The Aggregated Signature Scheme Based on SM9 Supporting Invalid Signature Localization

The article proposes an aggregated signature scheme based on the SM9 algorithm to deal with the problem that the signatures of multiple messages generated by the current SM9 signature scheme take up a large storage space. This scheme reduces the time overhead of verifying multiple signatures compared to the original SM9 scheme. On this basis, an aggregated signature scheme supporting invalid signature localization is proposed, which introduces an invalid signature localization algorithm that is able to find all invalid signatures in the signatures participating in the aggregation when the verification of the aggregated signatures fails, which improves the communication efficiency compared to the previous way of discarding the aggregated signatures. The security of the user's real identity is enhanced by designing the components of the user's pseudo-identity. This scheme does not have cryptographic operations that are more time-consuming to compute, which improves the computational efficiency when generating signatures and verifying signatures. Based on the q-SDH (q-strong Diffie-Hellman) problem, this scheme proves security under the stochastic metaphorical machine model. The final performance analysis shows that the proposed scheme in this chapter has good efficiency and performance compared to other schemes.