Commutative Supersingular Isogeny Diffie Hellman Key Exchange Using Edward Curves

In a post-quantum environment, we suggest a productive commutative group action appropriate for non-interactive key exchange. The Diffie–Hellman key exchange technique resulted from group action runs quickly and permits public key validation at extremely minimal cost. Castryck presented the isogeny-based CSIDH key exchange protocol in 2018. In this paper CSIDH is based on supersingular elliptic curve isogenies. The ideal class group action on the Fp-isomorphism classes of Montgomery curves serves as its foundation. The original CSIDH technique represented points as x-coordinates over Montgomery curves, requiring a computation over Fp.On Edwards curves, a unique coordinate known as the w coordinate is used to compute group operations and isogenies. We must take into account points defined over Fp^4 if we attempt to compute the class group action on Edwards curves using the w-coordinate in a manner similar to that on Montgomery curves. Consequently, it is not an easy operation to calculate the class group action on Edwards curves with w coordinates over just Fp. We construct the new CSIDH algorithm using Edwards curves with w-coordinates over Fp.