Adaptive framework combines prime testing with optimization techniques
Bridging Number-Theoretic Primality Testing And Algorithmic Optimization: An Adaptive Cryptographic Framework
Cryptography and SecurityMachine Learning
Summary
Modern encryption systems rely on very large prime numbers that are hard to find and prove prime. The authors propose a new system that uses traditional math alongside modern machine learning and hardware tricks to test and prove if large numbers are prime. They also consider new secure sources of randomness to keep the system safe even if the prime numbers are unevenly distributed. This approach helps improve the reliability and security of cryptographic keys.
What this means in practice
- •For cryptographic engineers: Generate and verify large prime numbers more securely and efficiently for public-key systems using adaptive precision and mixed testing methods.
- •For hardware designers: Implement hardware-level optimizations for primality testing that improve speed and maintain security even with biased prime distributions.
Authors
Tran Minh Thanh, Vo Hoai Viet
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.