Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Families of SNARK-friendly 2-chains of elliptic curves

Youssef El Housni 1 Aurore Guillevic 2, 3
1 GRACE - Geometry, arithmetic, algorithms, codes and encryption
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
3 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : At CANS'20, El Housni and Guillevic introduced a new 2-chain of pairing-friendly elliptic curves for recursive zero-knowledge Succinct Non-interactive ARguments of Knowledge (zk-SNARKs) made of the former BLS12-377 curve (a Barreto-Lynn-Scott curve over a 377bit prime field) and the new BW6-761 curve (a Brezing-Weng curve of embedding degree 6 over a 761-bit prime field). First we generalise the curve construction, the pairing formulas (e : G1 × G2 → GT) and the group operations to any BW6 curve defined on top of any BLS12 curve, forming a family of 2-chain pairing-friendly curves. Second, we investigate other possible 2-chain families made on top of the BLS12 and BLS24 curves. We compare BW6 to Cocks-Pinch curves of higher embedding degrees 8 and 12 (CP8, CP12) at the 128-bit security level. We explicit an optimal ate and optimal Tate pairing on our new CP curves. We show that both for BLS12 and BLS24, the BW6 construction always gives the fastest pairing and curve arithmetic compared to Cocks-Pinch curves. Finally, we suggest a short list of curves suitable for Groth16 and KZG-based universal SNARKs and present an optimized implementation of these curves. Based on Groth16 and PlonK (a KZGbased SNARK) implementations, we obtain that the BLS12-377/BW6-761 pair is optimized for the former while the BLS24-315/BW6-672 pair is optimized for the latter.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.inria.fr/hal-03371573
Contributor : Aurore Guillevic Connect in order to contact the contributor
Submitted on : Friday, October 8, 2021 - 5:46:26 PM
Last modification on : Saturday, October 16, 2021 - 11:26:10 AM

File

ElHousni-Guillevic-2021-Famili...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03371573, version 1

Citation

Youssef El Housni, Aurore Guillevic. Families of SNARK-friendly 2-chains of elliptic curves. 2021. ⟨hal-03371573⟩

Share

Metrics

Record views

58

Files downloads

37