For the 6th session of Proof is in the Pudding, we teamed up with Archetype to whiteboard an introduction to Data Availability (Sampling).
In this introduction we talk about rollups, Ethereum's DA system (with blobs), DA chains, verifiable sharding in general, and the foundations of data availability sampling.
In this final post of the series, we extend univariate KZG commitments to multilinear polynomials through Mercury. Building on Gemini, we fold half of the variables at once, use polynomial division to bind this large fold to the original commitment and reduce the remaining multilinear evaluations to a batched inner product check. We then walk through the end-to-end opening protocol. We conclude by examining its proof size, prover cost and verifier cost.
In this blog post, we extend univariate KZG commitments to multilinear polynomials through Gemini. We introduce recursive partial evaluations, derive the split-and-fold identity and express each fold as a univariate identity that can be checked using KZG openings. We then walk through the end-to-end opening protocol. We conclude by examining its proof size, prover cost, and verifier cost.
Many of us are using AI to generate code. Vibe coding cryptography is especially sensitive - you have to uphold strict mathematical correctness. This can lead to wrong security guarantees and soundness bugs. We will discuss what are some patterns to do it well.
In Session 07 of "Proof is in the Pudding," we explore the other dark forest, the realm of offchain public keys. We dive into zkLogin, ZK Email, and ZKPassport, examining how these protocols handle authentication and privacy. We also discuss the issue of unlinkability in privacy protocols and why replacing traditional signature verifications with zero-knowledge proofs could unlock more interesting and powerful ZK products.
In our third whiteboard session with Archetype, we dive into the fascinating world of cryptographic protocols by breaking down the intricacies of the Fiat-Shamir security model and the GKR protocol. Whether you're a cryptography enthusiast or just curious about how these complex mechanisms enhance security, this is a chance to explore the theories with us in a friendly and digestible way. Don't miss the opportunity to expand your understanding of this cutting-edge topic!
In Session 09 of "Proof is in the Pudding," we explore the intersection of zero-knowledge proofs and Bitcoin. We break down Bitcoin's UTXO model and Script limitations, then dive deep into approaches for verifying ZK proofs on Bitcoin, from MPC-based techniques to BitVM's optimistic verification with fraud proofs. We cover timelocks, the statelessness problem and Lamport signatures for state, Taproot, simulated covenants, BitVM 3 with hashlocks and garbled circuits, cut-and-choose security, and witness encryption (BABE).
Join us for a deep dive into the fascinating world of arithmetization as David from our team breaks down the process of converting logical statements into algebraic forms to create arithmetic circuits, essential for constructing ZK proofs. This unedited recording from our "Proof is in the Pudding" series offers a unique opportunity to grasp these foundational concepts, perfect for anyone keen on unlocking the mechanics behind zero-knowledge proofs. Curious? Check out the session on Archetype's channel!
Learn the fundamentals of Σ-protocols through the classic Schnorr protocol, exploring the three-step dance of commit, challenge, and respond. This post walks through knowledge soundness and witness extraction, then shows how to compose Sigma proofs with AND/OR logic and Pedersen commitments. See working SageMath implementations, discover how Fiat-Shamir transforms interactive proofs into non-interactive signatures, and understand the deeper mathematical structure as proofs of knowledge of homomorphism pre-images.
In this post, we explore LaBRADOR, a transparent, lattice-based proof system that achieves sublinear proof sizes through recursion. Built on the Module-SIS assumption, LaBRADOR lets a prover efficiently demonstrate knowledge of short vectors satisfying dot product constraints, general enough to express R1CS. The protocol’s key ideas include amortized openings, outer commitments, and a strategy to shrink the witness after each round of recursion. Together, these techniques make LaBRADOR a powerful, scalable framework for post-quantum zero-knowledge proofs.