deterministic polynomial time without knowing prime factors of n." />
For Full-Text PDF, please login, if you are a member of IEICE,|
or go to Pay Per View on menu list, if you are a nonmember of IEICE.
Two Discrete Log Algorithms for Super-Anomalous Elliptic Curves and Their Applications
Noboru KUNIHIRO Kenji KOYAMA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2000/01/25
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
elliptic curve discrete logarithm problem, super-anomalous elliptic curves, deterministic polynomial time algorithm,
Full Text: PDF(361.7KB)>>
Super-anomalous elliptic curves over a ring Z/nZ ;(n=Πi=1k piei) are defined by extending anomalous elliptic curves over a prime filed Fp. They have n points over a ring Z/nZ and pi points over Fpi for all pi. We generalize Satoh-Araki-Smart algorithm and Ruck algorithm, which solve a discrete logarithm problem over anomalous elliptic curves. We prove that a "discrete logarithm problem over super-anomalous elliptic curves" can be solved in deterministic polynomial time without knowing prime factors of n.