Performance Comparism Of Finite Fields Arithmetic In Elliptic Curve Based Cryptographic
Aliyu Danladi Hina · 2013
Finite fields are well studied discrete structures with a vast array of useful properties and are indispensable in the theory and application of cryptography. Arithmetic in finite field is an integral part of many public key algorithms. The performance of elliptic curve based schemes depends on the efficient arithmetic in the underlying field. ; Cryptography is one of the most prominent application areas of finite field arithmetic. Most of 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 research efforts that will render the best algorithms, architectures, implementations, and design practices. This paper aims to provide a concise perspective for efficient finite field arithmetic in the most widely used finite field for usage in cryptography, The Optimal Extension Field.