Description
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 377- bit 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 KZG- based 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.<br/> lien: https://univ-rennes1-fr.zoom.us/j/97066341266?pwd=RUthOFV5cm1uT0ZCQVh6QUcrb1drQT09
Prochains exposés
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Random lattices that are modules over the ring of integers
Orateur : Nihar Gargava - Institut de Mathématiques d'Orsay
We investigate the average number of lattice points within a ball where the lattice is chosen at random from the set of unit determinant ideal or modules lattices of some cyclotomic number field. The goal is to consider the space of such lattice as a probabilistic space and then study the distribution of lattice point counts. This is inspired by the connections of this problem to lattice-based[…]-
Cryptography
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Schéma de signature à clé publique : Frobénius-UOV
Orateur : Gilles Macario-Rat - Orange
L'exposé présente un schéma de signature à clé publique post-quantique inspiré du schéma UOV et introduisant un nouvel outil : les formes de Frobénius. L'accent est mis sur le rôle et les propriétés des formes de Frobénius dans ce nouveau schéma : la simplicité de description, la facilité de mise en oeuvre et le gain inédit sur les tailles de signature et de clé qui bat RSA-2048 au niveau de[…] -
Yoyo tricks with a BEANIE
Orateur : Xavier Bonnetain - Inria
TBD-
Cryptography
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Symmetrical primitive
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