In this paper we propose a three participants variation of the
Diffie--Hellman protocol. This variation is based on the Weil and Tate
pairings on elliptic curves, which were first used in cryptography as
cryptanalytic tools for reducing the discrete logarithm problem on some
elliptic curves to the discrete logarithm problem in a finite field.
Cryptosystem - Key exchange - Discrete logarithm - Elliptic curve - Pairing