List decoding of evaluation codes
S. Brazitikos,
T. Garefalakis, E. Tzanaki
arXiv
Research
My research interests include theoretical and algorithmic aspects of finite fields, cryptography, coding theory and combinatorics.
Preprints
Journal Publications
Translates of completely normal elements and the Morgan-Mullen
conjecture
T. Garefalakis, G. Kapetanakis
Canadian Mathematical Bulletin, to appear.
arXiv
T. Garefalakis, G. Kapetanakis
Canadian Mathematical Bulletin, to appear.
arXiv
Further results on the Morgan-Mullen conjecture
T. Garefalakis, G. Kapetanakis
Designs Codes and Cryptography, 87, 2639 - 2654, 2019.
PDF arXiv
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
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
T. Garefalakis, G. Kapetanakis
Finite Fields and Applications, 47, 85 - 93, 2017.
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
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
T. Garefalakis, G. Kapetanakis
Finite Fields and Applications, 35, 61 - 63, 2015.
On the Hansen-Mullen conjecture for self-reciprocal irreducible
polynomials
T. Garefalakis, G. Kapetanakis
Finite Fields and Applications, 18(4), 832 - 841, 2012.
PDF
T. Garefalakis, G. Kapetanakis
Finite Fields and Applications, 18(4), 832 - 841, 2012.
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
M. Christopoulou, T. Garefalakis, D. Panario, D. Thomson
Designs Codes and Cryptography, 62(1), 43 - 62, 2012.
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
T. Garefalakis
Journal of Pure and Applied Algebra, 215, 1835 - 1843, 2011.
Self-reciprocal irreducible polynomials with prescribed
coefficients
T. Garefalakis
Finite Fields and Applications, 17(2), 183 - 193, 2010.
PDF
T. Garefalakis
Finite Fields and Applications, 17(2), 183 - 193, 2010.
A transform property of Kloosterman sums
I.F. Blake, T. Garefalakis
Discrete Applied Mathematics, 158, 1064 - 1072, 2010.
PDF
I.F. Blake, T. Garefalakis
Discrete Applied Mathematics, 158, 1064 - 1072, 2010.
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
M. Christopoulou, T. Garefalakis, D. Panario, D. Thomson
Designs Codes and Cryptography, 49, 199 - 215, 2008.
Polynomial approximation of Bilinear-Diffie-Hellman
maps
I.F. Blake, T. Garefalakis
Finite Fields and Applications, 14(2), 379 - 389, 2008.
PDF
I.F. Blake, T. Garefalakis
Finite Fields and Applications, 14(2), 379 - 389, 2008.
Irreducible polynomials with consecutive zero
coefficients
T. Garefalakis
Finite Fields and Applications, 14(1), 201 - 208, 2008.
PDF
T. Garefalakis
Finite Fields and Applications, 14(1), 201 - 208, 2008.
The hidden number problem with non-prime modulus
T. Garefalakis
JP Journal of Algebra, Number Theory and Applications, 8(2), 193 - 211, 2007.
PDF
T. Garefalakis
JP Journal of Algebra, Number Theory and Applications, 8(2), 193 - 211, 2007.
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
I.F. Blake, T. Garefalakis and I.E. Shparlinski
Appl. Algebra in Engin., Commun. and Computing, 16(6), 397 - 404, 2006.
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
I.F. Blake, T. Garefalakis
J. of Complexity, 20(2-3), 148 - 170, 2004.
The generalized Weil pairing and the discrete logarithm problem
on elliptic curves
T. Garefalakis
Theoretical Comp. Sci. 321, 59 - 72, 2004.
PDF
T. Garefalakis
Theoretical Comp. Sci. 321, 59 - 72, 2004.
Public key infrastructure in mobile systems
J. Dankers, T. Garefalakis, R. Schaffelhofer and T. Write
Electronics & Communication Engineering Journal, 14(5), 2002.
PDF
J. Dankers, T. Garefalakis, R. Schaffelhofer and T. Write
Electronics & Communication Engineering Journal, 14(5), 2002.
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
T. Garefalakis, D. Panario
J. of Algorithms 44(1), 98 - 120, 2002.
On the security of the Digital Signature Algorithm
I.F. Blake, T. Garefalakis
Designs Codes and Cryptography, 26, 87 - 96, 2002.
PDF
I.F. Blake, T. Garefalakis
Designs Codes and Cryptography, 26, 87 - 96, 2002.
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
S.R. Blackburn, T. Garefalakis
Electronics Letters, 37(18), 1118 - 1119, 2001.
The Index Calculus Method Using Non-Smooth Polynomials
T. Garefalakis, D. Panario
Mathematics of Computation, 70(235), 1253 - 1264, 2001.
PDF
T. Garefalakis, D. Panario
Mathematics of Computation, 70(235), 1253 - 1264, 2001.
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.
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
T. Garefalakis, C.J. Mitchell
13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications
Lisboa, Portugal, 2002, pp. 1257 - 1259.
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.
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
T. Garefalakis
5th European Symposium on Algorithms
Graz, Austria, Lecture Notes in Computer Science, 1284 (1997), 200 - 216.