关于同时基于因子分解与离散对数问题的签名体制

On the digital signature schemes whose security based on solving discrete logarithms problem and factoring problem simultaneously

Shao Z 与 He Wei-hua 等人中提出了所谓同时基于大整数分解和离散对数问题的数字签名方案,其意图是只要这两个数学难题不同时被攻破,则其方案就是安全的。Xiao 等证明了 Shao的方案根本就不安全;而作者的结果表明,He 的方案在离散对数问题可解时是可破的。为此,作者试图对 He 的方案进行了修改,并提出了一个带消息恢复的,同时基于两个数学难题的数字签名方案。

Shao Z and He Wei-hua proposed some digital signature schemes which were expected to have the security property that any reasonable attack should solve the discrete logarithms problem (DLP) and the factoring problem simultaneously. It has been indicated by xiao that Shao’s scheme is basically insecure. it is shown and that He’s scheme can be cracked provided that DLP is solvable. Moreover, a modification of He’s scheme and a similar scheme based on the two hard problems with message recovery are proposed and analyzed.