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在研究二进制、带符号的二进制(NAF,Non-Adjacent Form)等常见标量乘法算法的基础上,结合椭圆曲线基点的周期特性和预计算倍点序列方式,提出了一种新的标量乘法算法,并给出了新算法的详细步骤.点的周期性和系数决定了直接进行标量乘法运算还是转化为求其逆元,预计算倍点序列方式避免了椭圆曲线密码体制(ECC,Elliptic Curve Cryptosystem)加解密过程中大量的重复运算.为验证算法的正确性,采用密钥长度为192 bit椭圆曲线,给出了一个具体实例.实例结果和算法分析表明:与二进制和NAF算法相比,新算法虽占用了一些存储空间,但省去了倍点运算的时间开销,同时减少了点加的运算次数,极大地提高了标量乘法运算的效率.该算法的提出对完善ECC理论和加快ECC在实际中的应用具有重要意义.
Based on the research of common scalar multiplication algorithms such as Binary and Non-Adjacent Form (NAF), a new scalar multiplication algorithm is proposed based on the periodic characteristics of the base point of elliptic curve and the method of pre-computing multiples point sequence. And gives the detailed steps of the new algorithm.The periodicity of the points and the coefficients determine whether to directly perform scalar multiplication or convert to find the inverse element, and pre-calculate the double point sequence to avoid the Elliptic Curve Cryptosystem (ECC) In order to verify the correctness of the algorithm, an example is given with a key length of 192 bit elliptic curve.Example results and algorithm analysis show that compared with the binary and NAF algorithms, the new algorithm Although it takes up some storage space, it eliminates the time cost of the double point operation and reduces the number of operation steps, which greatly improves the efficiency of scalar multiplication operation.The proposed algorithm improves the ECC theory and accelerates ECC in practice In the application of great significance.