Translates of completely normal elements and the
Morgan-Mullen conjecture
T. Garefalakis, G. Kapetanakis
arXiv
Research
My research interests include theoretical and algorithmic aspects of finite fields, cryptography, coding theory and combinatorics.
Preprints
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