Analysis of Success Threshold of (4,5) in Hybrid Series- Parallel Networks for Enhanced Cryptographic Key Reliability

Abstract

    This research presents an innovative hybrid network model designed to enhance the reliability of systems used in cryptographic frameworks and data protection. The primary scientific contribution lies in designing a structured architecture that integrates series and parallel configurations using five components with a success threshold of (4,5). Graph theory was employed to determine the minimum path and cut sets, and the system’s reliability formula was derived through reduction techniques to simplify the complex network. Numerical results demonstrate high reliability in cryptographic applications and overall system performance, achieving an optimal balance between complexity and security compared to traditional models. Monte Carlo simulation was used to confirm the consistency between theoretical derivations and applied results, and a sensitivity analysis was performed on critical components.