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

  • Authors

    https://doi.org/10.14419/9bppfw31

    Received date: November 10, 2025

    Accepted date: December 10, 2025

    Published date: December 17, 2025

  • Cryptography; Generative Adversarial Networks; Learning Parity with Noise; Prime Dataset; Pseudorandom Number Generator

  • Abstract

    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.

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  • How to Cite

    Asiedu, D., Mensah, P. K. ., Appiahene, P. ., & Nimbe, P. . (2025). Towards Generation of Secure Pseudorandom Prime Dataset ‎Using Generative Adversarial Networks and The Learning ‎Parity with Noise Problem. International Journal of Basic and Applied Sciences, 14(8), 382-398. https://doi.org/10.14419/9bppfw31