Candidate One-Way Functions on Non-Supersingular Elliptic Curves

Taiichi SAITO
Fumitaka HOSHINO
Shigenori UCHIYAMA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A    No.1    pp.144-150
Publication Date: 2006/01/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.1.144
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Elliptic Curve Cryptography
one-way function,  pairing-based cryptosystem,  distortion map,  the Weil and the Tate pairings,  co-Diffie-Hellman problem,  

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This paper proposes new candidate one-way functions constructed with a certain type of endomorphisms on non-supersingular elliptic curves. We can show that the one-wayness of our proposed functions is equivalent to some special cases of the co-Diffie-Hellman assumption. Also a digital signature scheme is explicitly described using our proposed functions.