Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions

Abstract. This paper describes an extremely efficient squaring operation in the so-called ‘cyclotomic subgroup’ of F× q6 , for q ≡ 1 mod 6. This result arises from considering the Weil restriction of scalars of this group from Fq6 to Fq2 , and provides efficiency improvements for both pairingbased and torus-based cryptographic protocols.

• Type: Conference
• Year: 2010
• Where: PKC
• Authors: Robert Granger, Michael Scott
• Keywords: Cryptology, Efficient Squaring Operation, PKC 2010, So-called ‘cyclotomic Subgroup, Torus-based Cryptographic Protocols