Abstract:

The rapid development of quantum computing technology poses an unprecedented potential threat to the existing public key cryptosystems. Thus the design and application of post-quantum cryptosystems have emerged, and isogeny-based cryptographic protocols are crucial components of them. However, to balance both security and efficiency, the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) protocol is one of the few available key exchange protocols in the field of isogeny-based cryptography. Therefore, this paper focuses on the study and acceleration of a series of key exchange protocols based on CSIDH. Specifically, we consider Montgomery curves defined over prime fields with(mod 8), whose endomorphism rings are isomorphic to , and then construct new key exchange protocol, CSIDH-G. Meanwhile, we prove that there is no key collisions in CSIDH-G that exist in other isogeny-based key exchange protocols, and propose compact user private key selection intervals. Finally, protocol operation efficiency experiments are carried out. By optimizing the key selection interval, the efficiency of the proposed protocol is improved by 5.95% over that of the original CSIDH protocol, verifying its accuracy and effectiveness. In conclusion, the algorithm has various advantages such as enhancing the efficiency of isogeny-based key exchange protocol, ensuring convenient public key verification, avoiding the private key collisions in the existing protocol, and increasing the diversity of post-quantum cryptosystems of Diffie-Hellman form.

Key words: post-quantum cryptography, isogeny-based cryptography, key exchange protocol, commutative supersingular isogeny Diffie-hellman protocol, montgomery supersingular elliptic curve