@Article {export:103203,
abstract = {We showthat the multiplication operation *c = a {\cdot} b {\cdot} r*^{−1} in
the field *GF(2*^{k}) 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(2*^{k}). 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.

},
author = {Cetin K. Koc and Tolga Acar},
booktitle = {Designs, Codes and Cryptography},
journal = {Designs, Codes and Cryptography},
month = {April},
pages = {57–69},
publisher = {Kluwer Academic},
title = {Montgomery multiplication in GF(2^k)},
url = {http://research.microsoft.com/apps/pubs/default.aspx?id=103203},
volume = {14},
year = {1998},
}