Efficient Message Space Extension for Automorphic Signatures

An automorphic signature scheme is a signature scheme that is structure-preserving (messages are group elements and never hashed or sliced into bits in the signing function) and allows self-signing (can sign its own verification-key, i.e., the message space covers the verification-key space). Given an automorphic signature scheme that can sign only one group element as a message, we show how to efficiently sign n group elements where n is sufficiently large or even unbounded. With an existing construction, the size of the resulting signature grows with factor of 4n and it is claimed to be optimal in some sense. Our constructions achieve 3n and even 2n. Since the signature scheme may be used repeatedly or even recursively in applications, the improvement in the multiplicative factor results in considerable efficiency gain in practice.