# Research

My research interests include theoretical and algorithmic aspects of finite fields, cryptography, coding theory and combinatorics.

### Journal Publications

T. Garefalakis, G. Kapetanakis, Further results on the Morgan-Mullen conjecture, Designs Codes and Cryptography, 87, 2639 - 2654, 2019.
T. Garefalakis, G. Kapetanakis, On the existence of primitive completely normal bases of finite fields, Journal of Pure and Applied Algebra, 223(3), 909 - 921, 2019.
T. Garefalakis, G. Kapetanakis, Enumerating permutation polynomials, Finite Fields and Applications, 47, 85 - 93, 2017.
F.E. Brochero Martinez, T. Garefalakis, L. Reis, E. Tzanaki, On the multiplicative order of the roots of $bX^{q +1} − aX^q + dX − c$, Finite Fields and Applications, 47, 33 - 45, 2017.
T. Garefalakis, G. Kapetanakis, A note on the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials, Finite Fields and Applications, 35, 61 - 63, 2015.
T. Garefalakis, G. Kapetanakis, On the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials, Finite Fields and Applications, 18(4), 832 - 841, 2012.
M. Christopoulou, T. Garefalakis, D. Panario, D. Thomson, Gauss periods as constructions of low complexity normal bases, Designs Codes and Cryptography, 62(1), 43 - 62, 2012.
T. Garefalakis, On the action of $\mathrm{GL}(2,q)$ on irreducible polynomials over $\mathbb{F}_q$, Journal of Pure and Applied Algebra, 215, 1835 - 1843, 2011.
T. Garefalakis, Self-reciprocal irreducible polynomials with prescribed coefficients, Finite Fields and Applications, 17(2), 183 - 193, 2010.
I.F. Blake, T. Garefalakis, A transform property of Kloosterman sums, Discrete Applied Mathematics, 158, 1064 - 1072, 2010.
M. Christopoulou, T. Garefalakis, D. Panario, D. Thomson, The trace of an optimal normal element and low complexity normal bases, Designs Codes and Cryptography, 49, 199 - 215, 2008.
I.F. Blake, T. Garefalakis, Polynomial approximation of Bilinear-Diffie-Hellman maps, Finite Fields and Applications, 14(2), 379 - 389, 2008.
T. Garefalakis, Irreducible polynomials with consecutive zero coefficients, Finite Fields and Applications, 14(1), 201 - 208, 2008.
T. Garefalakis, The hidden number problem with non-prime modulus, JP Journal of Algebra, Number Theory and Applications, 8(2), 193 - 211, 2007.
I.F. Blake, T. Garefalakis and I.E. Shparlinski, On the bit security of the Diffie-Hellman key, Appl. Algebra in Engin., Commun. and Computing, 16(6), 397 - 404, 2006.
I.F. Blake, T. Garefalakis, On the complexity of the discrete logarithm and the Diffie-Hellman problems, J. of Complexity, 20(2-3), 148 - 170, 2004.
T. Garefalakis, The generalized Weil pairing and the discrete logarithm problem on elliptic curves, Theoretical Comp. Sci. 321, 59 - 72, 2004.
J. Dankers, T. Garefalakis, R. Schaffelhofer and T. Write, Public key infrastructure in mobile systems, Electronics & Communication Engineering Journal, 14(5), 2002.
T. Garefalakis, D. Panario, Polynomials over Finite Fields Free from Large and Small Degree Irreducible Factors, J. of Algorithms 44(1), 98 - 120, 2002.
I.F. Blake, T. Garefalakis, On the security of the Digital Signature Algorithm, Designs Codes and Cryptography, 26, 87 - 96, 2002.
S.R. Blackburn, T. Garefalakis, Cryptanalysis of a Cryptosystem due to Yoo, Hong, Lee, Lim, Yi and Sung, Electronics Letters, 37(18), 1118 - 1119, 2001.
T. Garefalakis, D. Panario, The Index Calculus Method Using Non-Smooth Polynomials, Mathematics of Computation, 70(235), 1253 - 1264, 2001.

### Conference Publications

M. Christopoulou, T. Garefalakis, D. Panario, D. Thomson, The trace of an optimal normal element and low complexity normal bases, Proc.of the Workshop on Coding and Cryptography, 2007, INRIA, 79 - 88, 2007.
T. Garefalakis, C.J. Mitchell, Securing Personal Area Networks, 13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Lisboa, Portugal, 2002, pp. 1257 - 1259.

T. Garefalakis, The generalized Weil pairing and the discrete logarithm problem on elliptic curves, 3rd Latin American Theoretical Informatics Conference, Cancun, Mexico, Lecture Notes in Computer Science, 2286 (2002), 118 - 130.
T. Garefalakis, A New Family of Randomized Algorithms for List Accessing, 5th European Symposium on Algorithms, Graz, Austria, Lecture Notes in Computer Science,1284 (1997), 200 - 216.