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tl;dr: Notes on our current use of Groth16 for Aptos Keyless and how we might improve upon it. Should have applications to anonymous payments, confidential assets, zkVM proof wrapping etc.

tl;dr: The 1st multivariate polynomial commitment scheme based on a non-trivial generalization of KZG.

tl;dr: (Almost?) all of the cryptography deployed on Aptos. For users, for developers and for general security.

tl;dr: We present DeKART: a batched ZK range proof for a KZG-committed vector, inspired from Borgeaud’s unbatched protocol1. This is joint work with Dan Boneh, Trisha Datta, Kamilla Nazirkhanova and Rex Fernando. Note that this blog fixes up a previous non-ZK variant and allows for a trading off proving speed for faster verification. ...

$ \def\msg{m} \def\ctxt{C} \def\pk{\mathsf{pk}} \def\sk{\mathsf{sk}} \def\kgen{\mathsf{KGen}} \def\enc{\mathsf{Enc}} \def\dec{\mathsf{Dec}} % IBE \def\ibe{\mathsf{IBE}} \def\tibe{\mathsf{IBE}} \def\id{\mathsf{id}} \def\mpk{\mathsf{mpk}} \def\msk{\mathsf{msk}} \def\dk{\mathsf{dk}} \def\derive{\mathsf{Derive}} $ tl;dr: Encrypt to a phone number ...

tl;dr: This is how it all started: folks wanted to “encrypt.” What does that mean?

tl;dr: For now, this page gathers some resources on FRI[^BBHR18FRI].

tl;dr: Digital signatures are one of the most important cryptographic primitives today. They are used to establish HTTPS connections with your favorite website, to securely download software updates, to provably send emails to others, to sign legal electronic documents, or to transact on a cryptocurrency like Bitcoin.