Briefing
Current zero-knowledge succinct non-interactive arguments of knowledge (ZK-SNARKs) rely on assumptions vulnerable to quantum computers, posing a long-term threat to blockchain security. This research addresses the problem by proposing a novel folding scheme built entirely on lattice-based cryptography, a family of primitives considered quantum-resistant. The foundational breakthrough is the construction of a recursive proof system whose security is rooted in the Module Short Integer Solution (MSIS) problem, fundamentally replacing discrete logarithm-based commitments with a quantum-secure alternative. This new mechanism allows for the incremental verification of massive, streaming computations ∞ a capability critical for building highly scalable Layer 2 architectures that maintain provable security in a post-quantum environment.
Context
The prevailing theoretical limitation in high-performance zero-knowledge systems is twofold. First, most production-ready SNARKs, such as those relying on the KZG commitment scheme, are based on pairing-friendly elliptic curves, making them susceptible to Shor’s algorithm and a quantum adversary. Second, processing long-running or streaming computations, like the history of a rollup chain, traditionally requires the prover to generate a single, computationally massive proof at the end, necessitating the storage of the entire computation history in memory. This approach is both resource-intensive and slow, representing a major bottleneck for the practical application of verifiable computation in real-world systems with high transaction throughput.
Analysis
The core mechanism, a lattice-based folding scheme, adapts the concept of Incremental Verifiable Computation (IVC) to a quantum-resistant foundation. The process allows a prover to “fold” two separate instances of a computation into a single, smaller instance recursively. The fundamental difference from previous folding schemes (e.g. those based on elliptic curves) is the substitution of the underlying cryptographic commitments. The new primitive leverages the hardness of the Module Short Integer Solution (MSIS) problem over polynomial rings, which is a key primitive in lattice cryptography.
Conceptually, this allows the prover to continuously update a single, constant-size proof ∞ the “folded instance” ∞ as new computation steps arrive, eliminating the need to wait for the entire data stream to complete before verification can begin. This transforms proof generation from a batch process into a streamable, quantum-secure one.
Parameters
- Security Foundation ∞ Module Short Integer Solution (MSIS) problem. This is the specific lattice-based mathematical problem upon which the scheme’s quantum resistance is proven.
- Commitment Replacement ∞ Discrete Logarithm-based commitments. The scheme replaces these quantum-vulnerable primitives with lattice-based counterparts.
- Proof Size ∞ Constant. The recursive folding ensures the proof size remains constant regardless of the number of computation steps or folded instances.
Outlook
This foundational work establishes a new trajectory for zero-knowledge research by demonstrating the first practical path toward quantum-secure recursive proof systems. The immediate application is the creation of future-proof, highly efficient ZK-Rollups and other Layer 2 solutions, which will be able to process transactions incrementally while maintaining end-to-end security against a quantum adversary. In the next three to five years, this technology will unlock new categories of applications, including verifiable AI and private, long-running decentralized autonomous organizations (DAOs), where the integrity of vast, continuous data streams must be proven without reliance on pre-quantum cryptographic assumptions.
