Abstract : Elliptic Curve Cryptography (ECC) is more and more used in public-key cryptosystems, especially because it delivers the highest strength-per-bit of any public-key cryptography system known today. Consequently, ECC-based cryptosystems are smaller than RSA-based cryptosystems, thus ECC is more convenient for very contrained circuits (e.g. smart cards). Besides, ECC has gained some benets from the improvement of computer and curve arithmetic, which helps it to be a viable alternative to RSA in the industrial world. Although cryptosystem designers must improve continuously the performance of their devices, they must also protect them against physical attacks which can be a real threat for their security. Indeed, some efficient attacks called \side-channel" and \fault" attacks have been intensively developed. Thus, cryptosystem designers must embed some countermeasures to these attacks. Nevertheless, attention must be paid that these countermeasures must not add new vulnerabilities to the device and should induce a limited overhead to its global performance. It has been proposed during this Ph.D. thesis a new arithmetic unit architecture for ECC. Its performance are better than most of the published designs. This is mainly due to the choice of the used number representation, which is redundant (borrow-save representation). Another contribution of this study comes from the protection of this arithmetic unit against side-channel attacks : thanks to the state-of-the-art, the proposed side-channel-protected circuit becomes the quickest published ECC arithmetic unit. Finally, the parity-preservation principle has been studied in order to prevent our design from fault attacks. This latter contribution leads to encouraging results.