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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

LambdaClass And Starknet Foundation Going Forward

LambdaClass And Starknet Foundation Going Forward

We have a vision of how the future of the Internet should look, how it can be built collaboratively, decentralized and in the open, and we want to participate in that process. We want to build the digital avenues and the infrastructure of the new Internet.

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

What is property-based testing? Two examples in Rust

What is property-based testing? Two examples in Rust

This article will explore property-based tests and demonstrate their use in two of our open-source projects. First, let's explain what a property-based test (PBT) is: If a picture is worth a thousand words, a PBT is worth a thousand unit tests (although this is tunable, as we will

A walkthrough on the open source Aleo VM implemented with Arkworks and blockchain implemented with Tendermint

A walkthrough on the open source Aleo VM implemented with Arkworks and blockchain implemented with Tendermint

Introduction For the last 12 weeks, at LambdaClass, we have been developing an alternative implementation of the Aleo Blockchain. We want to thank Alex Pruden and Howard Wu from Aleo for their support throughout the process. At a high level, the project consists of a Consensus Layer using Tendermint and

Champagne SuperNova, incrementally verifiable computation

zero knowledge proofs

Champagne SuperNova, incrementally verifiable computation

Introduction In the lasts posts we've been writing about proving systems and incremental verifiable computation: * Pinocchio Virtual Machine: Nearly Practical Verifiable Computation * Decentralized private computation: ZEXE and VERI-ZEXE * Incrementally verifiable computation: NOVA Incremental proof systems offer some advantages over conventional proving systems: * They do not require static bounds

Proof aggregation schemes: SnarkPack and aPlonk

Proof aggregation schemes: SnarkPack and aPlonk

Introduction zk-SNARKs are powerful cryptographic primitives, allowing one party, known as the prover, to show to a second party, the verifier, that he knows a given secret, without revealing anything about it. This has applications, for example, in decentralized private computations, where we can delegate an expensive computation to an

Climbing the tower: field extensions

Climbing the tower: field extensions

Introduction Finite fields are a central piece in every cryptography and zk-SNARKs. The most common finite fields appearing in practice are the fields with prime order $\mathbb F_p$. There are multiple ways of defining them. A usual one is seeing $\mathbb F_p$ as the set $$ \{0, 1, \cdots,

ZPrize: eyes on the prize

zero knowledge proofs

ZPrize: eyes on the prize

Introduction This post contains a summary of different approaches to optimize multiscalar multiplication with CUDA, as presented for ZPrize. This is an important calculation in certain proving systems (zk-SNARKs), where it is necessary to add lots of points over an elliptic curve. These large sums can be broken down into

CUDA've been faster: learning CUDA from scratch

CUDA've been faster: learning CUDA from scratch

Practical CUDA CUDA is a parallel computing platform and programming model developed by NVIDIA for general computing on graphical processing units. We can use it to accelerate expensive computations, distributing the load over several processors. For example, in some zk-SNARKs, we have to calculate a multiscalar multiplication, which involves summing