Reducing the Complexity of Normal Basis Multiplication

Conference paper

DOI: 10.1007/978-3-319-16277-5_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9061)
Cite this paper as:
Eǧecioǧlu Ö., Koç Ç.K. (2015) Reducing the Complexity of Normal Basis Multiplication. In: Koç Ç., Mesnager S., Savaş E. (eds) Arithmetic of Finite Fields. WAIFI 2014. Lecture Notes in Computer Science, vol 9061. Springer, Cham


In this paper we introduce a new transformation method and a multiplication algorithm for multiplying the elements of the field GF\((2^k)\) expressed in a normal basis. The number of XOR gates for the proposed multiplication algorithm is fewer than that of the optimal normal basis multiplication, not taking into account the cost of forward and backward transformations. The algorithm is more suitable for applications in which tens or hundreds of field multiplications are performed before needing to transform the results back.

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of California Santa BarbaraSanta BarbaraUSA

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