Efficient Hardware Implementation of Finite Fields with Applications to Cryptography

Jorge Guajardo Merchan, Tim Güneysu, Sandeep Kumar, Chris­tof Paar, Jan Pelzl

Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications, Volume 93, Numbers 1-3, pp. 75-118, September 2006.


Abstract

The paper presents a survey of most common hardware architectures for finite field arithmetic especially suitable for cryptographic applications. We discuss architectures for three types of finite fields and their special versions popularly used in cryptography: binary fields, prime fields and extension fields. We summarize algorithms and hardware architectures for finite field multiplication, squaring, addition/subtraction, and inversion for each of these fields. Since implementations in hardware can either focus on high-speed or on area-time efficiency, a careful choice of the appropriate set of architectures has to be made depending on the performance requirements and available area.

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Tags: cryptography