Date of Award
8-2025
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
Committee Chair/Advisor
Felice Manganiello
Committee Member
Ryann Cartor
Committee Member
Rafael Gregorio Lucas D’Oliveira
Committee Member
Paolo Santini
Abstract
Quantum computing is developing at an expeditious rate, and once fully scalable quantum computers become realized, classical cryptographic systems face obsolescence. This approaching peril has prompted a paradigm shift away from pre-quantum cryptography and towards post-quantum primitives, such as those that arise from the field of coding theory. Among these, zero-knowledge proofs have emerged as a dynamic tool instrumental in constructing quantum-resilient digital signature schemes.
We being by introducing HammR, a pre-quantum zero-knowledge proof protocol designed to verify Hamming weight and entry constraints of error vectors, and comprehensively establish its security. Subsequently, we extend HammR to the multi-party computation setting, enabling instances to be distributed across many participants while ensuring zero-knowledge properties. By leveraging the multi-party computation in-the-head model, we develop a novel zero-knowledge proof protocol for the syndrome decoding problem by incorporating a multi-party amicable syndrome constraint verification step. The resulting scheme enjoys completeness and soundness, and can be batched in a compact manner.
This dissertation continues by analyzing the detection and correction of generic errors, which are those without any particular metric structure, and we utilize these foundational results in constructing a generic- error zero-knowledge proof protocol. We also present CROSS, an arithmetic-optimized post-quantum digital signature scheme based on the syndrome decoding problem, a promising post-quantum coding-theoretic problem. CROSS is currently a Round 2 candidate in the NIST Call for Additional Signatures standardization process, an acclamation shared with only one other code-based scheme.
Our results demonstrate the expedient security properties that zero-knowledge proof methods have to offer with regards to constructing secure post-quantum cryptographic schemes.
Recommended Citation
Slaughter, Freeman, "Constructing Code-Based Zero-Knowledge Proofs Leveraging Generic Errors and Bounded Vectors" (2025). All Dissertations. 4040.
https://open.clemson.edu/all_dissertations/4040
Author ORCID Identifier
0009-0000-5787-6183