Nathan Winningham | 2025 I.S. Symposium

Name: Nathan Winningham
Title: Implementation and Optimization of Lattice-Based Quantum-Resistant Encryption: Advancing and Understanding Secure Cryptographic Protocols
Major: Computer Science
Minor: Statistical & Data Sciences
Advisor: John Musgrave

Quantum computing threatens public privacy due to its potential to break modern cryptosystems such as RSA. Quantum algorithms, such as Grover’s algorithm, accelerate attacks on symmetric encryption methods such as AES, while Shor’s algorithm speeds up attacks on asymmetric encryption systems like RSA. Quantum computing is an emerging field that is predicted to break RSA 2048 within the next 10 years[23]. Post-quantum cryptography aims to combat this threat. Quantum-proof algorithms target the weaknesses of quantum computing and use them as bases for encryption. There are many promising methods of encryption that resist quantum algorithms. This paper took inspiration from a cryptosystem that was deemed to be impractical and turned it into a symmetric encryption scheme that is, in theory, quantum-resistant. This cryptosystem is built upon a simple lattice-based encryption scheme paired with other original techniques, creating a unique and theoretically secure cryptosystem. One such technique is a morphism tracking system, to force the ciphertext to stay within the Unicode range. It also includes a scrambling system that introduces an avalanche effect when incorrect keys are used. The lattice component of the algorithm utilizes high dimensionality, making it theoretically challenging for quantum computers to determine the correct key values. This is ensured by the scrambling operation, which requires that the values of the matrix to closely match the matrix key. This research covers areas of quantum computing and encryption to provide a background on why specific algorithmic choices were made along with explanations of how some quantum-resistant cryptosystems operate for comparison. Additionally, both a classical and theoretical quantum encryption algorithm were developed.

Posted in Symposium 2025 on May 1, 2025.