# 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…

## 3 Citations

Cocks–Pinch curves of embedding degrees five to eight and optimal ate pairing computation

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- 2019

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 $$H^{4}_{a,d}$$

- Computer Science, MathematicsJournal of Applied Mathematics and Computing
- 2021

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.

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