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
Chen proposes a signature with message recovery which is called anauthenticated encryption scheme or simply a signcryption. In this short note, we show that Chen'ssignature scheme has some mistakes and propose thr...Chen proposes a signature with message recovery which is called anauthenticated encryption scheme or simply a signcryption. In this short note, we show that Chen'ssignature scheme has some mistakes and propose three modified versions.展开更多
In this paper, we prove that the 0/1 balance knapsack module 2~N isequivalent to the standard balance knapsack with its weight matrix being the upper triangle matrix,its number equals to 2^(N(N-1)/2)N(! ), and the ith...In this paper, we prove that the 0/1 balance knapsack module 2~N isequivalent to the standard balance knapsack with its weight matrix being the upper triangle matrix,its number equals to 2^(N(N-1)/2)N(! ), and the ith component' s nolinear complexity of the outputsequence being i.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
文摘Chen proposes a signature with message recovery which is called anauthenticated encryption scheme or simply a signcryption. In this short note, we show that Chen'ssignature scheme has some mistakes and propose three modified versions.
文摘In this paper, we prove that the 0/1 balance knapsack module 2~N isequivalent to the standard balance knapsack with its weight matrix being the upper triangle matrix,its number equals to 2^(N(N-1)/2)N(! ), and the ith component' s nolinear complexity of the outputsequence being i.
