Two Discrete Log Algorithms for Super-Anomalous Elliptic Curves and Their Applications
نویسندگان
چکیده
Z/nZ (n = ∏k i=1 pi ei ) 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 [10], [11] and Rück algorithm [9], 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. key words: elliptic curve discrete logarithm problem, superanomalous elliptic curves, deterministic polynomial time algorithm
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