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标量乘运算是椭圆曲线密码方案中最耗费时间的运算,因此标量乘的运算速度决定了椭圆曲线密码方案的执行速度。为了提高标量乘的执行速度,人们提出了很多方案,如NAF、MOF等。在研究大量标量乘算法的基础上,提出了一种基于MOF算法的改进型ZLMOF算法。改进的算法与原算法相比,在汉明重基本保持不变的前提下,比特串长度上降到了最低,从而进一步减少了点加运算的次数。然后结合滑动窗口算法提出了一种比NAF—滑动窗口算法更加高效的ZLMOF—滑动窗口算法,ZLMOF—滑动窗口算法比NAF—滑动窗口算法需要更少的点加运算次数。又结合Shamir算法,提出了一种比Shamir—NAF算法更加高效的Shamir—ZLMOF多标量乘算法。Shamir—ZLMOF多标量乘算法比Shamir—NAF算法需要更少的点加运算次数。
The scalar multiplication operation is the most time-consuming operation in the elliptic curve cryptosystem, so the operation speed of the scalar multiplication determines the execution speed of the elliptic curve cryptosystem. In order to improve the execution speed of scalar multiplication, many schemes have been proposed, such as NAF, MOF and so on. On the basis of studying a large number of scalar multiplication algorithms, an improved ZLMOF algorithm based on MOF algorithm is proposed. The improved algorithm compared with the original algorithm, the Hamming weight under the premise of basically unchanged, the bit string length dropped to a minimum, thus further reducing the number of points plus the number of operations. Then, a more efficient ZLMOF sliding window algorithm than the NAF sliding window algorithm is proposed in combination with the sliding window algorithm. The ZLMOF sliding window algorithm requires less number of point additions than the NAF sliding window algorithm. Combined with Shamir algorithm, a Shamir-ZLMOF multi-scalar multiplication algorithm which is more efficient than Shamir-NAF algorithm is proposed. The Shamir-ZLMOF multi-scale multiplication algorithm requires fewer number of dot additions than the Shamir-NAF algorithm.