On the invisibility of designated confirmer signatures

Abstract

As an important cryptographic primitive, designated confirmer signatures are introduced to control the public verifiability of signatures. That is, only the signer or a semi-trusted party, called designated confirmer, can interactively assist a verifier to check the validity of a designated confirmer signature. The central security property of a designated confirmer signature scheme is called invisibility, which requires that even an adaptive adversary cannot determine the validity of an alleged signature without direct cooperation from either the signer or the designated confirmer. However, in the literature researchers have proposed two other related properties, called impersonation and transcript simulatability, though the relations between them are not clear. In this paper, we first explore the relations among these three invisibility related concepts and conclude that invisibility, impersonation and transcript simulatability forms an increasing stronger order. After that, we turn to study the invisibility of two designated confirmer signature schemes recently presented by Zhang et al. and Wei et al. By demonstrating concrete and effective attacks, we show that both of those two scheme fail to meet invisibility, the central security property of designated confirmer signatures.