Montgomery Multiplication in GF(2^k

Authors:
Cetin K. Koc;Tolga Acar
Affiliations:
Electrical and Computer Engineering, Oregon State University, Corvallis, Oregon 97331;Electrical and Computer Engineering, Oregon State University, Corvallis, Oregon 97331
Venue:
Designs, Codes and Cryptography
Year:
1998

Citing 10
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Abstract

We show that the multiplication operation c=a · b ·r^-1 in the field GF(2^k can be implementedsignificantly faster in software than the standard multiplication, where ris a special fixed element of the field. This operation is the finite fieldanalogue of the Montgomery multiplication for modular multiplication ofintegers. We give the bit-level and word-level algorithms for computing theproduct, perform a thorough performance analysis, and compare the algorithmto the standard multiplication algorithm in GF(2^k. TheMontgomery multiplication can be used to obtain fast softwareimplementations of the discrete exponentiation operation, and isparticularly suitable for cryptographic applications where k is large.