Overview and Future Prospects of zk-SNARKs Technology

Abstract

zk-SNARKs(ZKP) technology has received extensive attention and research in recent years as an important innovation in the field of blockchain. This article provides a systematic review of the development of zk-SNARKs technology over the past forty years, focusing on the design principles and application methods of circuit-based zk-SNARKs technologies, ZKVM, ZKEVM, and other models. The article also introduces the working mechanism and optimization directions of ZK Rollup as a Layer 2 scaling solution, as well as the latest developments in hardware acceleration and hybrid solutions. Finally, this article looks forward to emerging concepts such as ZKCoprocessor, ZKML, and ZKThreads, discussing their potential in enhancing the efficiency, security, and privacy protection of blockchain systems.

Catalog

1. Basics of zk-SNARKs
2. Non-interactive zk-SNARKs Three, circuit-based zk-SNARKs Four, zk-SNARKs model
3. Overview and Development of zk-SNARKs Virtual Machine
4. Overview and Development of Zero-Knowledge Ethereum Virtual Machine
5. Overview and Development of Zero-Knowledge Layer 2 Network Solutions
6. The Future Development Directions of zk-SNARKs
7. Conclusion

1. Basics of zk-SNARKs

1. Overview

zk-SNARKs(Zero-Knowledge Proof, ZKP) was first introduced by Goldwasser, Micali, and Rackoff in 1985. It is a protocol that can verify the correctness of certain propositions without revealing any additional information. ZKP has three fundamental properties: completeness, soundness, and zero-knowledge.

The core idea of ZKP is that the prover can prove to the verifier that they possess certain information without revealing the specific content of that information to the verifier. This feature makes ZKP play an important role in protecting privacy and enhancing blockchain scalability, becoming a focal point for academic research and industry applications.

2. zk-SNARKs example

Here is a simple zk-SNARKs example used to verify whether the prover possesses a certain secret number without directly revealing the number:

1. Setup: The prover chooses two large prime numbers p and q, computes n = p * q, and calculates v = s^2 mod n( where s is the secret number ).

2. Challenge: The validator randomly selects a bit a(0 or 1) to send to the prover.

3. Response: The prover calculates the response g based on the value of a. If a=0, g = r; if a=1, g = r * s mod n.

4. Verification: The verifier checks if g^2 mod n equals x( when a=0) or x * v mod n( when a=1).

By repeatedly going through this process, the probability of the prover deceiving the verifier through luck can be reduced to a very low level.

2. Non-Interactive zk-SNARKs

1. Background

Traditional zk-SNARKs typically require multiple rounds of interaction. However, in certain application scenarios, such as instant transactions or voting, multiple rounds of interaction are not feasible. Non-interactive zk-SNARKs ( NIZK ) have emerged to address this issue.

2. The proposal of NIZK

Blum, Feldman, and Micali first introduced the concept of NIZK in 1988. NIZK proofs are divided into three phases: setup, computation, and verification. The setup phase introduces the concept of a common reference string (CRS), which serves as the foundation for the subsequent computation and verification.

3. Fiat-Shamir transformation

The Fiat-Shamir transform is a method for converting interactive zero-knowledge proofs into non-interactive ones. This method uses hash functions to replace some randomness and interactivity, greatly simplifying the proof process.

4. Other Research

The research by Jens Groth and others has greatly advanced the application of NIZK in cryptography and blockchain technology. They proposed a perfect non-interactive zero-knowledge proof system suitable for any NP language, achieving significant progress in efficiency and security.

In addition, the non-interactive zk-SNARKs of specific validators, as well as methods based on key registration models, have also provided new ideas for the development of NIZK.

3. Circuit-based zk-SNARKs

1. Background

Circuit-based zk-SNARKs demonstrate advantages when handling specific types of computational tasks, especially in scenarios that require high levels of parallelism.

2. Basic Concepts and Characteristics of Circuit Models

The circuit model is mainly divided into two categories: arithmetic circuits and logic circuits. Arithmetic circuits are composed of addition and multiplication gates and are suitable for complex numerical calculations; logic circuits are made up of basic logic gates and are suitable for executing simple judgment logic and binary calculations.

3. Circuit Design and Applications in zk-SNARKs

In zk-SNARKs systems, the process of circuit design involves expressing the problem to be proven as a circuit, and then converting the circuit into a polynomial representation. This process includes steps such as problem representation, circuit optimization, polynomial conversion, and generating a common reference string.

4. Potential Defects and Challenges

The main challenges faced by circuit-based zk-SNARKs include circuit complexity and scale, optimization difficulties, and adaptability to specific computational tasks. Directions for addressing these issues include circuit compression techniques, modular design, and hardware acceleration.

4. zk-SNARKs Model

1. Common Algorithm Models

1. zkSNARK model: proposed by Bitansky et al. in 2011, it is an improved zero-knowledge proof mechanism.

2. Ben-Sasson model: a zk-SNARK model for executing programs on the von Neumann RISC architecture.

3. Pinocchio model: a complete non-interactive zero-knowledge proof generation suite, including an advanced compiler and quadratic arithmetic programs ( QAPs ).

4. Bulletproofs model: does not require a trusted setup, proof size grows logarithmically with the witness value size.

5. Ligero Model: A lightweight zk-SNARKs model, where the communication complexity is proportional to the square root of the size of the verification circuit.

2. A scheme based on linear PCP and discrete logarithm problem

These schemes include the Groth16 model, Sonic model, PLONK model, etc., based on elliptic curve pairing and quadratic arithmetic programs, providing an efficient non-interactive zk-SNARKs system.

3. Solutions Based on Ordinary Person Proof

The "proof of ordinary people" was proposed by Goldwasser, Kalai, and Rothblum and is applicable to a wide range of problems. Representative schemes include the Hyrax model, Libra model, and Spartan model.

4. Probability-based verifiable proof ( PCP ) zk-SNARKs

These solutions include STARK models, Aurora models, Succinct Aurora models, and Fractal models, which typically have transparent setups and post-quantum security features.

5. Classification of the setup phase for the general proof construction based on CPC(

Zero-knowledge proof systems can be divided into three generations: the first generation requires a trusted setup for each circuit individually; the second generation only needs an initial setup for all circuits; the third generation does not require a trusted setup.

5. Overview and Development of Zero-Knowledge Virtual Machines

) 1. Background

zk-SNARKs Virtual Machine ### ZKVM ( is a virtual machine focused on zk-SNARKs, which expands the functionality of traditional VMs and can universally lower the development threshold for zk-SNARK circuits.

) 2. Existing ZKVM categories

Mainly divided into three categories:

1. Mainstream ZKVM: such as RISCZero, PolygonMiden, zkWASM, etc.
2. EVM Equivalent ZKVM: Specifically designed to be compatible with the Ethereum Virtual Machine ###EVM(.
3. Optimized zk-SNARKs ZKVM: such as Cairo-VM, Valida, TinyRAM, etc.

) 3. Front-end and Back-end Paradigms

The ZKP system can generally be divided into two parts: frontend ### and backend (. The frontend mainly uses low-level languages to represent high-level languages, while the backend converts the circuits described by the low-level languages constructed by the frontend into proofs generation and correctness verification.

) 4. Advantages and Disadvantages of the ZKVM Paradigm

Advantages include utilizing existing instruction set architectures, supporting multiple programs with a single circuit, and circuits with repetitive structures. Disadvantages include the overhead brought by generality, high costs for certain operations, and high proof costs.

6. Overview and Development of Zero-Knowledge Ethereum Virtual Machine

( 1. Background

zk-SNARKs Ethereum Virtual Machine ) ZKEVM ### is specifically designed for Ethereum, mainly used to verify the correctness of smart contract execution while protecting transaction privacy.

2. The Working Principle of ZKEVM

The workflow of ZKEVM includes steps such as node program processing, generating ZK proofs, aggregating proofs, and sending them to the L1 contract.

( 3. Implementation process of ZKEVM

Mainly includes steps such as obtaining data, processing data, generating proofs, recursive proofs, and submitting proofs.

) 4. Features of ZKEVM

The main features of ZKEVM include enhanced transaction processing capabilities, privacy protection, and efficient verification.

7. Overview and Development of zk-SNARKs Layer 2 Network Solutions

1. Background

zk-SNARKs Layer 2 Network Solution ### ZK Rollup ### is an Ethereum scaling solution based on zk-SNARKs, aimed at improving transaction processing efficiency and reducing costs.

2. The working mechanism of zk Rollup

ZK Rollup significantly reduces the use of computational resources on the Ethereum main chain by executing transactions off-chain and generating validity proofs.

( 3. The optimization direction of zk Rollup

The main optimization directions include:

1. Optimize the computation of password algorithms
2. Mixed Optimistic and ZK Rollup
3. Develop a dedicated ZK EVM
4. Hardware Optimization

8. The Future Development Direction of zk-SNARKs

) 1. Accelerate the development of computing environments

Including the development of ZK-ASIC### dedicated integrated circuits### and ZKCoprocessor### co-processors(, aimed at improving the computational efficiency of zk-SNARKs.

) 2. The Proposal and Development of ZKML

zk-SNARKs Machine Learning ( ZKML ) applies zero-knowledge proof technology to the field of machine learning, allowing for the verification of machine learning computation results without disclosing data or model details.

3. Development of ZKP scaling technology

The concepts of ZKThreads and ZK Sharding are proposed to combine zk-SNARKs and sharding technology to enhance the scalability and customizability of blockchain.

( 4. The development of ZKP interoperability

Including the proposal of ZK State Channels and ZK Omnichain Interoperability Protocol, aimed at achieving cross-chain asset and data interoperability based on zk-SNARKs.

9. Conclusion

The zk-SNARKs technology demonstrates great potential in the blockchain field, particularly in enhancing privacy protection and processing capabilities. By analyzing the latest technologies and development trends, this article provides a comprehensive perspective for understanding and applying zk-SNARKs technology, showcasing its important role in improving the efficiency and security of blockchain systems. In the future, with further advancements in hardware acceleration, dedicated algorithms, and cross-chain interoperability, zk-SNARKs technology is expected to play a key role in a wider range of application scenarios.