SRAM-based Gaussian Noise Generation for Post- Quantum Cryptography: A Lightweight Hardware Approach

Abstract As quantum computing progresses, conventional public-key cryptographic schemes such as RSA and ECC face increasing vulnerability to quantum attacks. Post-quantum cryptography (PQC), especially schemes based on the learning with errors (LWE) problem, depends on Gaussian-distributed noise for security. However, traditional Gaussian noise generation methods—such as Box–Muller, rejection sampling, and Ziggurat—incur high computational and memory costs, making them unsuitable for lightweight or embedded systems. This paper proposes a hardware-based Gaussian noise generator that uses the inherent randomness of static random access memory (SRAM) power-on states. The method aggregates SRAM start-up bits and computes their Hamming weight to efficiently generate Gaussian-distributed integers without analog components, large lookup tables, or external random number generators. Experimental results show that the output closely matches a Gaussian distribution under various group sizes and environmental conditions. Statistical tests, including Shapiro–Wilk and Kolmogorov–Smirnov, achieve over 95% pass rates, while Kullback–Leibler divergence remains below 0.01. The generator also maintains Gaussian properties across a wide thermal range (−20 °C to 100 °C). These results demonstrate that the proposed SRAM-based generator offers a practical, lightweight, and thermally robust solution for PQC, particularly in lattice- and code-based cryptographic schemes.