Super-anomalous elliptic curves ol er a ring Z/nZ (n = Pi(i=1)(k) p(i)(epsilon i)) are defined by extending anomalous elliptic curves over a prime filed F-p. They have n points over a ring Z/nZ and p(i) points over F-...
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Super-anomalous elliptic curves ol er a ring Z/nZ (n = Pi(i=1)(k) p(i)(epsilon i)) are defined by extending anomalous elliptic curves over a prime filed F-p. They have n points over a ring Z/nZ and p(i) points over F-pt for all p(i). We generalize Satoh-Araki-Smart algorithm [10], [11] and Ruck 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 deterministicpolynomialtime without knowing prime factors of n.
For multiplicative representations /spl Pi//sub i=1//sup k//spl alpha//sub i//sup n(i)/ and /spl Pi//sub j=1//sup l//spl beta//sub j//sup m(j)/ where /spl alpha//sub i/, /spl beta//sub j/ are non-zero elements of some...
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ISBN:
(纸本)0818643706
For multiplicative representations /spl Pi//sub i=1//sup k//spl alpha//sub i//sup n(i)/ and /spl Pi//sub j=1//sup l//spl beta//sub j//sup m(j)/ where /spl alpha//sub i/, /spl beta//sub j/ are non-zero elements of some algebraic number field K and n/sub i/, m/sub j/ are rational integers, we present a deterministic polynomial time algorithm that decides whether /spl Pi//sub i=1//sup k//spl alpha//sub i//sup n(i)/ equals /spl Pi//sub j=1//sup l//spl beta//sub j//sup m(j)/. The running time of the algorithm is polynomial in the number of bits required to represent the number field K, the elements /spl alpha//sub i/, /spl beta//sub j/ and the integers n/sub i/, m/sub j/.
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