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Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions

Granger, Robert and Scott, Michael (2010) Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions In: The 13th International Conference on Practice and Theory in Public Key Cryptography (PKC 2010), 26-28 May 2010, Paris, France.

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Abstract

This paper describes an extremely efficient squaring operation in the so-called ‘cyclotomic subgroup’ of F× q6 , for q ≡ 1 mod 6. Our result arises from considering the Weil restriction of scalars of this group from Fq6 to Fq2 , and provides efficiency improvements for both pairing-based and torus-based cryptographic protocols. In particular we argue that such fields are ideally suited for the latter when the field characteristic satisfies p ≡ 1 (mod 6), and since torus-based techniques can be applied to the former, we present a compelling argument for the adoption of a single approach to efficient field arithmetic for pairing-based cryptography.

Item Type: Conference or Workshop Item (Conference Paper)
Divisions : Faculty of Engineering and Physical Sciences > Computing Science
Authors :
NameEmailORCID
Granger, Robertr.granger@surrey.ac.uk
Scott, Michael
Date : 26 May 2010
DOI : 10.1007/978-3-642-13013-7_13
Copyright Disclaimer : © Springer-Verlag Berlin Heidelberg 2010
Uncontrolled Keywords : Pairing-based cryptography; Torus-based cryptography; finite field arithmetic
Depositing User : Clive Harris
Date Deposited : 07 Feb 2019 14:49
Last Modified : 07 Feb 2019 14:49
URI: http://epubs.surrey.ac.uk/id/eprint/850404

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