Finite Field Arithmetic for Cryptography

Erkay Savas, Cetin Koc
2010 IEEE Circuits and Systems Magazine  
Cryptography is one of the most prominent application areas of the finite field arithmetic. Almost all public-key cryptographic algorithms including the recent algorithms such as elliptic curve and pairing-based cryptography rely heavily on finite field arithmetic, which needs to be performed efficiently to meet the execution speed and design space constraints. These objectives constitute massive challenges that necessitate interdisciplinary research efforts that will render the best
more » ... the best algorithms, architectures, implementations, and design practices. This paper aims to provide a concise perspective on designing architectures for efficient finite field arithmetic for usage in cryptography. We present different architectures, methods and techniques for fast execution of cryptographic operations as well as high utilization of resources in the realization of cryptographic algorithms. While it is difficult to have a complete coverage of all related work, this paper aims to reflect the current trends and important implementation issues of finite field arithmetic in the context of cryptography. at 02:22:54 UTC from IEEE Xplore. Restrictions apply. ■ cative groups and rings such as RSA, Elliptic curve cryptography, ■ Pairing-based cryptography. ■ Cryptographic algorithms utilize arithmetic in finite mathematical structures such as finite multiplicative groups, rings, and finite fields. Authorized licensed use limited to: CityU. Downloaded on May 30,2010 at 02:22:54 UTC from IEEE Xplore. Restrictions apply.
doi:10.1109/mcas.2010.936785 fatcat:y6ya7xmjk5doznqj5lxxrnodoe