Towards Generation of Secure Pseudorandom Prime Dataset Using Generative Adversarial Networks and The Learning Parity with Noise Problem

At present, prime numbers are an essential part of online security for secure key generation and digital signatures due to their unpredictabil-‎ity and resistance to factorization attacks, which has led to considerable interest in research on distributions of primes, especially prime gaps ‎and hidden patterns. Traditional prime analytical methods lack structural insight at the scale of cryptographic systems. This has led to greater ‎interest in applying machine learning (ML) techniques to prime analysis. However, due to a lack of publicly available high-quality datasets, ‎the evaluation of prime behavior using ML is often impeded. Furthermore, current prime generation techniques tend to become computa‎tionally inefficient when scaled to produce large quantities of high-bit-length prime numbers. In response, this paper proposes a novel generative pipeline, GANLPN, that leverages Generative Adversarial Networks (GANs) combined with the Learning Parity with Noise (LPN) ‎problem to generate bulk primes that are cryptographically secure. In this way, a publicly accessible dataset of 1,115,000 1024-bit primes ‎has been generated. The generated sequences passed all NIST SP800-22 statistical randomness tests with better inference time and throughput. The present work outlines a path for future ML-assisted studies of prime patterns, gaps, distributions, and the presence of weak keys in ‎cryptography.