Optimizing Galois Field Arithmetic for Diverse Processor Architectures and Applications

Galois field implementations are central to the design of many reliable and secure systems, with many systems implementing them in software. The two most common Galois field operations are addition and multiplication; typically, multiplication is far more expensive than addition. In software, multiplication is generally done with a look-up to a pre-computed table, limiting the size of the field and resulting in uneven performance across architectures and applications. In this paper, the authors first analyze existing table-based implementation and optimization techniques for multiplication in fields of the form GF(2 l).