On the security of probabilistic multisignature schemes and their optimality

Abstract

We first prove that the following three probabilistic multisignature schemes based on a trapdoor permutation have tight security; PFDH (probabilistic full domain hash) based multisignature scheme (PFDH-MSS), PSS (probabilistic signature scheme) based multisignature scheme (PSS-MSS), and short signature PSS based multisignature scheme (S-PSS-MSS). Second, we give an optimal proof (general result) for multisignature schemes, which derives the lower bound for the length of random salt. We also estimate the upper bound for the length in each scheme and derive the optimal length of a random salt. Two of the schemes are promising in terms of security tightness and optimal signature length. © Springer-Verlag Berlin Heidelberg 2005.