This is not a Monad Tutorial

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 DDoS 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

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

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 the tooling

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

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

zkp

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

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 all this.

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 see later)

Vm

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

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 on loop

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

Math

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,

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

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

zero knowledge proofs

Incrementally verifiable computation: NOVA

Introduction One of the current goals is to realize, in an efficient way, incrementally verifiable computation (IVC). This cryptographic primitive allows a given party to show the integrity of a given computer program's execution by providing proof that the result of each step is correct and that all previous ones

cryptography

Message Authentication Codes

Introduction We discussed previously how to ensure message confidentiality between two parties, Alice and Bob. We saw that we could use a symmetric key cipher, such as AES or ChaCha20, to encrypt messages between Alice and Bob so that only they can read them. However, when Bob gets a message

cryptography

Symmetric encryption

Introduction Encryption has been the main application of cryptography for a very long time. Its goal is to transform a message into another one and send it through an insecure channel, such that only the intended parties (who know all the elements necessary to reverse the transformation) can read it

zero knowledge proofs

Arithmetization schemes for ZK-SNARKs

Introduction Zero-knowledge proofs (ZKP) are gaining ground thanks to their many applications in delegating computations to untrusted servers and solving the scalability issues that decentralized ledgers suffer from. ZKP allow us to prove a given computation's validity without revealing sensitive data. One of the key advantages is that the proof

zero knowledge proofs

How to transform code into arithmetic circuits

Introduction The use of efficient zk-SNARKs (zero-knowledge succinct non-interactive arguments of knowledge) has given rise to many new and vital applications. For example, we can delegate expensive computations to untrusted servers and receive proof showing the integrity of the computations. This proof is short and can be verified much faster

zero knowledge proofs

Pinocchio Virtual Machine: Nearly Practical Verifiable Computation

At LambdaClass we set up a small research team to work on Zero Knowledge Proofs and Fully Homomorphic Encryption, who in the past few weeks implemented a virtual machine implementing the Pinocchio protocol in Rust. You can check out the repository at lambdaclass/pinocchio_lambda_vm. It was built by

zero knowledge proofs

Decentralized private computation: ZEXE and VERI-ZEXE

Introduction The ZEXE (Zero-knowledge EXEcution) protocol appeared in 2018, introducing the cryptographic primitive of decentralized private computation (DPC). It aims to solve two main drawbacks that decentralized ledgers suffer: privacy and scalability. Let's take the examples of Bitcoin and Ethereum. We see that the history of all transactions is public

zero knowledge proofs

The hunting of the (zk)-SNARK

Introduction Succinct Non-Interactive Arguments of Knowledge (SNARKs) are powerful cryptographic primitives with decentralized finances, governance, and computation applications. There are many different SNARKs, such as Marlin (the one Aleo uses), Plonk, STARKs, Groth16, etc., depending on the tools they are built on and with differences in performance, proof sizes, verification

zero knowledge proofs

Multiscalar Multiplication: Strategies and Challenges

Introduction Generating a zk-SNARK (zero-knowledge succinct non-interactive argument of knowledge), as the one Aleo uses, involves a lot of cryptographic calculations, almost all of which happen inside an elliptic curve over a finite field. Elliptic Curves The following is a short version of this. An elliptic curve point is a

zero knowledge proofs

Verifiable AES: encryption using zero-knowledge proofs

Encryption is transforming messages into random-looking texts to ensure confidentiality between two parties. What is our objective here? We want to generate proof allowing us to verify an encryption algorithm, ensuring it does what it was designed for.

Not a Monad Tutorial