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2011•HAL (Le Centre pour la Communication Scientifique Directe)Open access

Improvements on the Discrete Logarithm Problem in GF(p)

Razvan Barbulescu

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Abstract

This paper speeds up descrete logarithm algorithms in two ways. First we show how the Factorization Factory can be adapted to the discrete logarithm to drop the complexity from Lp(1/3,1.902) to Lp(1/3,1.639). Next we prove that an early abort strategy can decrease the complexity of the individual logarithm from Lp(1/3,1.447) to Lp(1/3,1.232).

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What this paper is about

This paper speeds up descrete logarithm algorithms in two ways. First we show how the Factorization Factory can be adapted to the discrete logarithm to drop the complexity from Lp(1/3,1.902) to Lp(1/3,1.639). Next we prove that an early abort strategy can decrease the complexity of the individual logarithm from Lp(1/3,1.447) to Lp(1/3,1.232).

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Available abstract

This paper speeds up descrete logarithm algorithms in two ways. First we show how the Factorization Factory can be adapted to the discrete logarithm to drop the complexity from Lp(1/3,1.902) to Lp(1/3,1.639). Next we prove that an early abort strategy can decrease the complexity of the individual logarithm from Lp(1/3,1.447) to Lp(1/3,1.232).

Key concepts: Discrete logarithm, Logarithm, Mathematics, Factorization, Natural logarithm, Discrete mathematics, Combinatorics, Arithmetic

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