## Cryptology ePrint Archive: Report 2009/565

Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions

Robert Granger and Michael Scott

Abstract: This paper describes an extremely efficient squaring operation in the so-called `cyclotomic subgroup' of $\F_{q^6}^{\times}$, for $q \equiv 1 \bmod{6}$. This result arises from considering the Weil restriction of scalars of this group from $\F_{q^6}$ to $\F_{q^2}$, and provides efficiency improvements for both pairing-based and torus-based cryptographic protocols.

Category / Keywords: implementation / Pairing-based cryptography, torus-based cryptography, finite field arithmetic.

Contact author: rgranger at computing dcu ie

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