An Authenticated Key Agreement Protocol Using Isogenies Between Elliptic Curves

All the current public-key cryptosystems will become insecure when size of a quantum register is sufficient. An Authenticated key agreement protocols, which is against the attack of quantum computer, is proposed. The strength of the proposed protocol is based on the problem of searching for an isogeny between elliptic curves. The time complexity for solving this problem is exponential, and the problem seems to be hard for solving with a quantum computer. The proposed protocol can provide the security properties known session key security, forward security, resistance to key-compromise impersonation attack and to unknown key-share attack, key control.