CAJ | 학술논문

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。
모멱승운산시실현공약밀마체제적일개흔중요적운산, 기운산속도종정체상결정료공약밀마체제적실현효솔。통과채용예처리기술, 장타원곡선적정점표량승적고정기창구방법응용재모멱운산중, 여SMM산법진행조합득도일충신적구모멱승산법——고정기창구방법。대산법적원리여효솔진행료분석, 실험결과표명, 산법적운산속도득도료유효제고。
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 multiplication of elliptic curve combined with SMM algorithm to compute g<sup>k</sup> 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 increased effectively.