【摘要】 应用密码学中,群元素gahb的计算是很常见和很重要的。特别地,在大多数签名协议的验证部分都需要计算gahb的形式。该文提出了计算群元素gahb的两个算法。针对一般的可换群,提出了自左而右的无符号三元联合表示编码算法,于是计算gahb只需要对(a,b)的联合二进制表示的一次扫描即可完成。针对椭圆曲线等求逆简单的密码体制,给出了五元联合稀疏形式的编码方法。理论分析和数值结果都表明:这两个算法在性能上与已有算法是相当的,但在实现上则更为简单。更多还原

【Abstract】 In applied cryptography,computing the group element gahbis very common and very important.Especially,in the verifying step of many digital signature algorithms,the computing of gahb is always required.Two methods on computing gahb in a group were proposed in this paper.For general groups,a new left-to-right encoding algorithm,which transforms(a,b)to its unsigned threeelement joint sparse form,was presented.Therefore,computing gahb needs to scan the binary representation only once.For the groups in which computing the inverse of a given element is easy,such as elliptic curve,a method for transforming(a,b)to its fiveelement joint sparse form was suggested.Theoretical analysis and numerical comparisons show that the developed methods are as effective as current encoding methods,but simpler than them.更多还原