Faster Explicit Formulae for Computing Pairings via Elliptic Nets and Their Parallel Computation

Onuki, Hiroshi; Teruya, Tadanori; Kanayama, Naoki; Uchiyama, Shigenori

doi:10.1007/978-3-319-44524-3_19

Cited by 3 publications

(1 citation statement)

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“…Fortunately, the most popular paring-friendly curves all meet this condition. Due to the particularity of the structure of elliptic nets, an parallel strategy for the ENA to compute pairings was proposed [28].…”

Section: Introductionmentioning

confidence: 99%

The Elliptic Net Algorithm Revisited

Cai¹,

Hu²,

Yao³

et al. 2021

Preprint

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Pairings have been widely used since their introduction to cryptography. They can be applied to identity-based encryption, tripartite Diffie-Hellman key agreement, blockchain and other cryptographic schemes. The Acceleration of pairing computations is crucial for these cryptographic schemes or protocols. In this paper, we will focus on the Elliptic Net algorithm which can compute pairings in polynomial time, but it requires more storage than Miller's algorithm. We use several methods to speed up the Elliptic Net algorithm. Firstly, we eliminate the inverse operation in the improved Elliptic Net algorithm. In some circumstance, this finding can achieve further improvements. Secondly, we apply lazy reduction technique to the Elliptic Net algorithm, which helps us achieve a faster implementation. Finally, we propose a new derivation of the formulas for the computation of the Optimal Ate pairing on the twisted curve. Results show that the Elliptic Net algorithm can be significantly accelerated especially on the twisted curve. The algorithm can be 80% faster than the previous ones on the twisted 381-bit BLS12 curve and 71.5% faster on the twisted 676-bit KSS18 curve respectively.

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Section: Introductionmentioning

confidence: 99%