Montgomery multiplication in GF(2^k)

We showthat the multiplication operation $c = a · b · r^{−1}$ 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.

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In  Designs, Codes and Cryptography

Publisher  Kluwer Academic
All copyrights reserved by Kluwer Academic 2007.


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