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Toward Separating Integer Factoring from Discrete Logarithm mod p
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
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
range injection reduction,
the Heath-Brown conjecture,
certified discrete logarithm,
Full Text: PDF(329KB)
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.