Pairing-Friendly Twisted Hessian Curves
@article{Chuengsatiansup2018PairingFriendlyTH, title={Pairing-Friendly Twisted Hessian Curves}, author={Chitchanok Chuengsatiansup and Chloe Martindale}, journal={IACR Cryptol. ePrint Arch.}, year={2018}, volume={2018}, pages={1026} }
This paper presents efficient formulas to compute Miller doubling and Miller addition utilizing degree-3 twists on curves with j-invariant 0 written in Hessian form. We give the formulas for both odd and even embedding degrees and for pairings on both \(\mathbb {G}_1 \times \mathbb {G}_2\) and \(\mathbb {G}_{2} \times \mathbb {G}_{1}\). We propose the use of embedding degrees 15 and 21 for 128-bit and 192-bit security respectively in light of the NFS attacks and their variants. We give a…
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