Designs, Codes and Cryptography

, Volume 14, Issue 1, pp 57–69 | Cite as

Montgomery Multiplication in GF(2k)

  • Cetin K. Koc
  • Tolga Acar


We show that the multiplication operation c=a · b · r-1 in the field GF(2k can be implemented significantly faster in software than the standard multiplication, where r is a special fixed element of the field. This operation is the finite field analogue of the Montgomery multiplication for modular multiplication of integers. We give the bit-level and word-level algorithms for computing the product, perform a thorough performance analysis, and compare the algorithm to the standard multiplication algorithm in GF(2k. The Montgomery multiplication can be used to obtain fast software implementations of the discrete exponentiation operation, and is particularly suitable for cryptographic applications where k is large.

finite fields multiplication cryptography 


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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Cetin K. Koc
    • 1
  • Tolga Acar
    • 1
  1. 1.Electrical and Computer EngineeringOregon State University, CorvallisOregon

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