Counting points on elliptic curves in medium characteristic
نویسندگان
چکیده
In this paper, we revisit the problem of computing the kernel of a separable isogeny of degree ` between two elliptic curves defined over a finite field Fq of characteristic p. We describe an algorithm the asymptotic time complexity of which is equal to e O(`(1 + `/p) log q) bit operations. This algorithm is particularly useful when ` > p and as a consequence, we obtain an improvement of the complexity of the SEA point counting algorithm for small values of p. More precisely, we obtain a heuristic time complexity e O(log q) and a space complexity O(log q), in the previously unfavorable case where p ' log q. Compared to the best previous algorithms, the memory requirements of our SEA variation are smaller by a log q factor.
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ورودعنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2006 شماره
صفحات -
تاریخ انتشار 2006