🔐 Quantum-Resistant Zero-Knowledge Proofs

NeaByteLab | August 2025 | Version 1.0.0

Research Implementation - Comprehensive TypeScript library for understanding quantum-resistant zero-knowledge proof protocols. Designed for research, education, and prototyping applications.

📋 Overview

A comprehensive TypeScript library implementing quantum-resistant zero-knowledge proof protocols using educational cryptographic concepts. This library provides educational implementations of four major post-quantum cryptography approaches:

• Hash-Based ZKP: Hash chain implementations using SHA-256/384/512
• Lattice-Based ZKP: Learning With Errors (LWE) implementations for lattice cryptography
• Multivariate ZKP: Polynomial system implementations for multivariate cryptography
• Hybrid ZKP: Multi-algorithm approaches for defense-in-depth concepts

✨ Key Features

• 🔬 Research Focus: Comprehensive implementations for understanding cryptographic concepts
• 📚 Detailed Documentation: Mathematical foundations and security analysis
• ⚡ Performance Benchmarks: Built-in benchmarking for algorithm comparison
• 🛡️ Security Analysis: Research-grade security assessments
• 📱 Cross-Platform: Node.js 22+ (browser support planned)
• 🧪 Prototyping Tools: Development utilities for testing concepts

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🏗️ Library Architecture

graph TB
    A[QuantumZKP Core] --> B[HashZKP]
    A --> C[LatticeZKP]
    A --> D[MultivariateZKP]
    A --> E[HybridZKP]
    
    A --> F[Benchmarking]
    A --> G[Documentation]
    
    style A fill:#e3f2fd,stroke:#1976d2,stroke-width:3px,color:#000000
    style B fill:#c8e6c9,stroke:#2e7d32,stroke-width:2px,color:#000000
    style C fill:#fff3e0,stroke:#f57c00,stroke-width:2px,color:#000000
    style D fill:#f3e5f5,stroke:#7b1fa2,stroke-width:2px,color:#000000
    style E fill:#f8bbd9,stroke:#c2185b,stroke-width:2px,color:#000000
    style F fill:#e8f5e8,stroke:#388e3c,stroke-width:2px,color:#000000
    style G fill:#fff3e0,stroke:#f57c00,stroke-width:2px,color:#000000

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📊 Algorithm Comparison

Algorithm	Foundation	Research Purpose	Performance Profile
Hash	SHA-256/384/512 hash functions	Understanding hash-based cryptography	1.76ms generation, 1.07ms verification
Lattice	Learning With Errors (LWE)	Researching lattice cryptography principles	389.67ms generation, 104.79μs verification
Multivariate	Multivariate polynomial systems	Studying polynomial cryptography concepts	377.03μs generation, 17.80μs verification
Hybrid	Multiple algorithm combination	Researching defense-in-depth concepts	1.33s generation, 654.66μs verification

Performance data based on real benchmarks on Apple M3 Pro hardware

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🚀 Quick Start

Installation

npm install @neabyte/quantum-zkp

Basic Usage

import { QuantumZKP } from '@neabyte/quantum-zkp'

// Create a quantum-resistant zero-knowledge proof
const secret = 'my-secret-data'
const zkp = new QuantumZKP()
const proof = zkp.createProof(secret, 'hash')

// Verify the proof
const verificationResult = zkp.verifyProof(proof)
console.log('Proof valid:', verificationResult.isValid) // true
console.log('Verification time:', verificationResult.verificationTime, 'ms')

Advanced Usage

import { LatticeZKP, HashZKP, MultivariateZKP, HybridZKP } from '@neabyte/quantum-zkp'

// Hash-based ZKP
const hashProof = HashZKP.createProof(secret, {
  chainLength: 1000
})

// Lattice-based ZKP
const latticeProof = LatticeZKP.createProof(secret, {
  dimension: 256,
  modulus: 2n ** 512n
})

// Multivariate ZKP
const multivariateProof = MultivariateZKP.createProof(secret, {
  variables: 8,
  equations: 12
})

// Hybrid ZKP
const hybridProof = HybridZKP.createProof(secret, {
  algorithms: ['hash', 'lattice'],
  weights: [0.6, 0.4]
})

🔧 Advanced Features

Threshold Cryptography

// Create distributed proof across multiple parties
const thresholdProof = zkp.createThresholdProof(secret, 3, 'lattice')
console.log('Threshold:', thresholdProof.threshold) // 2
console.log('Parties:', thresholdProof.parties) // 3

Batch Processing

// Process multiple proofs efficiently
const secrets = ['secret1', 'secret2', 'secret3', 'secret4']
const proofs = zkp.batchCreateProofs(secrets, 'hash', {
  parallel: true,
  batchSize: 2,
  progressCallback: (progress) => console.log(`Progress: ${progress * 100}%`)
})

---

Performance Benchmarking

// Benchmark all algorithms
const benchmarks = zkp.benchmarkAllAlgorithms()
benchmarks.forEach(result => {
  console.log(`${result.algorithm}: ${result.operationsPerSecond} ops/sec`)
})

---

🧠 Zero-Knowledge Proof Concepts

Basic ZKP Flow

flowchart LR
    A[Prover<br/>Secret Knowledge] --> B[Commitment<br/>Hide Secret]
    B --> C[Challenge<br/>Random Value]
    C --> D[Response<br/>Proof Without Secret]
    D --> E[Verification<br/>Check Validity]
    
    style A fill:#ffebee,color:#000000
    style E fill:#e8f5e8,color:#000000

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ZKP Properties

graph TD
    A[ZKP Properties] --> B[🔐 Completeness]
    A --> C[🛡️ Soundness]
    A --> D[🤐 Zero-Knowledge]
    A --> E[⚡ Efficiency]
    
    B --> B1[Valid proofs always verify]
    C --> C1[Invalid proofs rarely verify]
    D --> D1[No secret information revealed]
    E --> E1[Practical to generate/verify]
    
    style A fill:#ffffff,stroke:#000000,stroke-width:2px,color:#000000
    style B fill:#ffffff,stroke:#000000,stroke-width:2px,color:#000000
    style C fill:#ffffff,stroke:#000000,stroke-width:2px,color:#000000
    style D fill:#ffffff,stroke:#000000,stroke-width:2px,color:#000000
    style E fill:#ffffff,stroke:#000000,stroke-width:2px,color:#000000

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Hash-Based ZKP Flow

flowchart LR
    A[Secret] --> B[Hash Chain]
    B --> C[Commitment]
    C --> D[Challenge]
    
    A --> E[Witness]
    E --> F[Response]
    F --> G[Verification]
    G --> H[Result]
    
    D --> F
    
    subgraph "Research Features"
        I[📊 Hash Chain Concepts]
        J[🔒 Hash Function Security]
        K[⚡ Fast Performance]
    end
    
    style A fill:#ffebee,color:#000000
    style H fill:#e8f5e8,color:#000000
    style I fill:#e3f2fd,color:#000000
    style J fill:#fff3e0,color:#000000
    style K fill:#f3e5f5,color:#000000

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Lattice-Based ZKP Flow

flowchart LR
    A[Secret] --> B[LWE Problem]
    B --> C[Commitment]
    C --> D[Challenge]
    
    A --> E[Witness]
    E --> F[LWE Solution]
    F --> G[Verification]
    G --> H[Result]
    
    D --> F
    
    subgraph "Research Features"
        I[📊 Lattice Cryptography]
        J[🔒 LWE Hardness Assumption]
        K[⚡ Medium Performance]
    end
    
    style A fill:#ffebee,color:#000000
    style H fill:#e8f5e8,color:#000000
    style I fill:#e3f2fd,color:#000000
    style J fill:#fff3e0,color:#000000
    style K fill:#f3e5f5,color:#000000

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Multivariate ZKP Flow

flowchart LR
    A[Secret] --> B[Polynomial System]
    B --> C[Commitment]
    C --> D[Challenge]
    
    A --> E[Witness]
    E --> F[Polynomial Solution]
    F --> G[Verification]
    G --> H[Result]
    
    D --> F
    
    subgraph "Research Features"
        I[📊 Polynomial Cryptography]
        J[🔒 Polynomial System Solving]
        K[⚡ Complex Security]
    end
    
    style A fill:#ffebee,color:#000000
    style H fill:#e8f5e8,color:#000000
    style I fill:#e3f2fd,color:#000000
    style J fill:#fff3e0,color:#000000
    style K fill:#f3e5f5,color:#000000

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Hybrid ZKP Flow

flowchart LR
    A[Secret] --> B[Multiple Algorithms]
    B --> C[Combined Commitment]
    C --> D[Challenge]
    
    A --> E[Witness]
    E --> F[Weighted Response]
    F --> G[Multi-Verification]
    G --> H[Result]
    
    D --> F
    
    subgraph "Research Features"
        I[📊 Defense-in-Depth Concepts]
        J[🔒 Multiple Security Assumptions]
        K[⚡ Maximum Research Security]
    end
    
    style A fill:#ffebee,color:#000000
    style H fill:#e8f5e8,color:#000000
    style I fill:#e3f2fd,color:#000000
    style J fill:#fff3e0,color:#000000
    style K fill:#f3e5f5,color:#000000

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---

🔬 Research Use Cases

Blockchain & Web3 Research

// Research privacy-preserving transactions
const proof = zkp.createProof(transactionData, 'hash')
// Study how zero-knowledge proofs work in blockchain systems

Identity Management Research

// Research identity proof concepts
const identityProof = zkp.createProof(userCredentials, 'lattice')
// Study anonymous authentication concepts

IoT Security Research

// Research lightweight authentication concepts
const deviceProof = HashZKP.createProof(deviceSecret)
// Study device-to-device communication concepts

Financial Security Research

// Research digital signature concepts
const signature = HybridZKP.createProof(financialDocument)
// Study long-term document security concepts

---

⚡ Performance Characteristics

For detailed performance analysis and optimization recommendations, see PERFORMANCE.md.

Algorithm Performance (Real Benchmarks)

Algorithm	Generation Time	Verification Time	Proof Size	Memory Usage	Ops/sec
Hash	1.76ms	1.07ms	416.18 KB	~256 KB	569.1
Lattice	389.67ms	104.79μs	5.01 KB	~512 KB	2.6
Multivariate	377.03μs	17.80μs	9.26 KB	255.9 KB	2652.3
Hybrid	1.33s	654.66μs	431.54 KB	~1 MB	0.7

Benchmark results from Apple M3 Pro with Node.js 22.16.0

Hardware Requirements

• Minimum: Node.js 22+, 2GB RAM
• Recommended: 4GB+ RAM for research hybrid algorithms
• Research: 8GB+ RAM for comprehensive research demonstrations

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📚 API Reference

Core Class: QuantumZKP

Constructor

new QuantumZKP(config?: Partial<ZKPConfig>)

Methods

createProof(secret, algorithm?, parameters?)

Creates a quantum-resistant zero-knowledge proof.

Parameters:

• secret: Buffer | string - Secret to prove knowledge of
• algorithm: AlgorithmType - Algorithm to use (default: 'hash')
• parameters?: Partial<ProofParameters> - Algorithm-specific parameters

Returns: Proof - Quantum-resistant proof

verifyProof(proof)

Verifies a quantum-resistant proof.

Parameters:

• proof: Proof - Proof to verify

Returns: VerificationResult - Verification result with timing information

createThresholdProof(secret, parties?, algorithm?)

Creates distributed proof across multiple parties.

Parameters:

• secret: Buffer | string - Secret to prove knowledge of
• parties: number - Number of parties (default: 3)
• algorithm: AlgorithmType - Algorithm to use

Returns: ThresholdProof - Distributed proof with reconstruction key

batchCreateProofs(secrets, algorithm?, options?)

Efficiently creates multiple proofs.

Parameters:

• secrets: (Buffer | string)[] - Array of secrets
• algorithm: AlgorithmType - Algorithm to use
• options?: BatchProcessingOptions - Processing options

Returns: Proof[] - Array of proofs

benchmarkAllAlgorithms()

Benchmarks all supported algorithms.

Returns: BenchmarkResult[] - Performance comparison results

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Algorithm-Specific Classes

HashZKP

// Create hash-based proof
const proof = HashZKP.createProof(secret, { chainLength: 1000 })

// Verify hash-based proof
const isValid = HashZKP.verifyProof(proof)

// Get performance metrics
const metrics = HashZKP.getPerformanceMetrics()

// Get security level
const security = HashZKP.getSecurityLevel()

LatticeZKP

// Create lattice-based proof
const proof = LatticeZKP.createProof(secret, { 
  dimension: 256, 
  modulus: 2n ** 512n 
})

// Verify lattice-based proof
const isValid = LatticeZKP.verifyProof(proof)

MultivariateZKP

// Create multivariate proof
const proof = MultivariateZKP.createProof(secret, {
  variables: 8,
  equations: 12
})

// Verify multivariate proof
const isValid = MultivariateZKP.verifyProof(proof)

HybridZKP

// Create hybrid proof
const proof = HybridZKP.createProof(secret, {
  algorithms: ['hash', 'lattice'],
  weights: [0.6, 0.4]
})

// Verify hybrid proof
const isValid = HybridZKP.verifyProof(proof)

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🛠️ Development

Setup

git clone https://github.com/NeaByteLab/Quantum-ZKP.git
cd Quantum-ZKP
npm install

Available Scripts

npm run build          # Build the library
npm run dev           # Development mode with watch
npm run test          # Run tests
npm run lint          # Lint code
npm run format        # Format code
npm run benchmark     # Run performance benchmarks
npm run example       # Run basic usage example

Documentation

• README.md - Project overview and quick start
• PERFORMANCE.md - Detailed performance analysis and benchmarks
• SECURITY.md - Security analysis and cryptographic foundations
• LICENSE - Apache 2.0 license

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📄 License

This project is licensed under the Apache License 2.0 - see the LICENSE file for details.

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🔒 Security

This is a research implementation designed for understanding quantum-resistant cryptography concepts. While the implementations follow established cryptographic principles, they are intended for research and prototyping purposes.

For detailed security analysis and cryptographic foundations, see SECURITY.md.

For production quantum-resistant cryptography, consult with qualified cryptographic experts and use established, audited implementations that have undergone formal security analysis.

🤝 Contributing

We welcome contributions for research improvements, documentation enhancements, and bug fixes. Please read our Contributing Guidelines before submitting pull requests.

💬 Support

For research support, questions about implementation concepts, or consulting inquiries:

• Issues: GitHub Issues
• Consulting: Contact NeaByteLab

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Note: This library is designed for research purposes and prototyping. For production quantum-resistant cryptography implementations, please consult with qualified cryptographic experts.