! + 2^n -1, J. Theorie des Nombres Bordeaux, 2005, v.17, 859-870.
252. (with A. Winterhof) Noisy interpolation of sparse polynomials in finite fields. Appl. Algebra in Engin., Commun. and Computing, 2005, v.16, 307-317.
253. (with W. D. Banks and F. Luca) On certain sums related to multiple divisibility by the largest prime factor. Ann. Sci. Math. Quebec, 2005, v.29, 131-145.
254. (with R. Steinfeld) Chinese remaindering with multiplicative noise. Theory of Comp. Sys., 2005, v.40, 33-41.
255. (with D. Gomez-Perez and J. Gutierrez) Exponential sums with Dickson polynomials. Finite Fields and Their Appl., 2006, v.12, 16-25.
256. (with W. D. Banks and F. Luca) Arithmetic properties of \varphi(n)/\lambda(n) and the structure of the multiplicative group modulo n. Comment. Math. Helv., 2006, v.81, 1-22.
257. (with A. Winterhof) Constructions of approximately mutually unbiased bases. Proc. the 7th Latin American Theoretical Informatics Conference, Valdivia, Chile, 2006, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2006, v.3887, 793-799.
258. On the sum of iterations of the Euler function. J. Integer Sequences, 2006, no. 06.1.6, 1-5, (available from http://www.cs.uwaterloo.ca/journals/JIS/vol9.html ).
259. (with A. Winterhof) On the nonlinearity of linear recurrence sequences. Appl. Math. Letters, 2006, v.19, 340-344.
260. (with I. F. Blake and T. Garefalakis) On the bit security of the Diffie-Hellman key. Appl. Algebra in Engin., Commun. and Computing, 2006, v.16, 397-404.
261. On RSA moduli with prescribed bit patterns. Designs, Codes and Cryptography, 2006, v.39, 113-122.
262. (with S. Contini and E. Croot) Complexity of inverting the Euler function. Math. Comp., 2006, v.75, 983-996.
263. (with W. D. Banks, J. B. Friedlander and S. V. Konyagin) Incomplete exponential sums and Diffie-Hellman triples. Math. Proc. Cambr. Phil. Soc., 2006, v.140, 193-206.
264. On the energy of some circulant graphs. Lin. Algebra and Appl., 2006, v.414, 378-382.
265. (with F. Luca) Arithmetic properties of the Ramanujan function. Proc. Indian Acad. Sci., Math. Sci., 2006, v.116, 1-8.
266. (with W. D. Banks, J. B. Friedlander and M. Z. Garaev) Double character sums over elliptic curves and finite fields. Pure and Appl. Math. Quart., 2006, v.2, 179-197.
267. (with W. D. Banks) Multiplicative character sums with the sum of g-ary digits function. The Ramanujan J., 2006, v.11, 215-219.
268. (with W. D. Banks, J. B. Friedlander, F. Luca and F. Pappalardi) Coincidences in the values of the Euler and Carmichael functions. Acta Arith., 2006, v.122, 207-234.
269. On the Erdos distance problem over finite fields. Bull. Aust. Math. Soc., 2006, v.73, 285-292.
270. (with D. Coppersmith, N. A. Howgrave-Graham and P. Q. Nguyen) Testing the Adam isomorphism of circulant graphs. J. Discr. Algorithms, 2006, v.4, 324-335.
271. (with M. Z. Garaev and F. Luca) Catalan and Apery numbers in residue classes. J. Combin. Theory, Ser. A., 2006, v.113, 851-865.
272. (with M. Z. Garaev and F. Luca) Distribution of harmonic sums and Bernoulli polynomials modulo a prime. Math. Zeitschrift, 2006, v.253, 855-865.
273. (with S. R. Blackburn) Character sums and nonlinear recurrence sequences. Discr. Math., 2006, v.306, 1126-1131.
274. (with A. Winterhof) On the discrepancy and linear complexity of some counter-dependent recurrence sequences. Proc. Intern. Conf. on Sequences and Their Applications (SETA'06), Lect. Notes in Comp. Sci., Beijing, 2006, Springer-Verlag, Berlin, 2006, v.4086, 295-303.
275. (with E. El Mahassni and A. Winterhof) Distribution of nonlinear congruential pseudorandom numbers modulo almost squarefree integers. Monatsh. Math., 2006, v.148, 297-307.
276. (with M. Z. Garaev, F. Luca and A. Winterhof) On the lower bound of the linear complexity over F_p of Sidelnikov sequences. IEEE Trans. Inform. Theory, 2006, v.52, 3299-3304.
277. (with W. D. Banks) Short character sums with Beatty sequences. Math. Res. Letters, 2006, v.13, 539-547.
278. (with W. D. Banks, J. B. Friedlander and M. Z. Garaev) Character sums with exponential functions over smooth numbers. Indag. Math., 2006, v.17, 157-168.
279. (with W. D. Banks) Non-residues and primitive roots in Beatty sequences. Bull. Aust. Math. Soc., 2006, v.73, 433-443.
280. Truncations of L-functions in residue classes. Glasgow Math. J., 2006, v.48, 347-350.
281. (with J. von zur Gathen) GCD of random linear combinations. Algorithmica, 2006, v.46, 137-148.
282. (with F. Luca) Uniform distribution of some ratios involving the number of prime and integer divisors. Unif. Distrib. Theory, 2006, v.1, 15-26.
283. On the set of distances between two sets over finite fields. Intern. J. Math. and Math. Sci., 2006, v.2006, Article ID 59482, 1-5.
284. (with F. Luca) Elliptic curves with low embedding degree. J. Cryptology, 2006, v.19, 553-562.
285. (with W. D. Banks) Congruences and exponential sums with the Euler function. Rocky Mountain J. Math., 2006, v.36, 1415-1426.
286. (with W. D. Banks) Average value of the Euler function on binary palindromes. Bull. Polish Acad. Sci. Math., 2006, v.54, 95-101.
287. (with M. R. Murty) Group structure of elliptic curves over finite fields and applications. Topics in Geometry, Coding Theory and Cryptography, Springer-Verlag, 2006, 167-194.
288. (with S. R. Blackburn, D. Gomez-Perez and J. Gutierrez) Reconstructing noisy polynomial evaluation in residue rings, J. Algorithms, 2006, v.61, 47-90.
289. (with F. Luca) Uniformity of distribution modulo 1 of the geometric mean prime divisor. Bol. Soc. Matem. Mexicana, 2006, v.12, 155-163.
290. (with F. Luca) On the number of polynomial maps into Z_n. Tsukuba J. Math., 2006, v.30, 439-449.
291. (with F. Luca and J. McKee) Small exponent point groups on elliptic curves. J. Theorie des Nombres Bordeaux, 2006, v.18, 471-476.
292. (with F. Luca) Approximating positive reals by ratios of kernels of consecutive integers Sem. Math. Sci., Keio Univ., 2006, v.35, 141-149.
293. (with F. Luca) Pseudoprime values of the Fibonacci sequence, polynomials and the Euler function. Indag. Math., 2006, v.17, 611-625.
294. (with W. D. Banks and F. Luca) Common divisors of the Euler function at related arguments. Acta Sci. Math. (Szeged), 2006, v.72, 525-536.
295. Primitive points on a modular hyperbola. Bull. Polish Acad. Sci. Math., 2006, v.54, 193-200.
296. (with F. Luca) Some divisibilities amongst the terms of linear recurrences. Abh. Math. Sem. Univ. Hamburg, 2006, v.46, 143-156.
297. (with F. Luca) Pseudoprime Cullen and Woodall numbers. Colloq. Math., 2007, v.107, 35-43.
298. On some dynamical systems in finite fields and residue rings. Discr. and Cont. Dynam. Syst., Ser.A, 2007, v.17, 901-917.
299. (with W. D. Banks) Prime divisors in Beatty sequences. J. Number Theory, 2007, v.123, 413-425.
300. (with W. D. Banks and F. Luca) On rough and smooth neighbours. Revista Matematica Complutense, 2007, v.20, 109-118.
301. On the distribution of points on multidimensional modular hyperbolas. Proc. Jap. Acad. Sci., Ser.A, v.83, 5-9.
302. (with W. D. Banks) On values taken by the largest prime factor of shifted primes. J. Aust. Math. Soc., 2007, v.82, 133-147.
303. (with T. Lange) Distribution of some sequences of points on elliptic curves. J. Math. Cryptology, 2007, v.1, 1-11.
304. (with W. D. Banks) Integers with a large smooth divisor. Integers, 2007, v.7, A17, 1-11.
305. Communication complexity of some number theoretic functions. Appl. Math. Letters, 2007, v.20, 872-875.
306. On the distribution of angles of the Salie sums. Bull. Aust. Math. Soc., 2007, v.75, 221-227.
307. Bounds on the Fourier coefficients of the weighted sum function. Inform. Proc. Letters, 2007, v.103, 83-87.
308. Character sums over shifted smooth numbers. Proc. Amer. Math. Soc., 2007, v.135, 2699-2705.
309. (with F. Luca) Arithmetic functions with linear recurrence sequences. J. Number Theory, 2007, v.125, 459-472.
310. (with N. Saxena and S. Severini) Parameters of integral circulant graphs and periodic quantum dynamics. Intern J. Quant. Inform., 2007, v.5, 417-430.
311. (with J. B. Friedlander) Least totient in a residue class. Bull. London Math. Soc., 2007, v.39, 425-432.
312. (with D. Sutantyo) On the set of the largest prime divisors. Publ. Math. Debrecen, 2007, 71, 95-100.
313. Distribution of roots of polynomial congruences. Intern. J. Math. and Math. Sci., 2007, v.2007, Article ID 37853, 1-5.
314. (with M. Z. Garaev and F. Luca) Exponential sums with Catalan numbers. Indag. Math., 2007, v.18, 23-37.
315. (with A. Winterhof) Quantum period reconstruction of approximate sequences. Inform. Proc. Letters, 2007, v.103, 211-215. Preliminary version in Proc. ERATO Conf. on Quantum Inform. Sci., Tokyo, 2005, 7-8.
316. (with S. Balasuriya and F. Luca) Prime divisors of some recurrence sequence. Period. Math. Hung., 2007, v.54, 215-227.
317. Bounds of incomplete multiple Kloosterman sums. J. Number Theory, 2007, v.126, 68-73.
318. Distribution of points on modular hyperbolas. Sailing on the Sea of Number Theory: Proc. 4th China-Japan Seminar on Number Theory, Weihai, 2006, World Scientific, 2007, 155-189.
319. (with F. Luca) On finite fields for pairing based cryptography. Adv. Math. of Commun., 2007, v.1, 281-286.
320. (with F. Luca) On the square-free parts of [e n!]. Glasgow Math. J., 2007, v.49, 411-415.
321. (with F. Luca) Discriminants of complex multiplication fields of elliptic curves over finite fields. Canad. Math. Bull., 2007, v.50, 409-417.
322. (with F. Luca) Pseudoprimes in certain linear recurrences. Albanian J. Math., 2007, v.1, 125-131.
323. (with J. F. Voloch) Visible points on curves over finite fields. Bull. Polish Acad. Sci. Math., 2007, v.55, 193-199.
324. (with O. Ahmadi) Geometric progressions in sumsets over finite fields. Monatsh. Math., 2007, v.152, 177-185.
325. (with W. D. Banks and F. Luca) Estimates for Wieferich numbers. The Ramanujan J., 2007, v.14, 361-378.
326. (with W. D. Banks) Exponential sums with polynomial values of the discrete logarithm. Unif. Distrib. Theory, 2007, v.2, 67-72.
327. (with S. Balasuriya) Character sums with subsequence sums. Period. Math. Hung., 2007, v.55, 215-221.
328. (with O. Ahmadi) Distribution of matrices with restricted entries over finite fields. Indag. Math., 2007, v.18, 327-337.
329. (with M. Becheanu and F. Luca) On the sums of complementary divisors. Intern. J. Number Theory, 2007, v.3, 635-648.
330. (with I. Blake) Statistical distribution and collisions of the VSH. J. Math. Cryptology, 2007, v.1, 329-349.
331. On the distribution of Kloosterman sums. Proc. Amer. Math. Soc., 2008, v.136, 403-407.
332. Bilinear character sums over elliptic curves. Finite Fields and Their Appl., 2008, v.14, 132-141.
333. Infinite Hilbert class field towers over cyclotomic fields. Glasgow Math. J., 2008, v.50, 27-32.
334. (with S. R. Blackburn) On the average energy of circulant graphs. Lin. Algebra and Appl., 2008, v.428, 1956-1963.
335. (with A. C. Cojocaru) Distribution of Farey fractions in residue classes and Lang-Trotter conjectures on average. Proc. Amer. Math. Soc., 2008, v.136, 1977-1986.
336. (with A. Winterhof) On the number of distances between the coordinates of points on modular hyperbolas. J. Number Theory, 2008, v.128, 1224-1230.
337. Pseudorandom graphs from elliptic curves. Proc. the 8th Latin American Theoretical Informatics Conf. Rio de Janeiro, 2008, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2008, v.4957, 284-292.
338. (with F. Luca and R. Thangadurai) Quadratic non-residues versus primitive roots modulo $p$. J. Ramanujan Math. Soc. 2008, v.23, 1-8.
339. (with W. D. Banks, M. Z. Garaev and D. R. Heath-Brown) Density of non-residues in Burgess-type intervals and applications. Bull. London Math. Soc., 2008, v.40, 88-96.
340. Pseudorandom points on elliptic curves over finite fields. Algebraic Geometry and its Applications, World Scientific, 2008, 116-134.
341. (with E. El Mahassni) On the distribution of the elliptic curve power generator. Proc. 8th Conf. on Finite Fields and Appl., Melbourne, 2007, Contemp. Math., v.461, Amer. Math. Soc., 2008, 111-119.
342. (with F. Luca) On the values of the divisor function. Monatsh. Math., 2008, v.154, 59-69.
343. (with M. Khan and C. L. Yankov) On the convex closure of the graph of modular inversions. Experimental Math., 2008, v.17, 91-104.
344. On the Euler function on differences between the coordinates of points on modular hyperbolas Bull. Polish Acad. Sci. Math., 2008, v.56, 1-7.
345. (with W. van Dam) Classical and quantum algorithms for exponential congruences. Proc. the 3rd Workshop on Theory of Quantum Computation, Communication and Cryptography, Tokyo, 2008, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2008, v.5106, 1-10.
346. Approximation by several rationals. Bull. Aust. Math. Soc., 2008, v.77, 325-329.
347. Distribution of inverses and multiples of small integers and the Sato-Tate conjecture on average. Michigan Math. J., 2008, v.56, 99-111.
348. On the elliptic curve analogue of the sum-product problem. Finite Fields and Their Appl., 2008, v.14, 721-726.
349. (with J. Bourgain) Distribution of consecutive modular roots of an integer. Acta Arith., 2008, v.134, 83-91.
350. (with A. Winterhof) Visible points on multidimensional modular hyperbolas. J. Number Theory, 2008, v.128, 2695-2703.
351. (with J. Bourgain and S. Konyagin) Product sets of rationals, multiplicative translates of subgroups in residue rings and fixed points of the discrete logarithm. Intern. Math. Research Notices, 2008, v.2008, Article ID rnn090, 1-29.
352. On the solvability of bilinear equations in finite fields. Glasgow Math. J., 2008, v.50, 523-529.
353. Exponential sums and prime divisors of sparse integers. Period. Math. Hungarica, 2008, v.57, 93-99.
354. (with J. F. Voloch) Average distribution of prime ideals in families of number fields. Bull. Brazil Math. Soc., 2008, v.39, 417-425.
355. (with S. W. Graham) On RSA moduli with almost half of the bits prescribed. Disc. Appl. Math., 2008, v.156, 3150-3154.
356. On the size of the Jacobians of curves over finite fields. Bull. Brazil Math. Soc., 2008, v.39, 587-595.
357. (with K. Ford) On curves over finite fields with Jacobians of small exponent. Intern. J. Number Theory, 2008, v.4, 819-826.
358. (with R. Steinfeld) Collision in the DSA function. Coding and Cryptology, World Scientific, 2008, 226-232.
359. (with J. Gutierrez) On the distribution of rational functions on consecutive powers. Unif. Distrib. Theory, 2008, v.3, 85-91.
360. (with F. Luca) Arithmetic properties of Apery numbers. J. London Math. Soc., 2008, v.78, 545-562.
361. (with W. Kohnen and Y.-K. Lau) On the number of sign changes of Hecke eigenvalues of newforms. J. Aust. Math. Soc., 2008, v.85, 87-94.
362. (with F. Luca) Quadratic fields generated by polynomials. Archiv Math., 2008, v.91, 399-408.
363. Arithmetic and geometric progressions in product sets over finite fields. Bull. Aust. Math. Soc., 2008, v.78, 357-364.
364. On a generalised Lehmer problem for arbitrary powers. Contributions in General Algebra II, Bangkok, 2008, 197-216.
365. (with J. B. Friedlander and P. Kurlberg) Products in residue classes. Math. Res. Letters, 2008, v.15, 1133-1147.
366. (with S. Balasuriya and W. D. Banks) Congruences and exponential sums with the sum of aliquot divisors function. Intern. J. Number Theory, 2008, v.4, 903-909.
367. (with O. Ahmadi, N. Alon and I. F. Blake) Graphs with integral spectrum. Lin. Algebra and Appl., 2009, v.430, 547-552.
368. (with A. G. Abercrombie and W. D. Banks) Arithmetic functions on Beatty sequences. Acta Arith., 2009, v.136, 81-89.
369. On the distribution of arguments of Gauss sums. Kodai Math. J., 2009, v.32, 172-177.
370. Pseudorandom number generators from elliptic curves. Recent Trends in Cryptography, Contemp. Math., v.477, Amer. Math. Soc., 2009, 121-141.
371. (with W. D. Banks) Character sums with Beatty sequences on Burgess-type intervals. Analytic Number Theory - Essays in Honour of Klaus Roth, Cambridge Univ. Press, Cambridge, 2009, 15-21.
372. On the exponential sum-product problem. Indag. Math., 2009, v.19, 325-331.
373. Bilinear sums with exponential functions. Proc. Amer. Math. Soc., 2009, v.137, 2217-2224.
374. (with F. Luca and C. Pomerance) On Giuga numbers. Intern. J. Modern Math., 2009, v.4, 13-18.
375. On some weighted average values of L-functions. Bull. Aust. Math. Soc., 2009, v.79, 183-186.
376. (with A. C. Cojocaru and F. Luca) Pseudoprime reductions of elliptic curves. Math. Proc. Cambr. Phil. Soc., 2009, v.146, 513-522.
377. (with F. Luca) On special finite fields. Proc. Conf. on Arithmetic, Geometry, Cryptography and Coding Theory, Contemp. Math., v.487, Amer. Math. Soc., 2009, 163-168.
378. (with C. Pomerance) On pseudosquares and pseudopowers. Combinatorial Number Theory, Proc. of Integers Conf.'2007, Walter de Gruyter, Berlin, 2009, 171-184.
379. (with S. Balasuriya and D. Sutantyo) Multiplicative character sums with the Euler function. Studia Sci. Math. Hung., 2009, v.46, 223-229.
380. (with A. C. Cojocaru) On the embedding degree of reductions of an elliptic curve. Inform. Proc. Letters, 2009, v.109, 652-654.
381. (with K. Ford and F. Luca) On the largest prime factor of the Mersenne numbers. Bull. Aust. Math. Soc., 2009, v.79, 455-463.
382. On the distribution of solutions to linear equations. Glasnik Math., 2009, v.44, 7-10.
383. (with J. B. Friedlander) Elliptic twin prime conjecture. Proc. 2nd Intern. Workshop Coding and Cryptology Zhangjiajie, 2009, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2009, v.5557, 77-81.
384. On the values of Kloosterman sums. IEEE Trans. Inform. Theory, 2009, v.55, 2599-2601.
385. (with W. D. Banks, M. Z. Garaev and F. Luca) Uniform distribution of fractional parts related to pseudoprimes. Canad. J. Math., 2009, v.61, 481-502.
386. (with W. D. Banks) Prime numbers with Beatty sequences. Colloq. Math., 2009, v.115, 147-157.
387. (with J. von zur Gathen) Subset sum pseudorandom numbers: Fast generation and distribution. J. Math. Cryptology, 2009, v.3, 149-163.
388. Exponents of modular reductions of families of elliptic curves. Rev. Union Matem. Argentina, 2009, v.50, 69-74.
389. On a generalisation of a Lehmer problem. Math. Zeitschrift, 2009, v.263, 619-631.
390. (with F. Luca) Quadratic fields generated by the Shanks sequence. Proc. Edinburgh Math. Soc., 2009, v.52, 719-729.
391. (with S. Balasuriya and A. Winterhof) An average bound for character sums with some counter-dependent recurrence sequences. Rocky Mountain J. Math., 2009, v.39, 1403-1409.
392. (with N. M. Katz and M. Xiong) On character sums with distances on the upper half plane over a finite field. Finite Fields and Their Appl., 2009, v.15, 738-747.
393. (with W. D. Banks) Multiplicative character sums with twice-differentiable functions. Quart. J. Math., 2009, v.60, 401-411.
394. (with J. Bourgain, S. Konyagin and C. Pomerance) On the smallest pseudopower. Acta Arith., 2009, v.140, 43-55.
395. (with W. D. Banks) Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height. Israel J. Math., 2009, v.173, 253-277.
396. Exponential sums with Farey fractions. Bull. Polish Acad. Sci. Math., 2009, v.57, 101-107.
397. (with J. B. Friedlander) On the density of some special primes. J. Math. Cryptology, 2009, v.3, 265-271.
398. (with D. Naccache) Divisibility, smoothness and cryptographic applications. Algebraic Aspects of Digital Communications, IOS Press, 2009, 115-173.
399. (with R. R. Farashahi and F. Voloch) On hashing into elliptic curves. J. Math. Cryptology, 2009, v.3, 353-360.
400. Some special character sums over elliptic curves. Bol. Soc. Matem. Mexicana, 2009, v.15, 37-40.
401. On quadratic fields generated by discriminants of irreducible trinomials. Proc. Amer. Math. Soc., 2010, v.138, 125-132.
402. (with A. Ostafe) On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators. Math. Comp., 2010, v.79, 501-511.
403. Some counting questions for matrices with restricted entries. Lin. Algebra and Appl., 2010, v.432, 155-160.
404. (with A. Iosevich and M. Xiong) Sets with integral distances in finite fields. Trans. Amer. Math. Soc., 2010, v.362, 2189-2204.
405. (with R. R. Farashahi) On the number of distinct elliptic curves in some families. Designs, Codes and Cryptography, 2010, v.54, 83-99.
406. (with C. Pomerance) Rank statistics for a family of elliptic curves over a function field. Pure and Appl. Math. Quart., 2010, v.6, 21-40.
407. (with O. Ahmadi) Bilinear character sums and the sum-product problem on elliptic curves. Proc. Edinburgh Math. Soc., 2010, v.53, 1-12.
408. On the distribution of orbits of PGL_2(q) in F_{q^n} and the Klapper conjecture. SIAM J. Discr. Math., 2010, v.23, 2093-2099.
409. (with J. Cilleruelo, F. Luca and A. Quiros) On squares in polynomial products. Monat. Math., 2010, v.159, 215-223.
410. On point sets in vector spaces over finite fields that determine only acute angle triangles. Bull. Aust. Math. Soc., 2010, v.81, 114-120.
411. (with A. Ostafe) Pseudorandom numbers and hash functions from iterations of multivariate polynomials. Cryptography and Communications, 2010, v.2, 49-67.
412. Numbers at work and play. Notices Amer. Math. Soc., 2010, v.57, 334-342.
413. On the size of the Gelfond exponent. J. Number Theory, 2010, v.130, 1056-1060.
414. (with J. Cilleruelo and F. Luca) Power values of palindromes. J. Combin. and Number Theory, 2010, v.1, 101-108.
415. (with L. Glebsky) Short cycles in repeated exponentiation modulo a prime. Designs, Codes and Cryptography, 2010, v.56, 35-42.
416. Tate-Shafarevich groups and Frobenius fields of reductions of elliptic curves. Quart. J. Math., 2010, v.61, 255-263.
417. (with J. von zur Gathen and M. Mignotte) Approximate polynomial GCD: Small degree and small height perturbations. J. Symb. Comp., 2010, v.45, 879-886. Preliminary version in Proc. the 8th Latin American Theoretical Informatics Conf. Rio de Janeiro, 2008, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 2008, v.4957, 276-283.
418. (with R. Ferguson, C. Hoffman, F. Luca and A. Ostafe) Some additive combinatorics problems in matrix rings. Revista Matematica Complutense, 2010, v.23, 501-513.
419. (with A. Winterhof) Partitions into two Lehmer numbers. Monat. Math., 2010, v.160, 429-441.
420. (with A. Ostafe) On the length of critical orbits of stable quadratic polynomials. Proc. Amer. Math. Soc., 2010, v.138, 2653-2656.
421. (with S. V. Konyagin and C. Pomerance) On the distribution of pseudopowers. Canad. J. Math., 2010, v.62, 582-594.
422. (with O. Ahmadi and J. F. Voloch) Multiplicative order of Gauss periods. Intern. J. Number Theory, 2010, v.6, 877-882.
423. (with T. H. Chan) On the concentration of points on modular hyperbolas and exponential curves. Acta Arith., 2010, v.142 59-66.
424. (with O. Ahmadi) On the distribution of the number of points on algebraic curves in extensions of finite fields. Math. Res. Letters, 2010, v.4, 689-699.
425. (with A. Ostafe and A. Winterhof) On the generalized joint linear complexity profile of a class of nonlinear pseudorandom multisequences. Adv. Math. of Commun., 2010, v.4, 369-379.
426. (with W. D. Banks) Sums with convolutions of Dirichlet characters. Manuscr. Math., 2010, v.133, 105-114.
427. (with T. H. Chan) Visible points on modular exponential curves. Bull. Polish Acad. Sci. Math., 2010, v.58, 17-22.
428. (with J. Bourgain, K. Ford and S. Konyagin) On the divisibility of Fermat quotients. Michigan Math. J., 2010, v.59, 313-328.
429. (with A. Ostafe and E. Pelican) On pseudorandom numbers from multivariate polynomial system. Finite Fields and Their Appl., 2010, v.16, 320-328.
430. (with K. Ford and M. Khan) Geometric properties of points on modular hyperbolas. Proc. Amer. Math. Soc., 2010, v.138, 4177-4185.
431. Open problems on exponential and character sums. Number Theory: Proc. 5th China-Japan Seminar on Number Theory, Higashi-Osaka, 2008, World Scientific, 2010, 222-242.
432. (with J. Gutierrez) Expansion of orbits of some dynamical systems over finite fields. Bull. Aust. Math. Soc., 2010, v.82, 232-239.
433. (with S. S. Loiperdinger) On the distribution of the Euler function of shifted smooth numbers. Colloq. Math., 2010, v.120, 139-148.
434. (with K. Broughan and F. Luca) Some divisibility properties of binomial coefficients and converse of the Wolstenholme's theorem. Integers, 2010, v.10, 485-495.
435. (with J. B. Friedlander and K. Gong) Character sums over shifted primes. Matem. Zametki, 2010, v.88, 605-619 (in Russian).
436. (with K. Karabina, A. Menezes and C. Pomerance) On the asymptotic effectiveness of Weil descent attacks. J. Math. Cryptology, 2010, v.4, 175-191.
437. (with R. R. Farashahi) On pseudopoints of algebraic curves. Archiv Math., 2010, v.95,529-537.
438. (with F. Luca) On the g-ary expansions Apery, Motzkin, Schroder and other combinatorial numbers. Annals Comb., 2010, v.14, 507-524.
439. (with A. Ostafe) Pseudorandomness and dynamics of Fermat quotients. SIAM J. Discr. Math., 2011, v.25, 50-71.
440. On the average distribution of pseudorandom numbers generated by nonlinear permutations. Math. Comp., 2011, v.80, 1053-1061.
441. (with M. Krizek, F. Luca and L. Somer) On the complexity of testing elite primes. J. Integer Sequences, 2011, v.14, Article 11.1.2.
442. (with E. Fouvry, F. Luca and F. Pappalardi) Counting dihedral and quaternionic extensions. Trans. Amer. Math. Soc., 2011, v.363, 3233-3253.
443. Exponential sums with consecutive modular roots of an integer. Quart. J. Math., 2011, v.62, 207-213.
444. On small solutions to quadratic congruences, J. Number Theory, 2011, v.131, 1105-1111.
445. (with A. Ostafe) Twisted exponential sums over points of elliptic curves. Acta Arith., 2011, v.148 77-92.
446. (with A. Balog and K. Broughan) On the number of solutions of exponential congruences. Acta Arith., 2011, v.148 93-103.
447. (with S. V. Konyagin) On convex hull of points on modular hyperbolas. Moscow J. Comb. and Number Theory, 2011, v.1, 43-51.
448. Bounds of multiplicative character sums with Fermat quotients of primes. Bull. Aust. Math. Soc., 2011, v.83, 456-462.
449. (with S. Blackburn and A. Ostafe) On the distribution of the subset sum pseudorandom number generator on elliptic curves. Unif. Distrib. Theory, 2011, v.6, 127-142.
450. (with F. Luca) On the g-ary expansions of middle binomial coefficients and Catalan numbers. Rocky Mountain J. Math. 2011, v.41, 1291-1301.
451. (with A. Ostafe) On the Waring problem with Dickson polynomials in finite fields. Proc. Amer. Math. Soc., 2011, v.139, 3815-3820.
452. (with A. Ostafe and A. Winterhof) Multiplicative character sums of a class of nonlinear recurrence vector sequences. Intern. J. Number Theory, 2011, v.7, 1557-1571.
453. (with E. Fouvry) On a ternary quadratic form over primes. Acta Arith., v.150, 2011, 285-314.
454. On the distribution of irreducible trinomials. Canad. Math. Bull., v.54, 2011, 748-756.
455. Character sums with Fermat quotients. Quart. J. Math., v.62, 2011, 1031-1043.
456. (with N. Koblitz and A. Menezes) Discrete logarithms, Diffie-Hellman, and reductions. Vietnam J. Math., v.39, 2011, 267-285.
457. (with K. Bibak) On fully split lacunary polynomials in finite fields. Bull. Polish Acad. Sci. Math., v.59, 2011, 197-202.
458. Fermat quotients: Exponential sums, value set and primitive roots. Bull. London Math. Soc., 2011, v.43, 1228-1238.
459. (with E. Fouvry) Smooth shifted monomial products. Publ. Math. Debrecen, 2011, v.79, 423-432.
460. Computational Diffie-Hellman problem. Encyclop. of Cryptography and Security, Part 3, 2011, 240-244.
461. On the convex hull of solutions to polynomial congruences. J. Number Theory, v.132, 2012, 254-257.
462. On the value set of Fermat quotients. Proc. Amer. Math. Soc., 2012, v.140, 1199-1206.
463. (with S. V. Konyagin) On the consecutive powers of a primitive root: Gaps and exponential sums. Matematika, 2012, v.58, 11-20.
464. (with A. Ostafe) Exponential sums over points of elliptic curves with reciprocals of primes. Mathematika, 2012, v.58, 21-33.
465. On the restricted divisor function in arithmetic progressions. Revista Matem. Iberoamer., 2012, v.28, 231-238.
466. (with J. Jim\'enez Urroz and F. Luca) On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves. Math. Comp., 2012, v.81, 1093-1110.
467. (with S. Ling, R. Steinfeld and H. Wang) On the modular inversion hidden number problem. J. Symb. Comp., 2012, v.47, 358-367.
468. (with R. R. Farashahi) Pseudorandom bits from points on elliptic curves. IEEE Trans. Inform. Theory, 2012, v.58, 1242-1247.
469. (with A. Ostafe) On the power generator and its multivariate analogue. J. Compl. 2012, v.28, 238-249.
470. (with R. R. Farashahi) On group structures realized by elliptic curves over a fixed finite field. Experimental Math., 2012, v.21, 1-10.
471. (with W. D. Banks and F. Pappalardi) On group structures realized by elliptic curves over arbitrary finite fields. Experimental Math., 2012, v.21, 11-25.
472. (with O. Ahmadi, F. Luca and A. Ostafe) On stable quadratic polynomials. Glasgow Math. J., 2012, v.54, 359-369.
473. (with B. Mans) Random walks and bisections in random circulant graphs. Proc. the 10th Latin American Theoretical Informatics Conf., Arequipa, Peru, 2012, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, Springer-Verlag, Berlin, 2012, v.7256, 542-555.
474. Sum-product estimates and multiplicative orders of gamma and gamma + gamma^{-1} in finite fields. Bull. Aust. Math. Soc., 2012, v.85, 505-508.
475. (with J. Bourgain and S. Konyagin) Distribution of elements of cosets of small subgroups and applications. Intern. Math. Research Notices, 2012, v.2012, Article ID rnn097, 1968-2009.
476. (with A. Ostafe) Multiplicative character sums and products of sparse integers in residue classes. Period. Math. Hungarica, 2012, v.64, 247-255.
477. (with W. D. Banks, M. Z. Garaev and J. B. Friedlander) Exponential and character sums with Mersenne numbers. J. Aust. Math. Soc., 2012, v.92, 1-13.
478. (with J. A. Gonzalez, F. Luca and C. Pomerance) On numbers n dividing the nth term of a linear recurrence. Proc. Edinburgh Math. Soc., 2012, v.55, 271-289.
479. (with J. Cilleruelo and A. Zumalacarregui) Isomorphism classes of elliptic curves over a finite field in some thin families. Math. Res. Letters, 2012, v.19, 335-343.
480. (with A. Ostafe) Degree growth, linear independence and periods of a class of rational dynamical systems. Proc. Conf. on Arithmetic, Geometry, Cryptography and Coding Theory, Contemp. Math., v.574, Amer. Math. Soc., 2012, 131-119.
481. (with A. Balog and K. Broughan) Sum-products estimates with several sets and applications. Integers, 2012, v.12, 895-906.
482. (with K. E. Stange) Character sums with division polynomials. Canad. Math. Bull., 2012, v.55, 850-857.
483. On the distribution of solutions to polynomial congruences. Archiv Math., 2012, v.99, 345-351.
484. (with J. Cilleruelo, M. Z. Garaev and A. Ostafe) On the concentration of points of polynomial maps and applications. Math. Zeitschrift, 2012, v.272, 825-837.
485. Modular hyperbolas. Jap. J. Math., 2012, v.7, 235-294.
486. (with J. Bourgain, M. Z. Garaev and S. Konyagin) On the hidden shifted power problem. SIAM J. Comp., 2012, v.41, 1524-1557.
487. (with R. R. Farashahi, P.-A. Fouque, M. Tibouchi and F. Voloch) Indifferentiable deterministic hashing to elliptic and hyperelliptic curves. Math. Comp., 2013, v.82, 491-512.
488. (with A. Winterhof) Distribution of values of polynomial Fermat quotients. Finite Fields and Their Appl., 2013, v.19, 93-104.
489. (with R. C. Baker, W. D. Banks, J. Brudern and A. J. Weingartner) Piatetski-Shapiro sequences. Acta Arith., 2013, v.157, 37-68.
490. Elliptic curves over finite fields: Number theoretic and cryptographic aspects. Advances in Applied Mathematics, Modeling, and Computational Science , Fields Institute Communications, Springer-Verlag, Berlin, 2013, 65-90.
491. On vanishing Fermat quotients and a bound of the Ihara sum. Kodai Math. J., 2013, v.36, 99-108.
492. (with J. Bourgain, M. Z. Garaev and S. Konyagin) On congruences with products of variables from short intervals and applications. Proc. Steklov Math. Inst., 2013, v.280, 67-96.
493. Correcting noisy exponentiation black-boxes modulo a prime. Inform. Proc. Letters, 2013, v.113, 414-417.
494. (with D. Gomez-Perez, J. Gutierrez and A. Ibeas) Predicting masked linear pseudorandom number generators over finite fields. Designs, Codes and Cryptography, 2013, v.67, 395-402.
495. (with D. Gomez-Perez and A. Ostafe) Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators. Math. Comp., (to appear).
496. (with R. Dietmann and C. Elsholtz) On gaps between quadratic non-residues in the Euclidean and Hamming metric. Indag. Math., (to appear).
497. Joint distribution of discrete logarithms. Unif. Distrib. Theory, (to appear).
498. (with F. Luca) On the counting function of elliptic Carmichael numbers. Canad. Math. Bull., (to appear).
499. (with S. Ling and H. Wang) On the multidimensional distribution of the Naor-Reingold pseudo-random function. Math. Comp., (to appear).
500. (with J. Bourgain, M. Z. Garaev and S. Konyagin) {Multiplicative congruences with variables from short intervals. J. d'Analyse Math., (to appear).
501. (with J. Friedlander) Enumeration of certain varieties over a finite field. Proc. Amer. Math. Soc., (to appear).
502. I. E. Shparlinski, Additive combinatorics over finite fields: New results and applications. Finite fields and their applications: Character sums and polynomials, Walter de Gruyter, (to appear).
503. (with J. Cilleruelo) Concentration of points on curves in finite fields. Monatsh. Math., (to appear).
504. (with R. Heyman) On shifted Eisenstein poolynomials. Period. Math. Hungarica, (to appear).
505. (with D. Harvey) Statistics of different reduction types of Fermat curves. Experimental Math., (to appear).
506. On some exponential sums with exponential and rational functions. Rocky Mountain J. Math., (to appear).
507. (with J. Cilleruelo, A. Kumchev, F. Luca and J. Rue) On the fractional parts of a^n/n . Bull. London Math. Soc., (to appear).
508. (with R. Dietmann and C. Elsholtz) On gaps between primitive roots in the Hamming metric. Quart. J. Math.,
509. (with W. Steiner) On digit patterns in expansions of rational numbers with prime denominator. Quart. J. Math., (to appear).
510. (with D. Gomez-Perez and A. Ostafe) On irreducible divisors of iterated polynomials. Revista Matem. Iberoamer., (to appear).
511. On the Lang-Trotter and Sato-Tate conjectures on average for polynomials families of elliptic curves. Michigan Math. J., (to appear).
512. (with B. Kerr) On the distribution of values and zeros of polynomial systems over arbitrary sets. J. Number Theory, (to appear).
513. (with R. Heyman) On the number of Eisenstein polynomials of bounded height. Appl. Algebra in Engin., Commun. and Computing, (to appear).
514. On the Sato-Tate conjecture on average for polynomial families of elliptic curves. Forum Math., (to appear).
515. On the average number of square-free values of polynomials. Canad. Math. Bull., (to appear).
516. On products of primes and almost primes in arithmetic progressions. Period. Math. Hungarica, (to appear).

## Unrefereed Conference Proceedings, Preprints, Submitted Papers, Papers in Progress

1. A bound for complete exponential sums with recurrence sequences. All-Union Inst. Sci. and Techn. Inform., no.116-77, 1977, 1-13 (in Russian).
2. A bound of exponential sums and sums of characters with recurrence sequences. All-Union Inst. Sci. and Techn. Inform., no.1968-77, 1977, 1-13 (in Russian).
3. On fractional parts of certain recurrence sequences. All-Union Inst. Sci. and Techn. Inform., no.257-80, 1980, 1-10 (in Russian).
4. (with N. L. Novozhilov and V. V. Romanovcev) On modelling random flows. Proc. 6th All-Union Conf. on Planning and Automat. of Experiments in Sci. Researches, Part 2. Moscow, 1980, 100 (in Russian).
5. (with A. N. Vystavkin, L. L. Kosachevskaja and V. V. Romanovcev) An interactive system of experimental data deconvolution. Proc. 6th All-Union Conf. on Automatata and Sci. Research using Computers, Novosibirsk, 1981, 158-159 (in Russian).
6. On a property of a sequence of real numbers and the rate of convergence of some iteration processes. Proc. 2nd All-Union Conf. on Methods of Comp. Math., Krasnojarsk, 1981. Preprint of Comp. Center of Sibirian Depart. of Acad. Sci. of USSR, 1982, no.2, 47-48 (in Russian).
7. Addendum of the Translator. Kibern. Sbornik, 1983, v.19, 69-70 (in Russian).
8. (with A. G. D'jachkov and V. V. Rykov) On B_s sequences. Proc. All-Union Conf. on Discrete Math. and Its Applications, Moscow, 1986, p.191 (in Russian).
9. On the choice of parameters in the method of alternating directions. Proc. All-Union Workshop on Problems of Optimization of Computation, Simferopol, 1987, 112-113 (in Russian).
10. On the covering radius of linear cyclic codes. Proc. 8 All-Union Conf. on Problems of Theoretical Cybernetics, Gor'kiy, 1988, p.168 (in Russian).
11. Addendum of the Translator. Kibern. Sbornik, 1988, v.25, 82-84 (in Russian).
12. On irreducible polynomials over finite fields. Proc. All-Union Conf. on Constuctive Methods and Algorithms of Number Theory, Minsk, 1989, p.172 (in Russian).
13. (with A. J. van der Poorten and S. McCallum, Editors) Proceedings of The Conference on Computational Algebra and Number Theory, Macquarie University, 1995.
14. (with H. P. Schlickewei and S. A. Stepanov) On the distribution of normal bases of number fields. Macquarie Univ. Math. Report 97/215, 1997, 1-13.
15. (with I. F. Blake and F. Luca) VSH and multiplicative modular relations between small primes with polynomial exponents. Preprint, 2012, 1-8.
16. (with J. von zur Gathen) Generating safe primes. Preprint, 2013, 1-37.
17. (with B. Mans) Random walks, bisections and gossiping in circulant graphs. Preprint, 2012, 1-25.
18. (with F. Voloch) Generators of elliptic curves over finite fields. Preprint, 2011, 1-9.
19. (with A. V. Sutherland) On the distribution of Atkin and Elkies primes. Preprint, 2011, 1-14.
20. Evasive properties of sparse graphs and some linear equations in primes. Preprint,2013, 1-5.
21. (with D. Sutantyo) Distribution of elliptic twin primes in isogeny and isomorphism classes. Preprint, 2012, 1-16.
22. (with D. Aggarwal and U. Maurer) On the equivalence of strong RSA and factoring. Preprint, 2009, 1-14.
23. Close values of shifted modular inversions and the decisional modular inversion hidden number problem. Preprint, 2013, 1-9.
24. On solutions to some polynomial congruences in small boxes. Preprint, 2013, 1-9.
25. Products with variables from low-dimensional affine spaces and shifted power identity testing in finite fields. Preprint, 2012, 1-9.
26. (with D. Koh and C.-Y. Shen) Averaging operators over homogeneous varieties over finite fields. Preprint, 2013, 1-26.
27. (with O. Ahmadi) Exponential sums over points of elliptic curves. Preprint, 2012, 1-17.
28. (with M.-C. Chang, J. Cilleruelo, M. Z. Garaev, J. Hernandez and A. Zumalacarregui) Points on curves in small boxes and applications. Preprint, 2011, 1-31.
29. On the product of small Elkies primes. Preprint, 2013, 1-9.
30. Additive decompositions of subgroups of finite fields. Preprint, 2013, 1-12.
31. On the distribution of points on the generalised Markoff-Hurwitz and Dwork hypersurfaces. Preprint, 2013, 1-11.
32. (with F. Luca and P. Kurlberg) On the fixed points of the map x -> x^x modulo a prime. Preprint, 2013, 1-24.