Tran Minh THANH, Vo Hoai Viet · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.30935 · cited by 0 works (OpenAlex) · open-access PDF
La sécurité des systèmes cryptographiques modernes à clé publique, tels que RSA, Diffie-Hellman et ECC, dépend entièrement de l'intractabilité computationnelle de la factorialisation des nombres entiers et des problèmes de logarithmes discrètes. Pour que ces algorithmes asymétriques fonctionnent, une exigence fondamentale est que le système doit être capable de générer, tester et prouver simultanément la primauté des nombres extraordinaires. Pour répondre à ces exigences, cette étude propose un cadre complet, reliant la théorie des nombres classiques à des modèles modernes d'apprentissage automatique et à des algorithmes d'optimisation. Plus précisément, le document définit une architecture adaptative, arbitraire et précise dédiée exclusivement au
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The security of modern public-key cryptographic systems, such as RSA, Diffie-Hellman, and ECC, depends entirely on the computational intractability of the integer factorization and discrete logarithm problems. For these asymmetric algorithms to operate, a core requirement is that the system must be capable of generating, testing, and simultaneously proving the primality of extraordinarily large numbers. To meet those requirements, this study proposes a comprehensive framework, bridging clas- sical number theory with modern machine learning models and optimization algorithms. Specifically, the paper delineates an adaptive, arbitrary-precision architecture dedicated exclusively to primality testing. Concurrently, the research deeply analyzes the theoretical foundations of testing methods (both deterministic and probabilistic), hardware-level optimization techniques, and the application of quantum-secured entropy sources, while providing rigorous mathematical proofs to guarantee security even when the prime distribution is biased.
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Topics: Primality test, Cryptography, Computer science, Theoretical computer science, Discrete logarithm, Mathematical proof
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