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Bridging Number-Theoretic Primality Testing And Algorithmic Optimization: An Adaptive Cryptographic Framework

Tran Minh THANH, Vo Hoai Viet · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.30935 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

现代公钥密码系统的安全性,如RSA、Diffie-Hellman和ECC,完全取决于整数因子化和分离式算法问题的计算不可取代性。为了使这些不对称的算法运作,一个核心要求是系统必须能够生成、测试并同时证明非常大的数字的原始性。为了满足这些要求,本研究提出了一个综合的框架,将类数理论与现代机器学习模型和优化算法相结合。具体来说,该论文描述了一种专门用于原始性测试的适应性、任意准确性架构。同时,研究深入分析了测试方法(确定性和概率性)的理论基础,硬件级别的优化技术,以及量子源的应用,同时提供生物安全保障的基本数学分散性。

Machine translation (Meta M2M100); the English original follows.

Abstract

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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