Summary

This week, Anna and Nico catch up with Antonio Sanso, Researcher at the Ethereum Foundation and Youssef El Housni, Engineer at ConsenSys and builder of Linea. They discuss Antonio and Youssef’s new work, Families of prime-order endomorphism-equipped embedded curves on pairing-friendly curves and dive into Elliptic Curve cryptography, Bandersnatch and Verkle Tries amongst much more, before dissecting what terms in the title of this paper truly mean. After getting into the weeds of cryptographic technicalities, the group explores where this work could be used and what it would enable. Here’s some additional links for this episode:

• zkSummit: A new optimized elliptic curve for one layer proof composition - Youssef El Housni (EY)
• ZK7: Pairings in a SNARK - Youssef El Housni - ConsenSys
• ZK Study Club - ZEXE reading pt 1 (of 3)
• ZK Study Club - ZEXE reading pt 2 (of 3)
• ZK Study Club - ZEXE reading pt 3 (of 3)
• Introducing Bandersnatch: a fast elliptic curve built over the BLS12-381 scalar field by Masson and Sanso
• Verifiable Delay Functions from Supersingular Isogenies and Pairings by De Feo, Masson, Petit and Sanso
• Episode 117: Isogenies with Luca De Feo
• Families of prime-order endomorphism-equipped embedded curves on pairing-friendly curves
• C∅C∅: A Framework for Building Composable Zero-Knowledge Proofs by Kosba, Zhao, Miller, Qian, Chan, Papamanthou, Pass, Shelat and Shi
• Constructing Elliptic Curves with Prescribed Embedding Degrees by Barreto, Lynn and Scott
• Welcome/Opening + Invited Talk by Nadia Heninger (PKC 2024)
• SafeCurves: choosing safe curves for elliptic-curve cryptography

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