Proposal of a New Isogeny-Based Cryptographic Protocol: Formal Analysis and Comparison

‎This paper proposes a novel isogeny-based cryptographic protocol that leverages the dual hardness of the isogeny problem and linear code decoding for secure post-quantum key exchange‎. ‎The proposed protocol‎, ‎Isogeny-Based Key Exchange with Error-Correcting Codes (IKEC)‎, ‎offers enhanced security‎, ‎computational efficiency‎, ‎and practical applicability‎, ‎making it a viable alternative to existing schemes like SIDH‎. ‎We provide a rigorous mathematical description of the protocol‎, ‎including key generation‎, ‎key exchange‎, ‎security analysis‎, ‎and performance evaluation‎. ‎Additionally‎, ‎we present a formal analysis‎, ‎comprehensive comparisons with existing protocols‎, ‎and insights into potential attack vectors and countermeasures‎. ‎The discussion concludes with potential real-world applications‎, ‎advanced cryptographic techniques‎, ‎and future research directions‎.