Finite Field Arithmetic

Finite Field Models in Arithmetic Combinatorics

The study of many problems in additive combinatorics, such as Szemerédi’s theorem on arithmetic progressions, is made easier by first studying models for the problem in F p , for some fixed small prime p. We give a number of examples of finite field models of this type, which allows us to introduce some of the central ideas in additive combinatorics relatively cleanly. We also give an indicatio...

Finite field models in arithmetic combinatorics - ten years on

Acceleration of Finite Field Arithmetic with an Application to Reverse Engineering Genetic Networks

Finite field arithmetic plays an important role in a wide range of applications. This research is originally motivated by an application of computational biology where genetic networks are modeled by means of finite fields. Nonetheless, this work has application in various research fields including digital signal processing, error correcting codes, Reed-Solomon encoders/decoders, elliptic curve...

Finite Field Arithmetic Architecture Based on Cellular Array

Finite field arithmetic operations, especially for the binary field GF(2 m ), have been widely used in the areas of data communication and network security applications such as errorcorrecting codes [1,2] and cryptosystems such as ECC(Elliptic Curve Cryptosystem) [3,4]. The finite field multiplication is the most frequently studied. This is because the timeconsuming operations such as exponenti...

A High Performance VLIW Processor for Finite Field Arithmetic

Finite field arithmetic forms the mathematical basis for a variety of applications from the area of cryptography and coding. For finite fields of large extension degrees (as for cryptography), arithmetic operations are computation intensive and require dedicated hardware support under given timing constraints. We present a new architecture of a high performance VLIW processor that can perform b...

Efficient Software Implementations of Large Finite Fields GF (2) for Secure Storage Applications

Finite fields are widely used in constructing error-correcting codes and cryptographic algorithms. In practice, error-correcting codes use small finite fields to achieve high-throughput encoding and decoding. Conversely, cryptographic systems employ considerably larger finite fields to achieve high levels of security. We focus on developing efficient software implementations of arithmetic opera...