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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Verification of Rust Cryptographic Implementations with Aeneas
Orateur : Aymeric Fromherz - Inria
From secure communications to online banking, cryptography is the cornerstone of most modern secure applications. Unfortunately, cryptographic design and implementation is notoriously error-prone, with a long history of design flaws, implementation bugs, and high-profile attacks. To address this issue, several projects proposed the use of formal verification techniques to statically ensure the[…] -
On the average hardness of SIVP for module lattices of fixed rank
Orateur : Radu Toma - Sorbonne Université
In joint work with Koen de Boer, Aurel Page, and Benjamin Wesolowski, we study the hardness of the approximate Shortest Independent Vectors Problem (SIVP) for random module lattices. We use here a natural notion of randomness as defined originally by Siegel through Haar measures. By proving a reduction, we show it is essentially as hard as the problem for arbitrary instances. While this was[…] -
Endomorphisms via Splittings
Orateur : Min-Yi Shen - No Affiliation
One of the fundamental hardness assumptions underlying isogeny-based cryptography is the problem of finding a non-trivial endomorphism of a given supersingular elliptic curve. In this talk, we show that the problem is related to the problem of finding a splitting of a principally polarised superspecial abelian surface. In particular, we provide formal security reductions and a proof-of-concept[…]-
Cryptography
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