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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