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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

Incrementally verifiable computation: NOVA

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

Message Authentication Codes

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

Symmetric encryption

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

Arithmetization schemes for ZK-SNARKs

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

How to transform code into arithmetic circuits

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

Pinocchio Virtual Machine: Nearly Practical Verifiable Computation

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

Decentralized private computation: ZEXE and VERI-ZEXE

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

The hunting of the (zk)-SNARK

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

Multiscalar Multiplication: Strategies and Challenges

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

Verifiable AES: encryption using zero-knowledge proofs

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.

Fully private applications: A ZEXE protocol

zero knowledge proofs

Fully private applications: A ZEXE protocol

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

LambdaClass and FuzzingLabs Partner to Create 4G and 5G Telecommunication security solution

LambdaClass and FuzzingLabs Partner to Create 4G and 5G Telecommunication security solution

We're excited to announce a new partnership between LambdaClass and FuzzingLabs. This collaboration brings together two leaders in the tech industry, combining Lambda's expertise in distributed systems and cryptography with FuzzingLabs's advanced fuzzing tools, to help ensure the reliability and security of 4G and

Weird ways to multiply really fast with Karatsuba, Toom–Cook and Fourier

Weird ways to multiply really fast with Karatsuba, Toom–Cook and Fourier

Introduction The applicability and performance of algorithms depend on how fast certain routine computations can be done. For example, in elliptic curve cryptography, one needs to calculate the public key as $k\times g=g+g+g+....+g$, where $k$ is a very large integer (typically a number with a

An introduction to Fully Homomorphic Encryption (FHE)

Fully Homomorphic Encryption Featured

An introduction to Fully Homomorphic Encryption (FHE)

Fully homomorphic encryption (FHE) is a powerful cryptographic primitive which allows us parties to compute with encrypted data, without the need of decrypting it first.

Fully-homomorphic encryption, zero-knowledge proofs, and multiparty computation

Fully Homomorphic Encryption

Fully-homomorphic encryption, zero-knowledge proofs, and multiparty computation

ZKP can provide integrity of computations, FHE allows data sharing and calculation without compromising it and MPC gives the power to delegate expensive computations to other parties. In this post, we explain the basic ideas behind these primitives.

How to create your own crappy RSA as a software developer

How to create your own crappy RSA as a software developer

Introduction One of the key developments in cryptography was the introduction of public key (or asymmetric) cryptosystems. These rely on pairs of keys: one of them is the public key (known to everybody) and the other is the private key (known only to the specific user). The public key is

$Math Survival Kit for Developers$

Math Survival Kit for Developers

Introduction When working with cryptographic applications you need to understand some of the underlying math (at least, if you want to do things properly). For example, the RSA cryptographic system (which was one of the earliest methods and most widely adopted, until it lost ground to better methods, such as

Need for speed: Elliptic curves chapter

elliptic curves

Need for speed: Elliptic curves chapter

Introduction Elliptic curves (EC) have gained widespread acceptance as tools for cryptography. They offer several advantages over other methods, such as RSA, providing equal levels of security with shorter keys (for example, 228-bit keys in EC cryptography are as good as 2300-bit RSA keys). This represents an advantage, since more

What every developer needs to know about elliptic curves

What every developer needs to know about elliptic curves

Elliptic curves (EC) have become one of the most useful tools for modern cryptography. They were proposed in the 1980s and became widespread used after 2004. Its main advantage is that it offers smaller key sizes to attain the same level of security of other methods, resulting in smaller storage

Ethereum development made easy with Foundry

Ethereum development made easy with Foundry

As part of our trip to Devcon Amsterdam back in April, we attended the War Room Games Amsterdam competition, an Ethereum CTF where you "hacked" smart contracts to win points. The event was loads of fun, but we realized while playing that our main obstacle was not Ethereum/

Secure computation in Rust: Using Intel's SGX instructions with Teaclave and Fortanix

Secure computation in Rust: Using Intel's SGX instructions with Teaclave and Fortanix

TEEs can be thought of as processes that are running "isolated" from the OS and upper layers in a secure part of the CPU. The idea of this is to help to significantly reduce the attack surface.

Benchmarking and analyzing Rust code performance with Criterion and Iai

Benchmarking and analyzing Rust code performance with Criterion and Iai

In this post, we'll talk about our experience doing benchmarks in Rust, what tools we used and why it was important for us.

Simulations are about to get way, way faster with JuliaSim

Simulations are about to get way, way faster with JuliaSim

JuliaSim is a cloud-based simulation platform built on top of the Julia open source stack, including SciML and ModelingToolkit

BEAM all the things! ClojErl, an implementation of Clojure on the Erlang Virtual Machine

BEAM all the things! ClojErl, an implementation of Clojure on the Erlang Virtual Machine

An interview with its creator, Juan Facorro.