Efficient Implementation of Super-optimal Pairings on Curves with Small Prime Fields at the 192-bit Security Level
Jianming Lin, Sun Yat-sen University
Chang-An Zhao, Sun Yat-sen University
Yuhao Zheng, Sun Yat-sen University
Abstract
For many pairing-based cryptographic protocols such as Direct Anonymous Attestation (DAA) schemes, the arithmetic on the first pairing subgroup is more fundamental. Such operations heavily depend on the sizes of prime fields. At the 192-bit security level, Gasnier and Guillevic presented a curve named GG22D7-457 with CM-discriminant and embedding degree . Compared to other well-known pairing-friendly curves at the same security level, the curve GG22D7-457 has smaller prime field size and -value, which benefits from the fast operations on . However, the pairing computation on GG22D7-457 is not efficient.
In this paper, we investigate to derive a higher performance for the pairing computation on GG22D7-457. We first propose novel formulas of the super-optimal pairing on this curve by utilizing a -isogeny as GLV-endomorphism. Besides, this tool can be generalized to more generic families of pairing-friendly curves with -isogenies as endomorphisms. In our paper, we provide the explicit formulas for the super-optimal pairings exploiting -isogenies. Finally, we make a concrete computational cost analysis and implement the pairing computations on curve GG22D7-457 using our approaches. In terms of Miller function evaluation, employing the techniques in this paper obtain a saving of in -multiplications compared to the optimal ate pairing. As for the running time, the experimental results illustrate that the Miller loop on GG22D7-457 by utilizing our methods is faster than the state-of-the-art. Additionally, the performance of the super-optimal pairing on GG22D7-457 is competitive compared to the well-known pairing-friendly curves at the 192-bit security level. These results show that GG22D7-457 becomes an attractive candidate for the pairing-based protocols. Furthermore, our techniques have the potential to enhance the applications of super-optimal pairings on more pairing-friendly curves.
@misc{cryptoeprint:2024/1195,
author = {Jianming Lin and Chang-An Zhao and Yuhao Zheng},
title = {Efficient Implementation of Super-optimal Pairings on Curves with Small Prime Fields at the 192-bit Security Level},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/1195},
year = {2024},
url = {https://eprint.iacr.org/2024/1195}
}
Note: In order to protect the privacy of readers, eprint.iacr.org
does not use cookies or embedded third party content.