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Efficient Hardware Implementation of Finite Fields with Applications to Cryptography

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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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Authors and Affiliations

  1. Information and System Security Department, Philips Research, Eindhoven, The Netherlands

    Jorge Guajardo

  2. Horst-Görtz Institute for IT-Security, Ruhr-University, Bochum, Germany

    Tim Güneysu, Sandeep S. Kumar, Christof Paar & Jan Pelzl

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  1. Jorge Guajardo
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Guajardo, J., Güneysu, T., Kumar, S.S. et al. Efficient Hardware Implementation of Finite Fields with Applications to Cryptography. Acta Appl Math 93, 75–118 (2006). https://doi.org/10.1007/s10440-006-9072-z

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