This chapter excerpted from Hardware Implementation of Finite-Field Arithmetic, gives an example of finite-field applicationnamely, the implementation of the scalar product (point multiplication) over an elliptic curve. It is the basic computation primitive of elliptic curve cryptography.
The book, written by Jean-Pierre Deschamps, Jos Luis Imaa and Gustavo D. Sutter describes algorithms and circuits for executing finite-field operations, including addition, subtraction, multiplication, squaring, exponentiation and division.
Hardware Implementation of Finite-Field Arithmetic is published by McGraw-Hill. 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.
The book excerpt can be downloaded here.