As a solution to mitigate the key exposure problems in the digital signature, 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. However, there is no forward secure signature scheme whose all metrics have constant complexities. Furthermore, existing works do not support multi-user aggregation of signatures.
In this paper, we propose a forward secure aggregate signature scheme utilizing recursive zk-SNARKs (zero knowledge Succinct Non-interactive ARguments of Knowledge), whose all metrics including size and time have $O(1)$. The proposed forward secure signature scheme can aggregate signatures generated by not only a single user but also multiple users. The security of the proposed scheme is formally proven under zero-knowledge assumption and random oracle model.

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