## Cryptology ePrint Archive: Report 2006/471

Multiplication and Squaring on Pairing-Friendly Fields

Augusto Jun Devegili and Colm \'O~h\'Eigeartaigh and Michael Scott and Ricardo Dahab

Abstract: Pairing-friendly fields are finite fields that are suitable for the implementation of cryptographic bilinear pairings. In this paper we review multiplication and squaring methods for pairing-friendly fields $\fpk$ with $k \in \{2,3,4,6\}$. For composite $k$, we consider every possible towering construction. We compare the methods to determine which is most efficient based on the number of basic $\fp$ operations, as well as the best constructions for these finite extension fields. We also present experimental results for every method.

Category / Keywords: finite fields, pairings, efficient implementation

Date: received 13 Dec 2006, last revised 20 Feb 2007

Contact author: augusto at ic unicamp br

Available format(s): PDF | BibTeX Citation

Note: Correction of a typo in the formula for squaring in cubic extensions and reordering of the author list.

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