Introduction Ethereum has been quickly evolving to become the financial backend of the World. Research and development in zero-knowledge proofs have allowed Ethereum to scale with rollups, by batching transactions off-chain and then posting an update of the accounts together with a cryptographic proof attesting to the validity of the| LambdaClass Blog
Introduction In this article we review some of the optimizations for the SUMCHECK protocol as discussed in the recent article by Bagad, Dao, Domb and Thaler. The authors tackle the problem of disproportionate cost of field multiplications. In many SNARK applications, the sum-check protocol operates over extension fields, which are| LambdaClass Blog
Introduction In this article we briefly introduce a list of basic properties of multilinear polynomials that are convenient to have in mind when tackling a very interesting piece of work by Bagad, Dao, Domb and Thaler: "Speeding up SUM-CHECK proving". The authors focus on a specific setting for the SUMCHECK| LambdaClass Blog
Introduction The GKR (Goldwasser–Kalai–Rothblum) protocol provides an efficient way to verify computations over arithmetic circuits, avoiding re-execution and reducing the verifier’s work. In our previous post, GKR protocol: a step-by-step example, we explored how the protocol works in detail, focusing on its mathematical structure and walking through| LambdaClass Blog
Introduction Bitcoin was the first blockchain in history, enabling a peer-to-peer electronic cash system for the first time. Introduced in 2008 by Satoshi Nakamoto, it provided an elegant yet simple construction to enable people from across the world to store and exchange value over a permissionless and censorship-resistant network. An| LambdaClass Blog
Introduction At the heart of any Zero-Knowledge Proof (ZKP) system lies the concept of arithmetization, the process of transforming a computational problem into a mathematical problem that can be expressed and verified within a specific algebraic structure, such as polynomials or arithmetic circuits. Within the Binius framework, this arithmetization is| LambdaClass Blog
Warning: This post is more math heavy than other articles. Introduction In this article we continue our study of towers of binary fields, motivated by the proposal of Diamond and Posen for a complete protocol working over fields of characteristic 2, BINIUS. Previously we covered basic arithmetic of field elements| LambdaClass Blog
Introduction The development of general-purpose zkVMs has made writing verifiable applications easier, by allowing developers to write high-level code and then compiling it to RISC-V or another instruction set architecture (ISA) and running it on top of the virtual machine. The virtual machine then generates a succinct proof of execution| LambdaClass Blog
Introduction Ethereum relies on cryptographic data structures to efficiently store and verify its state. One of these structures is the Merkle Patricia Trie (MPT), which powers Ethereum’s state management. After exploring this tool in more depth, it becomes clear that the MPT is a complex structure—far more intricate| LambdaClass Blog
Introduction Few weeks ago, Succinct release their paper Jagged Polynomial Commitments and their verifier using the techniques described there, allowing them to prove Ethereum blocks in around 12 seconds, showing that real-time proving of the chain is possible. While this represents the average case and energy consumption is still high| LambdaClass Blog
At LambdaClass we believe that advancing science requires collaboration across disciplines and sectors. As part of our commitment to supporting scientific research and education, we recently made a donation to the Asociación Argentina de Astronomía (Argentine Astronomical Association), a non-profit organization dedicated to promoting astronomical research and knowledge in Argentina| LambdaClass Blog
We celebrate a year of development on Ethrex and talk about what sets it apart.| LambdaClass Blog
We’re pleased to announce our partnership with Nous Research to help develop Psyche, a decentralized AI training network. The system is designed to allow anyone to contribute to model training using idle compute, making AI development more open, efficient, and verifiable. This initiative addresses a long-standing problem in| LambdaClass Blog
We are very proud to celebrate over 18 months of collaboration between Miden and LambdaClass. The partnership began by helping Miden develop the client, facilitating the execution and proving of transactions for the Miden network. Over time, our collaboration deepened, and we expanded our efforts to support the development of| LambdaClass Blog
We interview the team developing Iroh, a Rust peer-to-peer library that just works.| LambdaClass Blog
Introduction An interactive proof is a protocol between two parties, a prover $\mathcal{P}$ and a verifier $\mathcal{V}$, where the prover attempts to convince the verifier of the validity of a statement. By leveraging randomness and interaction, the verifier can check the statement more efficiently than by doing everything| LambdaClass Blog
On January 26th Starkware informed us that they had found a critical issue in the Cairo VM related to a program that would successfully execute on the VM but would violate the AIR constraints. A fix was already implemented in a PR, merged, and a release was made and deployed.| LambdaClass Blog
TL;DR: this post addresses the paper introducing rStar-Math and the techniques for smaller language models to outperform more complex large language models on math-related tasks. You can check the code here. rStar-Math significantly improved the math reasoning abilities of SLMs. For instance, on the MATH benchmark, it enhanced Qwen2.| LambdaClass Blog
Introduction In a previous post, we explained how to define constraints for a continuous read-only memory, presenting it as an example to understand how constraints are defined in general. This time, we will continue digging into this example to introduce the LogUp construction, adapted to univariate polynomials, and explain how| LambdaClass Blog
Why you should avoid having complex codebases and departing from standards when developing zero-knowledge virtual machines TL;DR: We found a subtle bug in Succinct's SP1 virtual machine, which allows a malicious user to prove the validity of false statements by subtly manipulating register 0 in the guest code This| LambdaClass Blog
TL;DR Training Large Language Models (LLM) with billions of parameters is computationally intensive and involves large communication in specialized data centers. Nous Research released DeMo, showing how to reduce these communication costs by orders of magnitude, decreasing costs and enabling training with poorer connections and less expensive hardware. This| LambdaClass Blog
Introduction When we first explored the world of STARKs, one of the most confusing concepts we encountered was constraints. We kept asking ourselves: How is it possible to summarize highly complex relationships between trace values using just a few polynomials? It wasn’t until we started implementing some examples that| LambdaClass Blog
Introduction It has been over a year and a half since we launched lambdaworks, our cryptography library for zero-knowledge (ZK) proofs. We built it focusing on performance, ease of use, support for hardware acceleration, and teaching others how to develop and understand ZK. Several advances in ZK in the last| LambdaClass Blog