SRAM based Gaussian noise generation for post quantum cryptography

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 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.