Research

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

Preprints

Translates of completely normal elements and the Morgan-Mullen conjecture
T. Garefalakis, G. Kapetanakis
[arXiv]

List decoding of evaluation codes
S. Brazitikos, T. Garefalakis, E. Tzanaki
[arXiv]

Journal Publications

Further results on the Morgan-Mullen conjecture
T. Garefalakis, G. Kapetanakis
Designs Codes and Cryptography, 87, 2639 - 2654, 2019.
[pdf] [arXiv]

On the existence of primitive completely normal bases of finite fields
T. Garefalakis, G. Kapetanakis
Journal of Pure and Applied Algebra, 223(3), 909 - 921, 2019.
[pdf] [arXiv]

Enumerating permutation polynomials
T. Garefalakis, G. Kapetanakis
Finite Fields and Applications, 47, 85 - 93, 2017.
[pdf]

On the multiplicative order of the roots of \(bX^{q+1} − aX^q + dX − c\)
F.E. Brochero Martinez, T. Garefalakis, L. Reis, E. Tzanaki
Finite Fields and Applications, 47, 33 - 45, 2017.
[pdf] [arXiv]

A note on the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials
T. Garefalakis, G. Kapetanakis
Finite Fields and Applications, 35, 61 - 63, 2015.
[pdf]

On the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials
T. Garefalakis, G. Kapetanakis
Finite Fields and Applications, 18(4), 832 - 841, 2012.
[pdf]

Gauss periods as constructions of low complexity normal bases
M. Christopoulou, T. Garefalakis, D. Panario, D. Thomson
Designs Codes and Cryptography, 62(1), 43 - 62, 2012.
[pdf]

On the action of \(\mathrm{GL}(2,q)\) on irreducible polynomials over \(\mathbb{F}_q\)
T. Garefalakis
Journal of Pure and Applied Algebra, 215, 1835 - 1843, 2011.
[pdf]

Self-reciprocal irreducible polynomials with prescribed coefficients
T. Garefalakis
Finite Fields and Applications, 17(2), 183 - 193, 2010.
[pdf]

A transform property of Kloosterman sums
I.F. Blake, T. Garefalakis
Discrete Applied Mathematics, 158, 1064 - 1072, 2010.
[pdf]

The trace of an optimal normal element and low complexity normal bases
M. Christopoulou, T. Garefalakis, D. Panario, D. Thomson
Designs Codes and Cryptography, 49, 199 - 215, 2008.
[pdf]

Polynomial approximation of Bilinear-Diffie-Hellman maps
I.F. Blake, T. Garefalakis
Finite Fields and Applications, 14(2), 379 - 389, 2008.
[pdf]

Irreducible polynomials with consecutive zero coefficients
T. Garefalakis
Finite Fields and Applications, 14(1), 201 - 208, 2008.
[pdf]

The hidden number problem with non-prime modulus
T. Garefalakis
JP Journal of Algebra, Number Theory and Applications, 8(2), 193 - 211, 2007.
[pdf]

On the bit security of the Diffie-Hellman key
I.F. Blake, T. Garefalakis and I.E. Shparlinski
Appl. Algebra in Engin., Commun. and Computing, 16(6), 397 - 404, 2006.
[pdf]

On the complexity of the discrete logarithm and the Diffie-Hellman problems
I.F. Blake, T. Garefalakis
J. of Complexity, 20(2-3), 148 - 170, 2004.
[pdf]

The generalized Weil pairing and the discrete logarithm problem on elliptic curves
T. Garefalakis
Theoretical Comp. Sci. 321, 59 - 72, 2004.
[pdf]

Public key infrastructure in mobile systems
J. Dankers, T. Garefalakis, R. Schaffelhofer and T. Write
Electronics & Communication Engineering Journal, 14(5), 2002.
[pdf]

Polynomials over Finite Fields Free from Large and Small Degree Irreducible Factors
T. Garefalakis, D. Panario
J. of Algorithms 44(1), 98 - 120, 2002.
[pdf]

On the security of the Digital Signature Algorithm
I.F. Blake, T. Garefalakis
Designs Codes and Cryptography, 26, 87 - 96, 2002.
[pdf]

Cryptanalysis of a Cryptosystem due to Yoo, Hong, Lee, Lim, Yi and Sung
S.R. Blackburn, T. Garefalakis
Electronics Letters, 37(18), 1118 - 1119, 2001.
[pdf]

The Index Calculus Method Using Non-Smooth Polynomials
T. Garefalakis, D. Panario
Mathematics of Computation, 70(235), 1253 - 1264, 2001.
[pdf]

Conference Publications

The trace of an optimal normal element and low complexity normal bases
M. Christopoulou, T. Garefalakis, D. Panario, D. Thomson
Proc.of the Workshop on Coding and Cryptography, 2007, INRIA, 79 - 88, 2007.

Securing Personal Area Networks
T. Garefalakis, C.J. Mitchell
13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications
Lisboa, Portugal, 2002, pp. 1257 - 1259.
[pdf]

The generalized Weil pairing and the discrete logarithm problem on elliptic curves
T. Garefalakis
3rd Latin American Theoretical Informatics Conference
Cancun, Mexico, Lecture Notes in Computer Science, 2286 (2002), 118 - 130.

A New Family of Randomized Algorithms for List Accessing
T. Garefalakis
5th European Symposium on Algorithms
Graz, Austria, Lecture Notes in Computer Science, 1284 (1997), 200 - 216.
[pdf]