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.
Cryptographic software is error-prone and failures are catastrophic, therefore formal verification is a powerful and increasingly practical tool for greatly improving the assurances of our cryptographic software. But who verifies the formal verification? Formal verification itself is software too, what is proved, under which assumptions and its relation to the real-world implementation lie beyond the scope of the machine-checked proof. In this post, we want to give some insights into our three-week audit of the Ironwood formalization and some of the common pitfalls that formal verification more broadly can encounter.
In Session 11 of "Proof is in the Pudding," we look at what it takes to prove model inference. We cover transformer computation, sumcheck, GKR, lookup arguments, quantization, and KV caching, then discuss scaling and possible uses for verifiable ML.
We think that Clean is the future of circuit development, so we created a programmer-first introduction to show circuit developers who have never used formal verification how they can build circuits faster, safer and better.
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).
zkao 2.0 is out: a complete redesign of our continuous security scanning tool, a new pay-as-you-go model that replaces subscriptions, and a long list of improvements across scanning, triaging, and reporting.
In this blog post, we extend univariate KZG commitments to multilinear polynomials through Zeromorph. We introduce the univariatization map, encode the multilinear quotient identity as a univariate identity, and explain why the quotient encodings require degree checks. We then show how Zeromorph batches these checks into a single degree-bounded KZG opening and walk through its end-to-end opening protocol. We conclude by examining its proof size, prover cost, and verifier cost.
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.