Briefing
The foundational problem addressed is the quantum vulnerability inherent in most current efficient zero-knowledge proof systems, such as those relying on the KZG polynomial commitment scheme, which are based on elliptic curve pairings susceptible to Shor’s algorithm. This research introduces Greyhound , a novel polynomial commitment scheme constructed entirely from standard lattice-based assumptions, a class of cryptography considered post-quantum secure. The core breakthrough is the composition of a simple sigma protocol for polynomial evaluation with the LaBRADOR proof system, yielding a succinct argument of knowledge. This new primitive provides the necessary cryptographic foundation for all data-intensive scaling solutions, like ZK-rollups, to transition to a quantum-resistant architecture while maintaining the critical efficiency required for real-world deployment.
Context
Prior to this work, the prevailing challenge was the fundamental trade-off between the efficiency and quantum security of polynomial commitment schemes (PCS). Schemes like KZG offer optimal constant-size proofs and fast verification, but their reliance on the Discrete Logarithm Problem makes them insecure against a large-scale quantum computer. While lattice-based cryptography provides quantum resistance, previous lattice-based PCS constructions were either non-succinct, resulting in massive proof sizes, or concretely inefficient, creating a theoretical limitation that stalled the development of post-quantum secure, scalable decentralized systems.
Analysis
Greyhound’s core mechanism is a new sigma protocol that allows a prover to demonstrate the correct evaluation of a polynomial at a specific point. This protocol is rooted in the hardness of the Ring-Learning with Errors (Ring-LWE) problem, a standard lattice assumption. To transform this interactive proof into a succinct, non-interactive argument (a requirement for blockchain use), the sigma protocol is compiled using the LaBRADOR proof system.
This composition enables the prover to generate a commitment to a large polynomial and subsequently prove a specific evaluation with a proof size that is polylogarithmic in the polynomial’s degree. The design fundamentally differs from previous lattice-based attempts by optimizing the underlying algebraic structure to achieve concrete efficiency without compromising the security derived from the standard lattice assumption.
Parameters
- Proof Size for 230 Degree ∞ 93KB. This represents the size of the succinct proof for a polynomial with over a billion coefficients, a reduction of 8000x compared to a recent lattice-based construction.
- Verifier Runtime Complexity ∞ Sublinear. The time required for the verifier to check the proof grows slower than the size of the polynomial, ensuring fast verification for large computations.
- Cryptographic Assumption ∞ Standard Lattice Assumptions. The scheme’s security is based on the Ring-LWE problem, a well-studied problem considered resistant to quantum attacks.
Outlook
This research immediately opens a new avenue for post-quantum secure verifiable computation. In the next 3-5 years, this primitive will be integrated into the next generation of ZK-rollups, enabling them to inherit quantum resistance at the cryptographic layer. The low proof size and fast verification are crucial for data availability sampling protocols, suggesting that future decentralized architectures can achieve both massive scalability and long-term security simultaneously. The work establishes a new benchmark for lattice-based succinctness, accelerating academic research into fully post-quantum secure blockchain foundations.
