Explicit form for the discrete logarithm over the field GF ( p , k )

Gerasimos C. Meletiou

Archivum Mathematicum (1993)

  • Volume: 029, Issue: 1-2, page 25-28
  • ISSN: 0044-8753

Abstract

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For a generator of the multiplicative group of the field G F ( p , k ) , the discrete logarithm of an element b of the field to the base a , b 0 is that integer z : 1 z p k - 1 , b = a z . The p -ary digits which represent z can be described with extremely simple polynomial forms.

How to cite

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Meletiou, Gerasimos C.. "Explicit form for the discrete logarithm over the field ${\rm GF}(p,k)$." Archivum Mathematicum 029.1-2 (1993): 25-28. <http://eudml.org/doc/247429>.

@article{Meletiou1993,
abstract = {For $a$ generator of the multiplicative group of the field $GF(p,k)$, the discrete logarithm of an element $b$ of the field to the base $a$, $b\ne 0$ is that integer $z:1\le z \le p^k -1$, $b=a^z$. The $p$-ary digits which represent $z$ can be described with extremely simple polynomial forms.},
author = {Meletiou, Gerasimos C.},
journal = {Archivum Mathematicum},
keywords = {discrete logarithm; finite fields; cryptography; discrete logarithm; finite fields; cryptography; primitive element},
language = {eng},
number = {1-2},
pages = {25-28},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Explicit form for the discrete logarithm over the field $\{\rm GF\}(p,k)$},
url = {http://eudml.org/doc/247429},
volume = {029},
year = {1993},
}

TY - JOUR
AU - Meletiou, Gerasimos C.
TI - Explicit form for the discrete logarithm over the field ${\rm GF}(p,k)$
JO - Archivum Mathematicum
PY - 1993
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 029
IS - 1-2
SP - 25
EP - 28
AB - For $a$ generator of the multiplicative group of the field $GF(p,k)$, the discrete logarithm of an element $b$ of the field to the base $a$, $b\ne 0$ is that integer $z:1\le z \le p^k -1$, $b=a^z$. The $p$-ary digits which represent $z$ can be described with extremely simple polynomial forms.
LA - eng
KW - discrete logarithm; finite fields; cryptography; discrete logarithm; finite fields; cryptography; primitive element
UR - http://eudml.org/doc/247429
ER -

References

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  1. A subexponential algorithm for the discrete logarithm problem, with applications to cryptography, Proc. 20th IEEE Found. Comp. Sci. Symp. (1979), 55-60. (1979) 
  2. New directions in cryptography, IEEE Trans. Inform. Theory, IT-22 (1976), 644-654. (1976) MR0437208
  3. Discrete logarithms in finite fields and their cryptographic significance, Proc. of the Eurocrypt ’84. Zbl0594.94016
  4. An improved algorithm for computing logarithms over G F ( p ) and its cryptographic significance, IEEE Trans. Inform. Theory, IT-24 (1978), 106-110. (1978) MR0484737
  5. The fast Fourier transform in a finite field, Mathematics of computation 25 (1971), 365-374. (1971) Zbl0221.12015MR0301966
  6. A polynomial form for logarithms modulo a prime, IEEE Trans.Inform. Theory, IT-30 (1984), 845-846. (1984) Zbl0558.12009
  7. The art of computer programming, Reading MA III (1969), Addison Wesley. (1969) Zbl0191.18001MR0378456

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