Proof is in the Pudding is a IRL series of whiteboard sessions hosted by Archetype and zkSecurity.
For Session 01, David from zkSecurity started at the ground floor with arithmetization. Arithmetization involves the process of converting logical statements into algebraic form, which are then used to create arithmetic circuits, a key building block in the construction of a ZK proof.
Watch it on Archetype's channel!
Note that this is an unedited recording of the session.
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.
A practical guide to the trade-offs between KZG, IPA/Halo, and FRI, the three major polynomial commitment scheme families powering modern zero-knowledge proof systems. We compare proof sizes, verification costs, trust assumptions, benchmarks, and on-chain gas costs.
Groth16 is still the gold standard for succinct SNARKs: 128-byte proofs, constant-size verification, and a decade of real-world deployment. But despite its ubiquity, almost nobody explains *why* it works the way it does. In this post, we build Groth16 from the ground up, starting from R1CS and QAPs, then layer in pairings, trusted setup parameters, and the separator tricks (α, β, γ, δ) that make the scheme sound. By the end, you should have an intuitive grasp of every term in the final verifier equation.
We're diving into the world of Bitcoin's UTXO model and how recent advancements like BitVM can overcome its limitations, allowing for more complex computations without changing Bitcoin's core. This blog post explores cutting-edge techniques like covenants, statefulness, and circuit models, showing how they enable intricate logic on Bitcoin. We'll break down how these innovations make trustless cross-chain transactions possible, and highlight the potential of optimistic protocols to optimize the on-chain footprint. If you're curious about the future of Bitcoin's capabilities, this is the deep dive you need!
A Lean4 formalization of the paper "A Simplified Round-by-round Soundness Proof of FRI" by Albert Garreta, Nicolas Mohnblatt, and Benedikt Wagner, completed using Harmonic's Aristotle agent and Claude Code. Welcome to the strange world of machine-led formalization of cryptography.
We recently audited Aleo's blockchain consensus and found it to be impressively well-documented and high-quality. Our collaboration with Aleo's cooperative team helped us uncover several key issues, and the insights from this audit were well-received. In the blog, we dive into Aleo's Bullshark consensus protocol, explaining its step-by-step process and unique pipelining techniques. We also explore how leaders ensure commitments in even rounds and discuss essential aspects like quorum intersection and garbage collection. Whether you're a blockchain enthusiast or just curious about cutting-edge consensus protocols, this post has got some fascinating details to offer!
In this blog post, we dive into the fascinating world of zero-knowledge proofs using the MPC-in-the-Head transformation, a clever method that constructs proof systems from any secure multiparty computation protocol. Originally proposed in 2007, this transformation uses a creative approach involving "imaginary parties" to prove knowledge without revealing it. We explain how this technique can be applied to develop post-quantum signature schemes, providing insights into its practical implications and efficiency. By exploring these concepts, readers will uncover a unique intersection of cryptography and computer science.