Montgomery Multiplication in GF(2^k)

Cetin K. Koc and Tolga Acar

15 August 1996

We show that 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.

PDF file |

In Third Annual Workshop on Selected Areas in Cryptography

Publisher Springer Verlag

All copyrights reserved by Springer 2007.

Type | Inproceedings |

URL | http://cryptocode.net/docs/c14.pdf |

Pages | 95–106 |

Address | Queen's University, Ontario, Canada |

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