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Efficient Multiplication in Finite Field Extensions of Degree 5

  • Nadia El Mrabet
  • Aurore Guillevic
  • Sorina Ionica
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6737)

Abstract

Small degree extensions of finite fields are commonly used for cryptographic purposes. For extension fields of degree 2 and 3, the Karatsuba and Toom Cook formulæ perform a multiplication in the extension field using 3 and 5 multiplications in the base field, respectively. For degree 5 extensions, Montgomery has given a method to multiply two elements in the extension field with 13 base field multiplications. We propose a faster algorithm, which requires only 9 base field multiplications. Our method, based on Newton’s interpolation, uses a larger number of additions than Montgomery’s one but our implementation of the two methods shows that for cryptographic sizes, our algorithm is much faster.

Keywords

finite field arithmetic implementation interpolation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Nadia El Mrabet
    • 1
  • Aurore Guillevic
    • 2
    • 3
  • Sorina Ionica
    • 4
  1. 1.LIASD - Université Paris 8France
  2. 2.Laboratoire ChiffreThales Communications S.A.Colombes CedexFrance
  3. 3.Équipe crypto DI/LIENS, École Normale SupérieureFrance
  4. 4.TANC, Inria Saclay and LIX, École PolytechniqueFrance

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