The pairing is a mathematical notion which appeared in cryptography during the 80'. At the beginning, it was used to build attacks on cryptosystems, transferring the discrete logarithm problem on elliptic curves, to a discrete logarithm problem on finite fields. Now, pairings are used to construct some cryptographic protocols: diffie hellman tripartite, identity based encryption, or short signature. The main two pairings usually used are the tate and weil pairings. They use distortions and rational functions, and their complexities depend of the curve and the field involved.