This chapter excerpted from Hardware Implementation of Finite-Field Arithmetic describes several algorithms, namely, the integer division, the reduction mod Bk— a, the precomputation of Bik mod m, and the Barrett algorithm. All the mentioned algorithms have been synthesized and implemented within field programmable components.

The book, written by Jean-Pierre Deschamps, José Luis Imaña and Gustavo D. Sutter describes algorithms and circuits for executing finite-field operations, including addition, subtraction, multiplication, squaring, exponentiation and division.

Reproduced from the book Hardware Implementation of Finite-Field Arithmetic Copyright © 2009 McGraw-Hill. Reproduced by permission of McGraw-Hill. Written permission from McGraw-Hill is required for all other uses. The book is intended for electronic design engineers working with embedded systems, system on chip and FPGA implementations, as well as EE students and researchers and provides information on electronic circuit synthesis. It can be ordered for $115 from the McGraw-Hill website.