大整数模幂的固定基窗口组合算法

Fixed base windowing combination algorithm for large integer modular exponentiation

模幂乘运算是实现公钥密码体制的一个很重要的运算,其运算速度从整体上决定了公钥密码体制的实现效率。通过采用预处理技术,将椭圆曲线的定点标量乘的固定基窗口方法应用在模幂运算中,与SMM算法进行组合得到一种新的求模幂乘算法——固定基窗口方法。对算法的原理与效率进行了分析,实验结果表明,算法的运算速度得到了有效提高。

Modular exponentiation is an important operation of public-key cryptosystems, which heavily determines the overall implementation of the efficiency of a public-key cryptosystems. This paper proposed a new modular exponentiation algorithm named fixed base windowing algorithm. By precomputation, this algorithm utilized the fixed base windowing algorithm of scalar muhiplieation of elliptic curve combined with SMM algorithm to compute gk mod n. Furthermore, it presented the principle and efficiency analysis of the new algorithm. At last, experimental results show that the computational efficiency has been in- creased effectively.