In the week from February 12th to February 16th 2024, zkSecurity performed a security audit of Darkfi's built-in contracts and circuits. The audit was performed on the public darkfi repository.
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Variants of KZG: Part V, Multilinear Commitments with Mercury
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.
Variants of KZG: Part IV, Multilinear Commitments with Gemini
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.
Optimizing Cryptography with AI
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.
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Archetype x zkSecurity - Proof is in the Pudding: Privacy in Payment Networks
In Session 08 of "Proof is in the Pudding," we explore how different networks have approached privacy over the years. From E-Cash and Monero to MobileCoin and Zether, we break down blind signatures, Pedersen commitments, stealth addresses, ring signatures, and more. This session provides a comprehensive tour of the techniques used to break linkability, hide addresses, and obscure transaction data in the name of privacy and safety.
FRIDA: Data-Availability Sampling from FRI
We've just dropped a blog post exploring the cool world of Ethereum's latest EIP-4844 upgrade and how it tackles the data-availability conundrum with Proto-Danksharding. Get ready to dive into the intricacies of making data more accessible (and less pricey) by using nifty concepts like blobs and polynomial evaluations. Plus, we dish on the role of FRI in data-availability sampling and how it can streamline things even more. Curious? Check out the details and see how this all shapes Ethereum's future!
Become a Halo2 Hero: Master Zero-Knowledge Proofs with Our New Course
We're teaming up with the Zircuit team to bring you a new course on Halo2 development that's perfect for Rust developers eager to dive into creating Halo2 circuits from scratch. No need to be a cryptographer or have prior knowledge of Halo2, PlonK, or zkSNARKs. Our course starts with the basics and guides you through building increasingly complex circuits. By the end, you'll be a Halo Hero! Plus, you'll have access to complete, runnable code examples on GitHub. Ready to start your Halo2 journey? Check it out!
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Sum-Check as an Algebraic Tensor Reduction: Part I
This post introduces algebraic tensor reductions as a unifying framework for understanding recursive proof protocols, using sum-check as the main motivating example. It walks through one recursive step of sum-check, showing how the prover sends a univariate summary, the verifier checks sum consistency, and the original claim is reduced to a smaller claim with one fewer variable. A small bivariate example illustrates how this “peel off one variable, check, then fold with randomness” pattern works concretely. The post sets up the rest of the series, which will introduce the tensor language needed to recover classical sum-check as an algebraic tensor reduction.
zkBitcoin: Use Zero-Knowledge Applications (zkapps) on Bitcoin
We're excited to introduce zkBitcoin, a new tool that lets you create zero-knowledge applications on Bitcoin using a minimal layer 2 protocol. This innovation opens up a world of complex, privacy-focused apps by enhancing Bitcoin's scripting capabilities. We're currently on testnet, so you can jump in and explore the possibilities. Check out our whitepaper or watch some videos for a deeper dive. It's an exciting time for Bitcoin development, and we can't wait to see what you'll build!
Public report of Aleo's consensus (Bullshark)
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!