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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3 Citations

3 Citations

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This work extends the Cocks–Pinch algorithm to obtain pairing-friendly curves with an efficient ate pairing, and targets a 128-bit security level, and backs this security claim by time estimates for the DLP computation.
A new cryptosystem based on a twisted Hessian curve $$H^{4}_{a,d}$$
TLDR
A new public key Cryptosystem which is a variant of Cramer-Shoup public key cryptosystem on a twisted Hessian curves and study its security and efficiency, which is beneficial and interesting in cryptography.
Cryptography Over the Twisted Hessian Curve H3a, d

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