Briefing
This dissertation addresses the critical vulnerability of classical cryptography to emerging quantum computing capabilities by introducing novel code-based zero-knowledge proof protocols. It proposes HammR, a pre-quantum zero-knowledge proof for verifying error vector constraints, and extends it to multi-party computation, alongside a new zero-knowledge protocol for the syndrome decoding problem. This work culminates in the development of CROSS, an arithmetic-optimized post-quantum digital signature scheme, establishing a robust framework for quantum-resilient cryptographic primitives and enhancing the foundational security of future blockchain architectures.
Context
Before this research, the cryptographic landscape faced an impending challenge → the existential threat posed by scalable quantum computers to established classical encryption methods. Prevailing theoretical limitations centered on the reliance of current digital signature schemes and proof systems on computational hardness assumptions vulnerable to quantum algorithms, necessitating a paradigm shift towards post-quantum cryptography to maintain long-term security.
Analysis
The paper’s core mechanism involves constructing zero-knowledge proofs from coding theory, a branch of mathematics focused on error detection and correction. It introduces HammR, a zero-knowledge proof protocol designed to verify specific properties of error vectors, such as their Hamming weight, without revealing the vectors themselves. This protocol is then adapted for multi-party computation, allowing distributed verification.
A key breakthrough is a novel zero-knowledge proof protocol for the syndrome decoding problem, which leverages a multi-party “in-the-head” computation model and an amicable syndrome constraint verification step. This fundamentally differs from previous approaches by directly embedding zero-knowledge properties within code-based cryptographic primitives, creating proofs that are succinct, complete, and sound, and can be batched efficiently.
Parameters
- Core Concept → Code-Based Zero-Knowledge Proofs
- New Protocol → HammR
- New ZKP Application → Syndrome Decoding Problem
- Post-Quantum Scheme → CROSS Digital Signature
- Key Author → Freeman Slaughter
- Institution → Clemson University
- Date of Award → August 2025
Outlook
This research opens new avenues for developing quantum-resistant cryptographic solutions, particularly in digital signatures and privacy-preserving protocols. The next steps involve further optimization of these code-based ZKPs for practical deployment and integration into existing blockchain infrastructure. In 3-5 years, this theory could unlock truly quantum-secure digital identities, confidential transactions, and verifiable computation, establishing a new baseline for trust and security in a post-quantum world. It invites further academic exploration into the efficiency and versatility of code-based primitives for broader cryptographic applications.
