## Introduction

In the evolving world of blockchain technology, privacy and security are paramount. With financial transactions and sensitive data at stake, how can we ensure transactions are both private and verifiable? The answer lies in a powerful cryptographic tool called Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARKs).

zk-SNARKs, or Zero-Knowledge Succinct Non-Interactive Argument of Knowledge, is a cryptographic method that allows one party to prove to another that a specific piece of information is known, without revealing the information itself. This technology has been a game-changer for privacy in blockchain transactions.

Celo, an open-source blockchain platform, stands out for its user-friendly approach to financial tools and services, accessible to anyone with a mobile device. In this tutorial, we will dive into the world of Celo and zk-SNARKs, exploring how to implement privacy-preserving transactions on the Celo Blockchain.

## Introduction to zk-SNARKs

Letās refresh our understanding of zk-SNARKs first. Zk-SNARKs are a form of zero-knowledge proofs which allow one party (the prover) to prove to another (the verifier) that they know a value x, without conveying any information apart from the fact they know the value x.

A zk-SNARK consists of three algorithms:

**Key Generation (KG)**: This algorithm generates a pair of keys, one for proving (pk) and one for verification (vk). The key generation algorithm takes as input a security parameter Ī» and a program C, and outputs the keys (pk, vk).**Proving (P)**: This algorithm takes as input the proving key pk, a statement x, and a witness w. The output is a proof prf.**Verification (V)**: This algorithm takes as input the verification key vk, a statement x, and a proof prf. The output is either accept or reject.

### How zk-SNARKs work

Diagram below shows how zk-SNARKs work, including the key generation, proving, and verification steps.

Zk-SNARKs are āsuccinctā and ānon-interactiveā because the proof size is small and verification is efficient, and no interaction is required between the prover and verifier after the initial sharing of keys.

To get a deeper understanding on zksnarks, Click Here

## zk-SNARKs and Blockchain: Why We Need Them

In the context of blockchain, privacy is often a significant concern. Every transaction is visible to every participant in the network, and while addresses may not be directly linked to identities, the potential for de-anonymization exists. This openness is necessary for the decentralized verification of transactions but can be undesirable for users who want to keep their financial transactions private.

zk-SNARKs can solve this problem. They allow a network participant to prove that their transaction is valid, without revealing any other information about it. This means that you can have a blockchain where every transaction is verifiable, but private.

### zk-SNARKs and Blockchain

Diagram below illustrates how zk-SNARKs are used in a blockchain context for privacy preservation.

## Privacy Challenges on Celo Blockchain

The first step to using zk-SNARKs with Celo is to understand the Celo ecosystem and how it works. Celo uses a Byzantine Fault Tolerance (BFT) consensus algorithm and is EVM compatible, meaning you can write smart contracts for Celo in Solidity, just like you would for Ethereum.

Celo also has a unique feature where it uses phone numbers as public keys, which can be both an advantage and a disadvantage when it comes to privacy. On one hand, itās easy for anyone with a smartphone to use Celo. On the other hand, phone numbers arenāt as anonymous as traditional cryptographic keys.

While blockchains like Celo offer transparency and traceability, this also leads to potential privacy issues. Since all transactions are publicly recorded on the blockchain, thereās a lack of financial privacy. Anyone can trace all transactions back to your wallet address, see the balance and all other transaction details.

## Integrating Zk-SNARKs with Celo

To address the privacy concerns in Celo, we can use zk-SNARKs to conceal the information about transactions while still ensuring their validity.

A zk-SNARK circuit can be thought of as a program that takes some input and produces an output. The process of deploying such a circuit generally involves the following steps:

**Designing the circuit**: First, you need to define the computation that you want to be performed in zero knowledge. This is usually done in a high-level language that is specifically designed for zk-SNARK circuits. Languages like ZoKrates or Circom are commonly used for this purpose.**Compiling the circuit**: After the circuit has been defined, it is compiled into a format that can be interpreted by a zk-SNARK proving system. This typically involves converting the high-level code into a system of polynomial equations.**Setting up the circuit**: The compiled circuit must be set up before it can be used. This is a one-time process that involves generating a proving key and a verification key for the circuit. The proving key is used to generate proofs, and the verification key is used to verify them. This is often referred to as the ātrusted setupā phase because it must be done in a way that the secret parameters used during this process are securely destroyed. If these secret parameters are leaked, they could be used to generate false proofs.**Deploying the verification key**: The verification key is deployed to a smart contract on the blockchain. This allows anyone to verify proofs for the circuit by calling a function on the smart contract and passing in the proof.**Using the circuit**: After the verification key has been deployed, the circuit is ready to be used. Provers can generate proofs by performing the computation defined by the circuit with their private inputs and the proving key. These proofs can then be verified by anyone who has access to the verification key.

This is a simplified overview and the specifics can vary depending on the exact zk-SNARK protocol being used, the programming language, and the blockchain platform.

## Applications of zk-SNARKs on The Celo Blockchain

Besides the obvious privacy improvements, zk-SNARKs have a variety of other potential uses within the Celo ecosystem:

**Scalability**: By generating proofs of computation and validating them on-chain, zk-SNARKs can help to increase the scalability of the Celo blockchain. This is because verifying a proof is usually much faster and less resource-intensive than performing the original computation.**Interoperability**: zk-SNARKs can provide a trustless bridge between Celo and other blockchains. For instance, a proof can be generated that a transaction has taken place on another blockchain, and this proof can be verified on the Celo blockchain without the need for any trusted intermediaries.**Identity and Reputation Systems**: zk-SNARKs can be used to build privacy-preserving identity and reputation systems on Celo. Users could prove certain attributes or credentials without revealing any other information about themselves.**Voting Systems**: zk-SNARKs can be used to build confidential voting systems, where each participant proves that they are eligible to vote, and that they have not already voted, without revealing who they voted for.

## Tools and Libraries for Implementing zk-SNARKs in Celo

There are several tools and libraries that can aid in the implementation of zk-SNARKs in Celo:

**ZoKrates**: ZoKrates is a toolbox for zk-SNARKs on Ethereum and other EVM-compatible blockchains like Celo. It includes a high-level programming language, a compiler, and a setup scheme for creating and managing zk-SNARKs.**Libsnark**: Libsnark is a C++ library for zk-SNARK proofs. It provides a generic framework for describing computations and producing proofs.**Circom and SnarkJS**: Circom is a language for writing zk-SNARK circuits, and SnarkJS is a tool for generating and verifying proofs in JavaScript.

## zk-SNARKs and Celoās Light Client Protocol

Celoās Light Client Protocol is a method for lightweight clients (like mobile phones) to interact with the Celo blockchain without needing to download and verify the entire blockchain history. This protocol could benefit significantly from zk-SNARKs.

By using zk-SNARKs, itās possible to create a succinct proof that a given block is valid and is part of the longest chain, without requiring the client to verify every single block header from the genesis block to the current block. This could further reduce the amount of data that light clients need to download and verify, making Celo even more accessible for users with limited internet bandwidth or storage capacity.

## Conclusion

As we have seen, zk-SNARKs offer a promising solution to the privacy challenges faced by blockchain technology. By allowing participants to verify transactions without revealing any additional information about them, zk-SNARKs can provide a level of privacy that has so far been difficult to achieve in the blockchain space.

read more on zk-snarks here zkSNARKs in a Nutshell unicode (chriseth.github.io)

Celo, with its mission of making financial tools accessible to anyone with a mobile phone, can greatly benefit from the integration of zk-SNARKs. As weāve outlined, the implementation process is complex but feasible, involving the design, compilation, setup, and deployment of a zk-SNARK circuit.

Stay tuned for the next section in the pathway where we delve into the practical applications and examples of zk-SNARKs integration with the Celo blockchain. It is here that we will see these theoretical concepts come to life, further solidifying our understanding of this transformative technology.

We encourage you to continue your exploration of topics on zk proofs. If youāre interested in diving deeper, you can follow up on the pathway here Zero-Knowledge Proofs on the Celo Blockchain: A Comprehensive Tutorial Series - Pathways - Celo Academy

## About the author

Iām Jonathan Iheme, A full stack block-chain Developer from Nigeria. With a great passion for Zero Knowledge Technology.