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

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

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

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

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

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

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

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

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

Introduction One of the key issues in the current world is how to achieve consensus between trustless parties. Distributed ledgers have become popular since the advent of cryptocurrencies, built over a technology known as blockchain. One of the main problems is that these ledgers offer limited privacy and are quite