Constructing efficient and secure batch signature schemes

In ordinary signature schemes, such as RSA, DSA, ECDSA, the signing process is performed only for a single message. Due to performance issues, in some contexts, the above solutions will become unsuitable if a party needs to sign multiple messages simultaneously. For example, in the authenticated key exchange protocols based on signatures between client and server, the server is expected to handle multiple key exchange requests from different clients simultaneously. Batch signing is a solution that generates signatures for multi-messages simultaneously with a single (ordinary) signature generation. In this article, we will consider some of the existing batch signing solutions and point out a few of their weakness. To deal with these problems, the paper also proposes two secure types of batch signature schemes, but still ensures the same efficiency as the existing batch signing solution.