Advancements in Isogeny-Based Cryptography: A Mathematical Approach to Post-Quantum Security

In this paper, we have discussed isogeny-based cryptography as a rather appealing option for post-quantum security. We provide analysis of current protocols like SIDH (Supersingular Isogeny Diffie-Hellman) and SIKE (Supersingular Isogeny Key Encapsulation) setting up fundamental issues with their security and performance. In this work we introduce a novel isogeny pathfinding algorithm that employs graph theory as well as probabilistic models in order to lower its computational complexity. The results show significant improvement in both efficiency and security, strengthening the case for the use of isogeny based systems in a quantum-resilient cryptographic space.