Parameters for Secure Elliptic Curve Cryptosystem - Improvements on Schoof's Algorithm
نویسندگان
چکیده
The security of elliptic curve cryptosystem depends on the choice of an elliptic curve on which cryptographic operations are performed. Schoof’s algorithm is used to define a secure elliptic curve, 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, isogeny cycles method, and baby-step-giant-step algorithm, 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-bit.
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cient Implementation of Schoof ' s Algorithm
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