Towards a Lattice-Based Non-interactive Aggregate Signature Scheme Following the Fiat-Shamir with Aborts Paradigm

The Fiat-Shamir with Aborts (FSwA) paradigm is a well-established approach to construct lattice-based signatures, leading to many efficient and practical schemes. One of popular implementations is Dilithium, which has been selected as the standardization in the post-quantum project by NIST. An important question now is whether the signature schemes following the FSwA framework allow for additional features, such as aggregation of different signatures. To our knowledge, only a few schemes have been proposed, most of them lack a sound security proof or suffer from inefficiency, highlighting the need for further research. Motivated by this circumstance, we propose a FSwA-based non-interactive aggregate signature scheme which not only achieves the aggregate signature smaller than the trivial concatenation of all individual signatures, but also gives a provable security proof. In addition, we review the state of the art of the FSwA-based aggregate signatures, including the schemes presented by Boudgoust and Roux-Langlois in the Computer Journal (2023) and by Tomita and Shikata (IACR eprint 2023/471), and observe certain issues in their constructions which inspire our design.