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!
zk.golf is a platform where people can compete on creating the most efficient zk circuits for specific problems. It is enabled by what we call "fearless optimization", which is achieved by combining formal verification and frontier AI models. By the end, you will be convinced that nobody should look at constraints ever again in their life.
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.
Last weekend, we had a blast crafting challenges for a CTF event at the MOCA Italian hacker camp. One cryptography challenge, "2+2=5," involved the Jolt zkVM and a RISC-V program. In this post, we share the ins and outs of the challenge, the clever use of a modified Jolt library, and how we managed to prove an invalid execution without triggering verification alarms. Get ready to dive into the world of Jolt and pick up some nifty insights on exploiting cryptographic systems like a true hacker.