Select Publications
Journal articles
2013, 'Additive decompositions of subgroups of finite fields', SIAM Journal on Discrete Mathematics, 27, pp. 1870 - 1879, http://dx.doi.org/10.1137/130924470
,2013, 'Generating safe primes', Journal of Mathematical Cryptology, 7, pp. 333 - 365, http://dx.doi.org/10.1515/jmc-2013-5011
,2013, 'On digit patterns in expansions of rational numbers with prime denominator', Quarterly Journal of Mathematics, 64, pp. 1231 - 1238, http://dx.doi.org/10.1093/qmath/has027
,2013, 'On gaps between primitive roots in the hamming metric', Quarterly Journal of Mathematics, 64, pp. 1043 - 1055, http://dx.doi.org/10.1093/qmath/has022
,2013, 'On the average number of square-free values of polynomials', Canadian Mathematical Bulletin, 56, pp. 844 - 849, http://dx.doi.org/10.4153/CMB-2012-021-8
,2013, 'Statistics of different reduction types of fermat curves', Experimental Mathematics, 22, pp. 243 - 249, http://dx.doi.org/10.1080/10586458.2013.790201
,2013, 'On gaps between quadratic non-residues in the Euclidean and Hamming metrics', Indagationes Mathematicae, 24, pp. 930 - 938, http://dx.doi.org/10.1016/j.indag.2013.02.005
,2013, 'Concentration of points on curves in finite fields', Monatshefte fur Mathematik, 171, pp. 315 - 327, http://dx.doi.org/10.1007/s00605-013-0498-x
,2013, 'On products of primes and almost primes in arithmetic progressions', Periodica Mathematica Hungarica, 67, pp. 55 - 61, http://dx.doi.org/10.1007/s10998-013-2736-3
,2013, 'On the distribution of values and zeros of polynomial systems over arbitrary sets', Journal of Number Theory, 133, pp. 2863 - 2873, http://dx.doi.org/10.1016/j.jnt.2013.02.012
,2013, 'On the Lang-Trotter and Sato-Tate conjectures on average for polynomial families of elliptic curves', Michigan Mathematical Journal, 62, pp. 491 - 505, http://dx.doi.org/10.1307/mmj/1378757885
,2013, 'Functional graphs of polynomials over finite fields', Journal of Combinatorial Theory. Series B, http://dx.doi.org/10.1016/j.jctb.2015.07.003
,2013, 'On some exponential sums with exponential and rational functions', Rocky Mountain Journal of Mathematics, 43, pp. 361 - 371, http://dx.doi.org/10.1216/RMJ-2013-43-1-361
,2013, 'Erratum: Sum-product estimates and multiplicative orders ofΓ and Γ + Γ-1 in finite fields (Bulletin of the Australian Mathematical Society)', Bulletin of the Australian Mathematical Society, 87, pp. 527 - 528, http://dx.doi.org/10.1017/S0004972712001062
,2013, 'On the number of Eisenstein polynomials of bounded height', Applicable Algebra in Engineering, Communications and Computing, 24, pp. 149 - 156, http://dx.doi.org/10.1007/s00200-013-0187-y
,2013, 'Predicting masked linear pseudorandom number generators over finite fields', Designs, Codes, and Cryptography, 67, pp. 395 - 402, http://dx.doi.org/10.1007/s10623-012-9615-4
,2013, 'On the Sato-Tate conjecture on average for some families of elliptic curves', Forum Mathematicum, 25, pp. 647 - 664, http://dx.doi.org/10.1515/FORM.2011.141
,2013, 'On congruences with products of variables from short intervals and applications', Proceedings of the Steklov Institute of Mathematics, 280, pp. 61 - 90, http://dx.doi.org/10.1134/S0081543813010057
,2013, 'On vanishing Fermat quotients and a bound of the Ihara sum', Kodai Mathematical Journal, 36, pp. 99 - 108, http://dx.doi.org/10.2996/kmj/1364562722
,2013, 'Correcting noisy exponentiation black-boxes modulo a prime', Information Processing Letters, 113, pp. 414 - 417, http://dx.doi.org/10.1016/j.ipl.2013.03.016
,2013, 'Evasive properties of sparse graphs and some linear equations in primes', Theoretical Computer Science, http://dx.doi.org/10.1016/j.tcs.2014.06.005
,2013, 'Elliptic curves over finite fields: Number theoretic and cryptographic aspects', Fields Institute Communications, 66, pp. 65 - 90, http://dx.doi.org/10.1007/978-1-4614-5389-5_4
,2013, 'Piatetski-Shapiro sequences', Acta Arithmetica, 157, pp. 37 - 68, http://dx.doi.org/10.4064/aa157-1-3
,2013, 'Indifferentiable deterministic hashing to elliptic and hyperelliptic curves', Mathematics of Computation, 82, pp. 491 - 512, http://dx.doi.org/10.1090/S0025-5718-2012-02606-8
,2013, 'Distribution of values of polynomial Fermat quotients', Finite Fields and their Applications, 19, pp. 93 - 104, http://dx.doi.org/10.1016/j.ffa.2012.10.004
,2013, 'Number Theory and Related Fields: In Memory of Alf van der Poorten', Springer Proceedings in Mathematics and Statistics, 43, http://dx.doi.org/10.1007/978-1-4614-6642-0
,2013, 'On the fractional parts of an/n', Bulletin of the London Mathematical Society, 45, pp. 249 - 256, http://dx.doi.org/10.1112/blms/bds084
,2012, 'On the hidden shifted power problem', SIAM Journal on Computing, 41, pp. 1524 - 1557, http://dx.doi.org/10.1137/110850414
,2012, 'Character sums with division polynomials', Canadian Mathematical Bulletin, 55, pp. 850 - 857, http://dx.doi.org/10.4153/CMB-2011-126-x
,2012, 'On the concentration of points of polynomial maps and applications', Mathematische Zeitschrift, 272, pp. 825 - 837, http://dx.doi.org/10.1007/s00209-011-0959-7
,2012, 'Modular hyperbolas', Japanese Journal of Mathematics, 7, pp. 235 - 294, http://dx.doi.org/10.1007/s11537-012-1140-8
,2012, 'On the distribution of solutions to polynomial congruences', Archiv der Mathematik, 99, pp. 345 - 351, http://dx.doi.org/10.1007/s00013-012-0436-5
,2012, 'Multiplicative character sums and products of sparse integers in residue classes', Periodica Mathematica Hungarica, 64, pp. 247 - 255, http://dx.doi.org/10.1007/s10998-012-6771-2
,2012, 'On numbers n dividing the nth term of a linear recurrence', Proceedings of the Edinburgh Mathematical Society, 55, pp. 271 - 289, http://dx.doi.org/10.1017/S0013091510001355
,2012, 'Sum-product estimates and multiplicative orders of γ and γ+γ -1 in finite fields', Bulletin of the Australian Mathematical Society, 85, pp. 505 - 508, http://dx.doi.org/10.1017/S0004972711002887
,2012, 'Random walks and bisections in random circulant graphs', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7256 LNCS, pp. 542 - 555, http://dx.doi.org/10.1007/978-3-642-29344-3_46
,2012, 'Distribution of elements of cosets of small subgroups and applications', International Mathematics Research Notices, 2012, pp. 1968 - 2009, http://dx.doi.org/10.1093/imrn/rnr097
,2012, 'Erratum: Pseudoprime reductions of elliptic curves (Mathematical Proceedings of the Cambridge Philosophical Society (2009) 146 (513-522))', Mathematical Proceedings of the Cambridge Philosophical Society, 152, pp. 571, http://dx.doi.org/10.1017/S0305004111000399
,2012, 'On stable quadratic polynomials', Glasgow Mathematical Journal, 54, pp. 359 - 369, http://dx.doi.org/10.1017/S001708951200002X
,2012, 'On the modular inversion hidden number problem', Journal of Symbolic Computation, 47, pp. 358 - 367, http://dx.doi.org/10.1016/j.jsc.2011.09.002
,2012, 'On the value set of fermat quotients', Proceedings of the American Mathematical Society, 140, pp. 1199 - 1206, http://dx.doi.org/10.1090/S0002-9939-2011-11203-6
,2012, 'On the number of isogeny classes of pairing-friendly elliptic curves and statistics of mnt curves', Mathematics of Computation, 81, pp. 1093 - 1110, http://dx.doi.org/10.1090/S0025-5718-2011-02543-3
,2012, 'Exponential and character sums with mersenne numbers', Journal of the Australian Mathematical Society, 92, pp. 1 - 13, http://dx.doi.org/10.1017/S1446788712000109
,2012, 'Pseudorandom bits from points on elliptic curves', IEEE Transactions on Information Theory, 58, pp. 1242 - 1247, http://dx.doi.org/10.1109/TIT.2011.2170054
,2012, 'Degree growth, linear independence and periods of a class of rational dynamical systems', ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY, 574, pp. 131 - 143, http://dx.doi.org/10.1090/conm/574/11426
,2012, 'Exponential sums over points of elliptic curves with reciprocals of primes', Mathematika, 58, pp. 21 - 33, http://dx.doi.org/10.1112/S0025579311001719
,2012, 'Isomorphism classes of elliptic curves over a finite field in some thin families', Mathematical Research Letters, 19, pp. 335 - 343, http://dx.doi.org/10.4310/MRL.2012.v19.n2.a6
,2012, 'On group structures realized by elliptic curves over a fixed finite field', Experimental Mathematics, 21, pp. 1 - 10, http://dx.doi.org/10.1080/10586458.2012.632754
,2012, 'On group structures realized by elliptic curves over arbitrary finite fields', Experimental Mathematics, 21, pp. 11 - 25, http://dx.doi.org/10.1080/10586458.2011.606075
,2012, 'On the consecutive powers of a primitive root: Gaps and exponential sums', Mathematika, 58, pp. 11 - 20, http://dx.doi.org/10.1112/S0025579311002117
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