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   Vol.E90-A   No.1   pp.48-53
Publication Date: 2007/01/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.1.48
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Foundations
preimage functions,  range injection reduction,  the Heath-Brown conjecture,  integer factoring,  certified discrete logarithm,  

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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 IFPF. 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.