Forward-Secure Multi-User Aggregate Signatures Based on zk-SNARKs

As a solution to mitigate the key exposure problems in the digital signature, the forward security has been proposed. The forward security guarantees the integrity of the messages generated in the past despite leaks of a current time period secret key by evolving a secret key on each time period. In this paper, we propose a new forward secure aggregate signature scheme utilizing recursive zk-SNARKs (zero knowledge Succinct Non-interactive ARguments of Knowledge). Our proposal has constant complexities in key/signature sizes, signature generation, and verification time. The proposed forward secure signature scheme can aggregate signatures generated by multiple users as well as a single user. The security of the proposed scheme is formally proven under zero-knowledge assumption and random oracle model. The experiment results show that our signature scheme yields 12 s for signing time, 1 ms for verification time, 25 s for aggregation time, with the 1.6 KB secret key size and signature size independent of the number of time periods.