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Original Research | Mathematics | Volume 15 Issue 7, July 2026 | Pages: 1272 - 1276 | India
A Reliability-Theoretic Framework for Deterministic RSA Exponent Generation Using Linear Diophantine Equations
Abstract: The deterministic generation of cryptographic parameters has become increasingly important in applications requiring transparency, reproducibility, and formal verification. This paper introduces a reliability-theoretic framework for deriving the public exponent of an RSA cryptosystem from the structured mathematical model. In the proposed methodology, the public encryption exponent is deterministically derived from the reliability polynomial associated with a documented network topology. Subsequently, the corresponding private decryption exponent is computed by solving the linear Diophantine equationed?1 (mod φ(n)) using the Extended Euclidean Algorithm. This procedure preserves the algebraic framework of the classical RSA cryptosystem while introducing a mathematically reproducible mechanism for public exponent generation. To demonstrate the proposed methodology, a five-component Wheatstone bridge network is employed as the underlying reliability model. The reliability polynomial of the network is first constructed and subsequently used to generate the public exponent. The remaining stages of RSA key generation, encryption, and decryption follow the standard cryptographic procedures. The mathematical correctness of the proposed framework is established through theoretical analysis, and its computational characteristics are compared with those of the conventional RSA algorithm. The results indicate that the proposed approach retains the computational efficiency and security properties of classical RSA while providing a deterministic, traceable, and verifiable key-generation methodology. Such a framework is particularly well suited to engineering applications in which documented reliability models and cryptographic infrastructures coexist, thereby facilitating greater accountability, reproducibility, and trust in cryptographic key management.
Keywords: Public-key cryptography, Reliability polynomial, Coherent systems, Linear Diophantine equations, RSA cryptosystem, Extended Euclidean Algorithm, Structure function, Number theory, Mathematical cryptography
How to Cite?: Dr. C. Manjula, Dr. Chaya Kumari Divakarla, "A Reliability-Theoretic Framework for Deterministic RSA Exponent Generation Using Linear Diophantine Equations", Volume 15 Issue 7, July 2026, International Journal of Science and Research (IJSR), Pages: 1272-1276, https://www.ijsr.net/getabstract.php?paperid=SR26715135831, DOI: https://dx.doi.org/10.21275/SR26715135831