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If you don't know, look it up or how to create lookup tables for zero knowledge proofs

If you don't know, look it up or how to create lookup tables for zero knowledge proofs

Introduction ZK-SNARKs (zero-knowledge succinct, non-interactive arguments of knowledge) and STARKs (scalable transparent arguments of knowledge) are powerful cryptographic constructions with applications in decentralized private computing and blockchain scaling. They allow one party, the prover, to show that he carried a computation correctly to a second party, the verifier, in a

Have you checked your sums?

Have you checked your sums?

Introduction There has recently been a growing interest in zk-SNARKs (zero-knowledge, succinct, non-interactive arguments of knowledge) due to their capabilities in decentralized private computations and scaling blockchains. These constructions involve a protocol between two parties, a prover and a verifier, where the former attempts to convince the latter of the

An overview of the Groth16 proof system

zero knowledge proofs

An overview of the Groth16 proof system

Introduction Over the last decade, SNARKs (succinct, non-interactive arguments of knowledge) and STARKs (scalable, transparent arguments of knowledge) have been gaining attention due to their applications in verifiable private computation and scalability of blockchains. Groth introduced this proof system in 2016 and saw an early application in ZCash. The protocol

An overview of the Stone Cairo STARK Prover

An overview of the Stone Cairo STARK Prover

Introduction About one month ago, Starkware open-sourced its Stone Prover, which is currently in production in Starknet. It is a library that allows one to produce proofs of computational integrity using STARKs (Scalable Transparent Arguments of Knowledge). The codebase has around 100k lines of code, written mainly in C++. It

Lambda’s engineering philosophy

Lambda’s engineering philosophy

What makes Lambda different We often hear that Lambda has a different way of operating compared with other companies. Many people we’ve worked with have praised the speed and quality of our delivery. We attribute that to a set of principles that anyone can apply, and might benefit others.

Don't trust, verify or why you should care about benchmarks

Don't trust, verify or why you should care about benchmarks

Recently, there has been quite a lot of debate between researchers and engineers on the best proof system. For example, Justin Thaler and Srinath Setty have been discussing whether FRI or KZG based SNARKs are better in computational terms, following some calculations by Eli Ben-Sasson during SBC. Before jumping into

Inner Product Argument (IPA) and a Polynomial Commitment Scheme

Inner Product Argument (IPA) and a Polynomial Commitment Scheme

In this blogpost, we'll take a closer look at the Inner Product Argument. We'll start by understanding the basics of this technique and then shift our focus to its variant within the Halo2 proving system. Specifically, we'll explore how Halo2 ingeniously employs the Inner

Lambda Crypto Doctrine

Lambda Crypto Doctrine

We believe crypto has been incredibly successful at providing a trustless financial layer for the 21st century. In particular it has found product market fit in two main areas: * In developing countries providing aids and tools to individuals that need to fight against inflation, censorship and for companies and individuals

How to code FRI from scratch

How to code FRI from scratch

Introduction STARKs (scalable transparent arguments of knowledge) have gained a lot of attention in recent years due to their capacity to help scale Ethereum and other L1s. They provide a way to guarantee the integrity of a computation carried out by an untrusted party via cryptographic proof. This proof can

First Lambda-Ingo ZK CTF: ZK challenges using LambdaWorks

First Lambda-Ingo ZK CTF: ZK challenges using LambdaWorks

Introduction From July 14th to 16th, we organized, together with Ingonyama, the first Lambda-Ingo ZK capture the flag (CTF), where more than 60 teams and 160 people participated. The CTF involved several challenges related to zero-knowledge proofs (using Lambdaworks) and fully-homomorphic encryption. We are thrilled with the whole experience, especially

Please stop drinking the Rust Kool-Aid

Please stop drinking the Rust Kool-Aid

We've been using Rust since 2014. We're big fans of Rust. This doesn't imply that Rust is the perfect language that solves all your problems. Security vulnerabilities come in a wide array of flavors. Some of them allow a malicious actor to take over

Exciting times at the intersection of Compilers and Applied Cryptography: Cairo and MLIR

Exciting times at the intersection of Compilers and Applied Cryptography: Cairo and MLIR

Making a Cairo not reinventing the wheel I love jazz. Of all the jazz styles I love, jazz fusion is the one I enjoy most because I find any fusion of different things more stimulating. Something exciting is happening at the intersection of programming language theory, compiler implementation, and applied

All you wanted to know about Plonk

All you wanted to know about Plonk

Introduction Zero-knowledge proofs, also known as ZKPs, are becoming popular due to their numerous applications in delegating computations to untrusted servers and addressing scalability issues in decentralized ledgers. By using ZKPs, we can prove the validity of a given computation without revealing sensitive information, and the proof is short and

How to get a true headache: brute forcing NTRU

How to get a true headache: brute forcing NTRU

Introduction Lattice cryptography is a type of cryptographic scheme that relies on the hardness of certain computational problems related to lattices, which are geometric structures formed by repeating a pattern of points in space. Lattice-based cryptography is considered a promising candidate for post-quantum cryptography, as it is believed to be

I want to break free from Lattice-based cryptography, but not even a quantum computer can help me

I want to break free from Lattice-based cryptography, but not even a quantum computer can help me

Introduction Public key encryption is a secure way of sending information over the internet. It uses two keys: a public key and a private key. We use the public key to encrypt messages. We can share this key publicly. The private key is kept secret and only known to the

Do You Want Quality Code? Learn How to Use Differential Fuzzers!

Do You Want Quality Code? Learn How to Use Differential Fuzzers!

Let’s be honest, who hasn’t missed testing an edge case in their life? Surely it has happened to you, and maybe you realized it months after having implemented it (maybe when it’s already in production!). Some cases escape even the most experienced tester, and to avoid explanations

Transforming the Future with Zero-Knowledge Proofs, Fully Homomorphic Encryption and new Distributed Systems algorithms

zero knowledge proofs

Transforming the Future with Zero-Knowledge Proofs, Fully Homomorphic Encryption and new Distributed Systems algorithms

Disclaimer: To maintain brevity and clarity, we have simplified certain concepts. In this discussion, Zero Knowledge Proofs and Computational Integrity are considered as a single concept, and we will not address the distinct security properties of Proof of Work and Proof of Stake. The evolution of every scientific discipline or

Using Metal and Rust to make FFT even faster

Using Metal and Rust to make FFT even faster

A couple of months ago, we wrote about CUDA, a programming model developed by NVIDIA to accelerate expensive computations. We explained why, in the context of ZK-SNARKs, it is useful for performing large multiplications. Today, we want to discuss another development kit that provides an interface to communicate with the

How to use the Consenys's Gnark Zero Knowledge Proof library and disclosure of a DoS bug

How to use the Consenys's Gnark Zero Knowledge Proof library and disclosure of a DoS bug

Zero Knowledge Proofs (ZKP) are a powerful cryptographic technique that allows two parties to exchange information without revealing any sensitive data. This method has the potential to revolutionize the way we handle privacy and security in various industries, such as finance, healthcare, and government. However, developing ZKP applications has traditionally

Better sane defaults in Zero Knowledge Proofs libraries or how to get the prover's private key

Better sane defaults in Zero Knowledge Proofs libraries or how to get the prover's private key

Introduction Many ZK libraries allow the creation of pair of points $(x,y)$ which do not belong to the elliptic curve they are working with when building circuits. Some also do not check that the points belong to the appropriate subgroup, which can lead to vulnerabilities. The argument being made

How we are shaping the future of modular blockchains with Zero Knowledge Proof, Starknet and Ethereum

How we are shaping the future of modular blockchains with Zero Knowledge Proof, Starknet and Ethereum

We believe in a permissionless future where individuals can cooperate and coordinate in scalable blockchain environments. With ten years of experience in distributed systems and a new obsession with cryptography, we can help builders achieve their goals. To realize this future, we believe that developers don't have all

Our small contribution to Paradigm’s Reth to diversify Ethereum clients

Our small contribution to Paradigm’s Reth to diversify Ethereum clients

In December, last year, we heard about Reth, and it immediately piqued our interest. A greenfield new implementation of an Ethereum full node? Where do we sign up!? The project, started and driven by @gakonst from Paradigm (if you haven’t heard about it yet, we encourage you to read

Diving DEEP FRI in the STARK world: learning your daily moon math with a concrete example

zero knowledge proofs

Diving DEEP FRI in the STARK world: learning your daily moon math with a concrete example

Introduction At LambdaClass, we are building Lambdaworks, a library for developing zero-knowledge stuff. One important proof system is STARKs (Scalable, transparent arguments of knowledge). STARKs are a powerful tool that allows us to prove the integrity of a given computation. For an overview of STARKs, you can look at our

LambdaWorks or how we decided to create our zkSNARKs library and a STARK prover

LambdaWorks or how we decided to create our zkSNARKs library and a STARK prover

Introduction We think that most ZK libraries are not yet easy-to-use. Most of them assume that the user had a significant cryptography background, making it hard for a newcomer to learn from them, even if he had all the code in front of him. We also found that some commonly

Everything you wanted to know about periodic constraints in STARKs but nobody told you

zero knowledge proofs

Everything you wanted to know about periodic constraints in STARKs but nobody told you

As you might have already guessed we are studying all the literature and code available to become one of big players in the industry. We want to thank Eli Ben-Sasson and Starkware for the amazing work they've been doing in the space and for helping us to learn