基于SM9聚合签名局部可验证算法

Aggregate signature local verifiability algorithm based on SM9

针对目前SM9签名方案生成的n条消息的签名占用较大存储空间的问题,提出了一种基于SM9算法的聚合签名方案。该方案使得验证多条签名的时间开销相较于原SM9方案有所降低,空间开销约为原SM9方案的66.7%。在此基础上,针对目前聚合签名算法在验证签名时,验证者仅需验证特定消息的正确性,但仍需知道完整消息列表的问题,提出了基于SM9聚合签名局部可验证方案。对于单个用户生成的n条消息的聚合签名S,签名者生成特定消息m的验证提示信息aux,验证者可以在不知道完整的消息列表的情况下,对消息m的签名正确性进行验证。理论与实验分析表明,该方案在给定聚合签名S的情况下,验证特定消息的时间复杂度为O(1)。

This paper proposed an aggregate signature scheme based on the SM9 algorithm to address the issue of excessive storage space occupied by the signatures of n messages generated by the conventional SM9 signature scheme.This scheme reduced the time cost of verifying multiple signatures compared to the original SM9 scheme,with a space cost of about 66.7%of the original SM9 scheme.Furthermore,the scheme introduced a locally verifiable approach based on the SM9 aggregate signature to tackle the problem where validators need only verify the correctness of specific messages when verifying signatures in current aggregate signature algorithms but still require knowledge of the complete message list.For the aggregated signatures S of n messages generated by a single user,the signer generated verification tags for a specific message m,enabling the verifier to verify the correctness of the message’s signature without knowledge of the complete message list.Theoretical and experimental analysis confirm that the proposed scheme achieves a time complexity of O(1)for verifying specific messages given an aggregated signature.