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Toward Separating Integer Factoring from Discrete Logarithm mod p
Shuji ISOBE Wataru KUMAGAI Masahiro MAMBO Hiroki SHIZUYA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E90A
No.1
pp.4853 Publication Date: 2007/01/01 Online ISSN: 17451337
DOI: 10.1093/ietfec/e90a.1.48 Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security) Category: Foundations Keyword: preimage functions, range injection reduction, the HeathBrown conjecture, integer factoring, certified discrete logarithm,
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Summary:
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 HeathBrown 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.

