Shuji Isobe

Toward Separating Integer Factoring from Discrete Logarithm mod p

This paper studies the reduction among cyptographic functions. Our main result is that the prime factoring function IF does not reduce to the certified discrete logarithm function modulo a prime nor its variant with respect to some special reducibility, i.e. the range injection reducibility, under the assumption that the Heath-Brown conjecture is true and IF âx88x89 PF. Since there is no known direct relationship between these functions, this is the first result that could separate these functions. Our approach is based on the notion of the preimage functions.

Making Cryptographic Primitives Harder

This paper studies a method for transforming ordinary cryptographic primitives to new harder primitives. Such a method is expected to lead to general schemes that make present cryptosystems secure against the attack of quantum computers. We propose a general technique to construct a new function from an ordinary primitive function f with a help of another hard function g so that the resulting function is to be new hard primitives. We call this technique a lifting of f by g. We show that the lifted function is harder than original functions under some simple conditions.