Recently, many cryptographers have put a lot of research in multilinear maps for cryptography. These are a generalization of bilinear maps, also known as bilinear pairings, and which have already been proved to have many applications in cryptography, as for instance a secure key exchange between three people, known as the 3-partite one-round Diffie-Hellman key exchange by Antoine Joux, 2000, a direct generalization of the classical Diffie-Hellman key exchange protocol by Diffie and Hellman in 1976. Roughly speaking, by key exchange protocol, we mean that two (or more?) people want to share a common message (a key) by communicating over an insecure channel. The goals of this talk are first to first define such multilinear maps; second to study some elliptic curve arithmetic and bilinear pairings (especially, the Weil pairing) on elliptic curves, in order to, third, understand the key exchange protocol on elliptic curves by Joux. To conclude, a direct application of multilinear maps in order to generalize these results.