论文信息 - Counting Points on Elliptic Curves Over F2m

Counting Points on Elliptic Curves Over F2m

In 1985, Schoof [136] presented a polynomial time algorithm for computing #E(F q ), the number of Fq-rational points on an elliptic curve E defined over the field F q . The algorithm has a running time of 0(log8 q) bit operations, and is rather cumbersome in practice. Buchmann and Muller [20] combined Schoof’s algorithm with Shanks’ baby-step giant-step algorithm, and were able to compute orders of curves over Fp, where p is a 27-decimal digit prime. The algorithm took 4.5 hours on a SUN-1 SPARC-station.

R. Zuccherato | A. Menezes | S. Vanstone

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