The key operation in Elliptic Curve Cryptosystems(ECC) is point scalar multiplication. Making use of Frobenius endomorphism, Muller and Smart proposed two efficient algorithms for point scalar multiplications over eve...The key operation in Elliptic Curve Cryptosystems(ECC) is point scalar multiplication. Making use of Frobenius endomorphism, Muller and Smart proposed two efficient algorithms for point scalar multiplications over even or odd finite fields respectively. This paper reduces the corresponding multiplier by modulo Υk-1 +…+Υ+ 1 and improves the above algorithms. Implementation of our Algorithm 1 in Maple for a given elliptic curve shows that it is at least as twice fast as binary method. By setting up a precomputation table, Algorithm 2, an improved version of Algorithm 1, is proposed. Since the time for the precomputation table can be considered free, Algorithm 2 is about (3/2) log2 q - 1 times faster than binary method for an elliptic curve over展开更多
基金Supported by the National Natural Science Foundation of China(No.90104004) the National 973 High Technology Projects(No.G1998030420)
文摘The key operation in Elliptic Curve Cryptosystems(ECC) is point scalar multiplication. Making use of Frobenius endomorphism, Muller and Smart proposed two efficient algorithms for point scalar multiplications over even or odd finite fields respectively. This paper reduces the corresponding multiplier by modulo Υk-1 +…+Υ+ 1 and improves the above algorithms. Implementation of our Algorithm 1 in Maple for a given elliptic curve shows that it is at least as twice fast as binary method. By setting up a precomputation table, Algorithm 2, an improved version of Algorithm 1, is proposed. Since the time for the precomputation table can be considered free, Algorithm 2 is about (3/2) log2 q - 1 times faster than binary method for an elliptic curve over
