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2001•Journal of Zhejiang University(Engineering Science)Requires access

Bits security of discrete logarithm

Jinsong Tang

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Abstract

Discrete logarithm is used in cryptography far and wide. All cryptographic algorithm is based on the assumption computing discrete logarithm is hard. This paper dedicated in the equivalency between computing the most significant bits of discrete logarithm and computing discrete logarithm. Particularly we discussed the bits security of discrete logarithm in the case of strong prime, utilizing the method presented by D.Boneh. This case is frequently used in cryptology. We show that if the most significant bits can get then there is an efficient algorithm to compute discrete logarithm in the particular case.

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What this paper is about

Discrete logarithm is used in cryptography far and wide. All cryptographic algorithm is based on the assumption computing discrete logarithm is hard. This paper dedicated in the equivalency between computing the most significant bits of discrete logarithm and computing discrete logarithm. Particularly we discussed the bits security of discrete logarithm in the case of strong prime, utilizing the method presented by D.Boneh. This case is frequently used in cryptology. We show that if the most significant bits can get then there is an efficient algorithm to compute discrete logarithm in the particular case.

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Available abstract

Discrete logarithm is used in cryptography far and wide. All cryptographic algorithm is based on the assumption computing discrete logarithm is hard. This paper dedicated in the equivalency between computing the most significant bits of discrete logarithm and computing discrete logarithm. Particularly we discussed the bits security of discrete logarithm in the case of strong prime, utilizing the method presented by D.Boneh. This case is frequently used in cryptology. We show that if the most significant bits can get then there is an efficient algorithm to compute discrete logarithm in the particular case.

Key concepts: Discrete logarithm, Logarithm, Cryptography, Iterated logarithm, Post-quantum cryptography, Mathematics, Natural logarithm, Discrete mathematics

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