Efficient Software-Implementation of Finite Fields with Applications to Cryptography

Jorge Guajardo Merchan, 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. 3-32, September 2006.


In this work, we present a survey of efficient techniques for software implementation of finite field arithmetic especially suitable for cryptographic applications. We discuss different algorithms for three types of finite fields and their special versions popularly used in cryptography: Binary fields, prime fields and extension fields. Implementation details of the algorithms for field addition/subtraction, field multiplication, field reduction and field inversion for each of these fields are discussed in detail. The efficiency of these different algorithms depends largely on the underlying micro-processor architecture. Therefore, a careful choice of the appropriate set of algorithms has to be made for a software implementation depending on the performance requirements and available resources.

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Tags: cryptography