Briefing
The core research problem is the lack of a quantum-resistant digital signature scheme that also provides the massive data compression required for scalable blockchain architecture. Established post-quantum candidates produce large signatures, which, when aggregated linearly, would lead to unsustainable block size bloat, effectively trading quantum security for scalability. This paper introduces the first construction for a non-interactive, many-time lattice-based aggregate signature scheme whose size grows only logarithmically in the number of aggregated signatures, O(log N). This foundational breakthrough fundamentally re-architects blockchain data structures by enabling near-constant-size proof aggregation, dramatically reducing storage and bandwidth requirements while securing the ledger against future quantum computing attacks.
Context
The prevailing theoretical limitation in securing public ledgers against quantum computers centers on the aggregate signature primitive. The industry standard for efficient aggregation, the BLS signature scheme, relies on bilinear pairings and is vulnerable to Shor’s algorithm. While post-quantum alternatives based on lattices (like CRYSTALS-Dilithium) are secure, their large individual signature sizes ∞ often an order of magnitude larger than pre-quantum schemes ∞ create a new scalability trilemma.
Prior lattice-based aggregation attempts were either only “one-time” or resulted in aggregate sizes that grew linearly with the number of signatures, O(N), which is a non-starter for high-throughput, decentralized systems. The challenge was to achieve both post-quantum security and the sublinear compression necessary for a scalable ledger.
Analysis
The paper’s core mechanism constructs an aggregate signature by leveraging the algebraic structure of Module-Lattices and the inherent hardness of the Short Integer Solution (SIS) problem. The scheme integrates a succinct proof of knowledge directly into the signature generation process. Conceptually, instead of appending every individual signature, the scheme computes a single, short “vector” that simultaneously satisfies the signing equations for all aggregated messages and public keys. This vector’s shortness is the cryptographic guarantee of correctness, derived from the difficulty of finding short vectors in a high-dimensional lattice (the SIS problem).
The key innovation is an aggregation technique that ensures the combined proof size is proportional to the security parameter plus a logarithmic factor of the number of signatures, O(λ + log N), making the aggregate signature size nearly constant in practice. This differs from previous linear-growth schemes by encoding the entire set of verification challenges into a single, compact lattice element.
Parameters
- Signature Size Growth ∞ O(log N) in the number of signatures aggregated. This is the first known many-time, non-interactive lattice scheme to achieve this sublinear compression rate.
- Security Basis ∞ Short Integer Solution (SIS) problem over Module-Lattices. This is a foundational, worst-case hard problem believed to be quantum-resistant.
- Aggregation Type ∞ Non-interactive and Many-time. Non-interactive aggregation allows anyone to combine signatures without coordination from the original signers.
Outlook
This research defines a critical building block for the next generation of decentralized infrastructure. The immediate strategic application is the implementation of quantum-resistant transaction aggregation in high-volume systems, such as rollups and data availability layers, where signature verification is a primary cost driver. In 3-5 years, this primitive could be integrated into the core consensus layers of major blockchains, dramatically reducing the storage footprint of the entire ledger and lowering the barrier to entry for full node operation. The next steps in this academic area will focus on removing the scheme’s reliance on the Random Oracle Model (ROM) to achieve a provably secure construction in the more stringent standard model.
