Abstract
The subject of my thesis is the study of pairings, and particularly pairing based cryptography. My first works deal with arithmetic of pairings. First I compare the efficiency of the Weil and Tate pairings. Then I use an original representation of elements in a finite field to optimise the multiplications in an extension of this finite field. I proposed an arithmetic specifically for elliptic curves of embedding degree 15, in order to improve the arithmetic for these curves. Working on the arithmetic allowed me to have a clear picture of the arithmetic underlying pairing based cryptography. I was able to work on the weakness of pairing based cryptography with respect to side channel attacks.