Efficient Undeniable Signature Schemes Based on Ideal Arithmetic in Quadratic Orders

Abstract

In undeniable signature schemes the correctness or incorrectness of a signature of some message cannot be checked without the agreement of and the interaction with the signer. This is a favorable property for some applications. Well-known undeniable signature schemes presented in the literature will cause operations for the signer which take cubic running time. For a real world implementation, e.g., on a chip card or a web server this might be too inefficient. In this paper, we present new efficient undeniable signature schemes which are constructed over an imaginary quadratic field. We compare our schemes to the only really competitive scheme so far, which is based on RSA. In all signature protocols presented here the signer’s part involving the secret key is always of quadratic complexity, which is much faster in practice than the signer’s part in the RSA-based undeniable signature protocol.