Modular Reduction in GF(2n) without Pre-computational Phase

  • M. Knežević
  • K. Sakiyama
  • J. Fan
  • I. Verbauwhede
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5130)


In this study we show how modular multiplication with Barrett and Montgomery reductions over certain finite fields of characteristic 2 can be implemented efficiently without using a pre-computational phase. We extend the set of moduli that is recommended by Standards for Efficient Cryptography (SEC) by defining two distinct sets for which either Barrett or Montgomery reduction is applicable. As the proposed algorithm is very suitable for a fast modular multiplication, we propose an architecture for the fast modular multiplier that can efficiently be used without pre-computing the inverse of the modulus.


Modular multiplication Barrett reduction Montgomery reduction elliptic curve cryptography public-key cryptography 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • M. Knežević
    • 1
  • K. Sakiyama
    • 1
    • 2
  • J. Fan
    • 1
  • I. Verbauwhede
    • 1
  1. 1.Department Electrical Engineering - ESAT/SCD-COSIC and IBBTKatholieke Universiteit LeuvenLeuven-HeverleeBelgium
  2. 2.Dept. of Information and Communication Eng.University of Electro-CommunicationsTokyoJapan

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