Forward Secure Sequential Aggregate Signature Schemes on Lattice

Abstract

The forward secure sequential aggregate (Fss-Agg) signature has the advantages of forward secure signature and the sequential aggregate signature at the same time. Since its proposal in 2007, it has been widely applied in many application scenarios, such as logging systems, e-business, e-government, blockchain, etc. Although there have been several Fss-Agg signature schemes, all of them are based on the classic number theory problem, which are no longer secure in the quantum era when the general quantum computers become reality. So looking for the quantum-immune Fss-Agg signature is much urgent. In this paper, the definition of Fss-Agg signature scheme is described, and the forward security and the existential unforgeability under the chosen message attack are combined to define the existential unforgeability of Fss-Agg signature aganist chosen message attack. Based on the small integer solution assumption on lattice, using the pre-image sampling and the lattice basis delegation techniques, the quantum-immune Fss-Agg signature is proposed, which is the first lattice-based Fss-Agg signature scheme. It is proven to be correct, forward secure and existentially unforgeable in the random oracle model.

Keywords

• lattice
• sequential aggregate signature
• forward secure
• unforgeability
• quantum-immune
• small integer solution