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A fast software implementation for arithmetic operations in GF(2n)

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Advances in Cryptology — ASIACRYPT '96 (ASIACRYPT 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1163))

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Abstract

We present a software implementation of arithmetic operations in a finite field GF(2n), based on an alternative representation of the field elements. An important application is in elliptic curve crypto-systems. Whereas previously reported implementations of elliptic curve cryptosystems use a standard basis or an optimal normal basis to perform field operations, we represent the field elements as polynomials with coefficients in the smaller field GF(216). Calculations in this smaller field are carried out using pre-calculated lookup tables. This results in rather simple routines matching the structure of computer memory very well. The use of an irreducible trinomial as the field polynomial, as was proposed at Crypto'95 by R. Schroeppel et al., can be extended to this representation. In our implementation, the resulting routines are slightly faster than standard basis routines.

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Authors and Affiliations

  1. ESAT-COSIC, Katholieke Universiteit Leuven, K. Mercierlaan 94, B-3001, Heverlee, Belgium

    Erik De Win (N.F.W.O. research assistant), Antoon Bosselaers, Servaas Vandenberghe, Peter De Gersem (N.F.W.O. research assistant) & Joos Vandewalle

Authors
  1. Erik De Win
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  2. Antoon Bosselaers
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  3. Servaas Vandenberghe
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  4. Peter De Gersem
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  5. Joos Vandewalle
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Editor information

Kwangjo Kim Tsutomu Matsumoto

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© 1996 Springer-Verlag

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De Win, E., Bosselaers, A., Vandenberghe, S., De Gersem, P., Vandewalle, J. (1996). A fast software implementation for arithmetic operations in GF(2n). In: Kim, K., Matsumoto, T. (eds) Advances in Cryptology — ASIACRYPT '96. ASIACRYPT 1996. Lecture Notes in Computer Science, vol 1163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034836

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  • DOI: https://doi.org/10.1007/BFb0034836

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  • Print ISBN: 978-3-540-61872-0

  • Online ISBN: 978-3-540-70707-3

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