Reducing the Complexity of Normal Basis Multiplication

  • Ömer Eǧecioǧlu
  • Çetin Kaya KoçEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9061)


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.


Normal Representation Normal Basis Elliptic Curve Cryptography Elliptic Curve Point Montgomery Multiplication 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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