Complexity Analysis of the Cryptographic Primitive Problems through Square-Root Exponent(<Special Section>Discrete Mathematics and Its Applications)

概要

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To examine the computational complexity of cryptographic primitives such as the discrete logarithm problem, the factoring problem and the Diffie-Hellman problem, we define a new problem called square-root exponent, which is a problem to compute a value whose discrete logarithm is a square root of the discrete logarithm of a given value. We analyze reduction between the discrete logarithm problem modulo a prime and the factoring problem through the square-root exponent. We also examine reductions among the computational version and the decisional version of the square-root exponent and the Diffie-Hellman problem and show that the gap between the computational square-root exponent and the decisional square-root exponent partially overlaps with the gap between the computational Diffie-Hellman and the decisional Diffie-Hellman under some condition.
社団法人電子情報通信学会の論文
2004-05-01