How to Construct Forward Secure Single-Server, Multi-Server and Threshold-Server Assisted Signature Schemes Using Bellare-Miner Scheme

Abstract

Server-assisted signature plays an important role in all kinds of applications in electronic commerce. It can be applied to the settings where a user employs public network servers to help her execute digital signature operations. In this paper, we discuss a problem of how to construct forward secure single-server, multi-server and threshold-server assisted signature schemes using Bellare-Miner Scheme and propose three signature schemes. In the single-server assisted signature scheme, the user (signer) can employ a server to help her produce a signature. In themulti-server assisted scheme, the number of employed servers is increased to n, therefore, it is infeasible for an attacker to forge a valid signature if she can’t corrupt all servers and the signer. In the threshold-server assisted signature scheme, the generation of a valid signature needs the cooperation of the user and a quorum of servers. The scheme is more robust because the system can still get the correct signature as soon as no more than threshold servers are corrupted. These three schemes maintain the forward secure property, that is, even if the current secret key is exposed, an adaptive chosen-message adversary can’t forge any signature pertaining to previous time period. Finally, we prove the proposed schemes are correct and forward secure.