Towards Lattice Based Aggregate Signatures

Abstract

We propose the first lattice-based sequential aggregate signature (SAS) scheme that is provably secure in the random oracle model. As opposed to factoring and number theory based systems, the security of our construction relies on worst-case lattice problems. Generally speaking, SAS schemes enable any group of signers ordered in a chain to sequentially combine their signatures such that the size of the aggregate signature is much smaller than the total size of all individual signatures. This paper shows how to instantiate our construction with trapdoor function families and how to generate aggregate signatures resulting in one single signature. In particular, we instantiate our construction with the provably secure NTRUSign signature scheme presented by Stehle and Steinfeld at Eurocrypt 2011. This setting allows to generate aggregate signatures being asymptotically as large as individual ones and thus provide optimal compression rates as known from RSA based SAS schemes.