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

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

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

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,

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

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 AI:

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

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

TL;DR: This post discusses Pod, a new notion of consensus that achieves optimal latency of one round-trip (about 200 ms), by removing inter-replica communication. We believe this paper and the work by pod network is groundbreaking and we want others to share our excitement and passion for their work,

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.

TL;DR: We found two security bugs that can be combined to perform an exploit in Succinct's SP1 zkVM, which allows you to generate false proofs. In severe cases, this could lead to loss of funds. This was found thanks to a collaboration between the top notch research

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

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

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

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

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

Introduction The elliptic curve BN254 is currently the only curve with precompiled contracts on Ethereum, making it the most practical choice of a pairing-friendly curve suitable for on-chain zk-SNARK verification with proof systems such as Groth16 and PlonK. This work arises from the need to have our own implementation of

For the past few weeks we have been working on a reimplementation of ZKsync's (out of circuit) EraVM. The goal is to improve on its current performance and explore the possibility of adding parallel execution through BlockSTM. For that, we first had to make a deep dive into

We recently contributed $100,000 to the Rust Foundation and would like to share the reasoning behind our decision and the process that led us to this commitment. A slice of Lambda's history is that it started as a group of engineers with experience working on scalable and

1. Introduction 1.1 Motivation Imagine you want to do a complex computation, that you cannot carry out in your computer, or you need to get the results from a computer that you don't trust. How can you be sure it was done correctly without redoing it yourself

Introduction Scalable, transparent arguments of knowledge (STARKs) have gained widespread attention due to their applications in verifiable computing and blockchain scalability. We can use STARKs to generate a short string that attests to the integrity of a computation and a verifier can verify it very fast. The steps to generate

We implemented 75% of the functionality of the Ethereum Virtual Machine, in two weeks, with five new hires, compiling the VM opcode logic to native machine code with a state of the art compiler backend. Why did we do this? How? The TL;DR is: to get a performance boost