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Erschienen in:
1998 | OriginalPaper | Buchkapitel
Efficient Implementation of Schoof’s Algorithm
verfasst von : Tetsuya Izu, Jun Kogure, Masayuki Noro, Kazuhiro Yokoyama
Erschienen in: Advances in Cryptology — ASIACRYPT’98
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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Schoof’s algorithm is used to find a secure elliptic curve for cryptosystems, as it can compute the number of rational points on a randomly selected elliptic curve defined over a finite field. By realizing efficient combination of several improvements, such as Atkin-Elkies’s method, the isogeny cycles method, and trial search by match-and-sort techniques, we can count the number of rational points on an elliptic curve over GF(p) in a reasonable time, where p is a prime whose size is around 240-bits.