Diskretnaya Matematika, Tome 8 (1996) no. 3, pp. 22-30
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M. A. Cherepnev. On a connection between the complexities of the discrete logarithmization and the Diffie–Hellman problems. Diskretnaya Matematika, Tome 8 (1996) no. 3, pp. 22-30. http://geodesic.mathdoc.fr/item/DM_1996_8_3_a1/
@article{DM_1996_8_3_a1,
author = {M. A. Cherepnev},
title = {On a connection between the complexities of the discrete logarithmization and the {Diffie{\textendash}Hellman} problems},
journal = {Diskretnaya Matematika},
pages = {22--30},
year = {1996},
volume = {8},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_1996_8_3_a1/}
}
TY - JOUR
AU - M. A. Cherepnev
TI - On a connection between the complexities of the discrete logarithmization and the Diffie–Hellman problems
JO - Diskretnaya Matematika
PY - 1996
SP - 22
EP - 30
VL - 8
IS - 3
UR - http://geodesic.mathdoc.fr/item/DM_1996_8_3_a1/
LA - ru
ID - DM_1996_8_3_a1
ER -
%0 Journal Article
%A M. A. Cherepnev
%T On a connection between the complexities of the discrete logarithmization and the Diffie–Hellman problems
%J Diskretnaya Matematika
%D 1996
%P 22-30
%V 8
%N 3
%U http://geodesic.mathdoc.fr/item/DM_1996_8_3_a1/
%G ru
%F DM_1996_8_3_a1
We prove that under some assumptions of a theoretical nature the complexity $L$ of the discrete logarithm problem in an arbitrary cyclic group of order $m$ is estimated in the rather general case in terms of the complexity $D$ of the Diffie–Hellman problem by the formula $$ L \le \exp \left\{{\log D\log m\over \log\log m\log\log\log m}\right\}, $$ which gives a subexponential estimate for $L$ provided a polynomial estimate for $D$ is valid.
