LWE Based Quantum-Resistant Pseudo-Random Number Generator

Abstract

In the realm of cryptography, computational statistics, gaming, simulation processes, gambling, and other related fields, the design of Cryptographically Secure Pseudo-Random Number Generators (CSPRNGs) poses a significant challenge. With the rapid advancement of quantum computing, the imminent "quantum-threat" looms closer, posing a risk to our current cryptographically secure PRNGs. Consequently, it becomes crucial to address these threats seriously and develop diverse tools and techniques to ensure that cryptographically secure Pseudo-Random Number Generators (PRNGs) remain unbreakable by both classical and quantum computers. this paper presents a novel approach to constructing an effective Quantum-Resistant Pseudo-Random Number Generator (QRPRNG) using the principles of lattice-based Learning with Errors (LWE). LWE is considered quantum-resistant due to its reliance on the hardness of problems like the Shortest Vector Problem and Closest Vector Problem. Our work focuses on developing a QRPRNG that utilizes a Linear Feedback Shift Register (LFSR) to generate a stream of pseudo-random bits. To construct a secure seed for the QRPRNG, LWE is employed. The proposed QRPRNG incorporates a secure seed input to the LFSR, and employs a Homomorphic function to protect the security of the finite states within the LFSR. NIST statistical tests are conducted to evaluate the randomness of the generated output by the constructed QRPRNG. The proposed QRPRNG achieves a throughput of 35.172 Mbit/s.