Acta Appl Math DOI 10.1007/s10440-006-9046-1 Efficient Software-Implementation of Finite Fields with Applications to Cryptography Jorge Guajardo · Sandeep S. Kumar · Christof Paar · Jan Pelzl © Springer Science + Business Media B.V. 2006 Abstract In this work, we present a survey of efficient techniques for software imple- mentation 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 under- lying 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. Mathematics Subject Classifications 12-02 · 12E30 · 12E10 Key words field arithmetic · cryptography · efficient implementation · binary field arithmetic · prime field arithmetic · extension field arithmetic · optimal extension fields J. Guajardo (B ) Information and System Security Department, Philips Research, Eindhoven, The Netherlands e-mail: Jorge.Guajardo@philips.com S. S. Kumar · C. Paar · J. Pelzl Horst-Görtz Institute for IT-Security, Ruhr-University Bochum, Bochum, Germany S. S. Kumar e-mail: kumar@crypto.rub.de C. Paar e-mail: cpaar@crypto.rub.de J. Pelzl e-mail: pelzl@crypto.rub.de