Elliptic Curve MQV (ECMQV)

Elliptic Curve Cryptography (ECC) is based on the algebraic structure of elliptic curves over finite fields. The use of elliptic curves in cryptography was independently suggested by Neal Koblitz and Victor Miller in 1985.

MQV (Menezes-Qu-Vanstone) is an authenticated protocol for key agreement based on the Diffie-Hellman scheme. Like other authenticated Diffie-Hellman schemes, MQV provides protection against an active attacker. The protocol can be modified to work in an arbitrary finite group, and elliptic curve groups, where it is known as Elliptic Curve MQV (ECMQV).

Elliptic Curve Menezes-Qu-Vanstone (ECMQV) is a key agreement performed using elliptical curves rather than traditional integers. The protocol was introduced by Laurie Law, Alfred Menenzes and others in “An Efficient Protocol for Authenticated Key Agreement”. ECMQV is authenticated, so it does not suffer Man in the Middle (MitM) attacks.

However Elliptic Curve MQV leaks private session information, and a Fully Hashed MQV protocol should be used instead. Authentication is necessary to avoid Man-in-the-middle attacks. Static public keys do not provide forward secrecy or key-compromise impersonation resilience. For unauthenticated Diffie-Hellman using elliptic curves, see Elliptic Curve Diffie-Hellman Exchange (ECDHE).

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia articles “MQV”, “Elliptic Curve Cryptography” and “Elliptic Curve Menezes-Qu-Vanstone”.