In this third whiteboard session in partnership with Archetype, we explain how a recent paper on Fiat-Shamir security and the GKR protocol works.
Proof is in the Pudding · Part 3 of 10
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The Year Finding and Exploiting Bugs Became Cheap, and What to Do About It
The economics of security have changed. AI has made finding and exploiting bugs cheaper, including in cryptographic and zero-knowledge code, while validation and remediation remain slow. Here is our view of what happened, what comes next, and how teams should change the way they secure their stack to defend against AI-assisted attackers.
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.
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Archetype x zkSecurity (Whiteboard Session) - Proof is in the Pudding: Arithmetization
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!
Archetype x zkSecurity (Whiteboard Session) - Proof is in the Pudding: zkTLS
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Trust, But Measure: A Friendly Intro to TEEs with Intel TDX
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Public report of auditing Penumbra's circuits
We conducted an audit of Penumbra's main circuits and found eight issues, including the critical "double spend" and "double vote" bugs, which the Penumbra team promptly fixed. Our findings highlight Penumbra's robust documentation and code testing. Readers will get insights into how Penumbra uses zero-knowledge proofs for privacy, its decentralized exchange features, and its governance model. The post also provides detailed pseudocode for various cryptographic protocols, emphasizing how Penumbra ensures secure and private transactions. It's a deep dive into the technical details for those intrigued by privacy-focused blockchain technologies.
AI meets Cryptography 1: What AI Found in Cloudflare's CIRCL
We pointed our AI audit pipeline at Cloudflare's CIRCL experimental cryptography library and confirmed seven real bugs, from a critical float64 precision loss in threshold RSA to a complete access-control break in attribute-based encryption. All seven are now fixed upstream. This is the first post in a series on bugs our agents found across open source cryptography.
Variants of KZG: Part I, Univariate
In this blog post, we dive into the world of polynomial commitment schemes (PCS), which are crucial for constructing most practical SNARKs. We cover the basics of how PCS works, focusing on KZG10, known for its efficiency in proof size and verification time. You'll learn about the essential properties of binding and hiding and explore technical concepts like homomorphism, batching, and unconditionally hiding. We break down various methods to achieve these features, offering insight into how PCS maintains the security and privacy of polynomials in cryptographic systems. Get ready to understand these powerful concepts and their applications in modern cryptography!