Abstract:
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 crypto-
graphy: 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. 

BibTeX:
@Article{A-GKPP06,
author   = {Jorge Guajardo and Sandeep S. Kumar and 
           Christof Paar and Jan Pelzl},
title    = "{Efficient Software-Implementation of Finite Fields 
           with Applications to Cryptography}",
journal  = {Acta Applicandae Mathematicae: An International 
           Survey Journal on Applying Mathematics and 
           Mathematical Applications},
year     = {2006},
OPTkey   = {},
volume   = {93},
number   = {1--3},
pages    = {3--32},
month    = {August}
}