Toward Separating Integer Factoring from Discrete Logarithm mod p
Shuji Isobe, Wataru Kumagai, Masahiro Mambo, Hiroki Shizuya · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · 2007
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 ∉ 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.