NeaByteLab | August 2025 | Version 1.0.0

This document provides a comprehensive security analysis of the Quantum-ZKP library implementations. The analysis covers cryptographic foundations, security assumptions, and research considerations for each algorithm.

Foundation: SHA-256/384/512 hash functions Security Assumption: Collision resistance of cryptographic hash functions

Implementation Details:

• Uses SHA-256 for primary hashing operations
• Implements hash chains with configurable length (default: 1000)
• Employs HMAC for challenge-response authentication
• Includes Merkle tree verification for integrity

Security Considerations:

• Hash function security depends on SHA-256 collision resistance
• Chain length affects computational complexity
• Merkle tree provides efficient verification
• No quantum-specific vulnerabilities identified in hash-based approach

Research Applications:

• Study hash-based zero-knowledge proof concepts
• Understand collision resistance implications
• Research hash chain security properties

Foundation: Learning With Errors (LWE) problem Security Assumption: Hardness of LWE problem against quantum attacks

Implementation Details:

• Uses 256-dimensional lattice with 512-bit modulus
• Implements discrete Gaussian error sampling
• Employs polynomial commitments for additional security
• Includes RLWE (Ring-LWE) optimizations

Security Considerations:

• LWE security depends on lattice problem hardness
• Dimension and modulus size affect security level
• Error distribution impacts proof soundness
• Quantum resistance based on lattice problem complexity

Research Applications:

• Study lattice cryptography principles
• Understand LWE problem security
• Research polynomial commitment schemes

Foundation: Multivariate polynomial systems Security Assumption: Difficulty of solving multivariate polynomial systems

Implementation Details:

• Uses 8 variables and 12 equations by default
• Implements quadratic polynomial systems
• Includes sparse coefficient optimization
• Employs polynomial evaluation for verification

Security Considerations:

• Security depends on polynomial system complexity
• Variable and equation count affect difficulty
• Sparse systems may have reduced security
• Quantum resistance based on polynomial solving complexity

Research Applications:

• Study multivariate cryptography concepts
• Understand polynomial system security
• Research sparse polynomial optimization

Foundation: Multiple cryptographic approaches Security Assumption: Combined security of multiple algorithms

Implementation Details:

• Combines hash, lattice, and multivariate approaches
• Uses weighted algorithm combination
• Implements defense-in-depth strategy
• Includes cross-algorithm verification

Security Considerations:

• Security depends on weakest component
• Algorithm combination provides redundancy
• Weighted approach affects security distribution
• Quantum resistance through multiple assumptions

Research Applications:

• Study defense-in-depth strategies
• Understand multi-algorithm security
• Research hybrid cryptographic approaches

Definition: Valid proofs always verify successfully

Implementation Verification:

• All algorithms implement proper ZKP protocol
• Commitment, challenge, and response phases verified
• Mathematical correctness of proof generation
• Verification algorithms match proof generation

Definition: Invalid proofs rarely verify successfully

Implementation Verification:

• Challenge-response mechanism prevents forgery
• Cryptographic primitives provide soundness
• Mathematical hardness assumptions enforced
• Verification algorithms reject invalid proofs

Definition: No secret information revealed during proof

Implementation Verification:

• Witness values properly randomized
• Response generation doesn't leak secrets
• Challenge generation uses Fiat-Shamir transform
• Commitment values hide original secrets

For Research Use:

• Use hash-based for basic ZKP concepts
• Use lattice-based for quantum resistance research
• Use multivariate for polynomial cryptography study
• Use hybrid for comprehensive security research

For Prototyping:

• Start with hash-based for simplicity
• Progress to lattice-based for quantum resistance
• Consider multivariate for specific use cases
• Use hybrid for maximum security requirements

Current Status: Research implementation Alignment: Follows established cryptographic principles Standards: Based on NIST PQC candidate approaches

Key Considerations:

• Lattice-based approaches align with NIST selections
• Hash-based approaches provide established security
• Multivariate approaches offer alternative security
• Hybrid approaches provide defense-in-depth

Implementation Standards:

• Uses established cryptographic primitives
• Implements proper random number generation
• Follows secure coding practices
• Includes comprehensive error handling

Security Considerations:

• No hardcoded secrets or keys
• Proper input validation and sanitization
• Secure memory handling practices
• Comprehensive logging and monitoring

Current Understanding:

• Hash-based: Resistant to known quantum attacks
• Lattice-based: Based on quantum-resistant problems
• Multivariate: Resistant to Shor's algorithm
• Hybrid: Multiple quantum-resistant approaches

Research Limitations:

• No formal security proofs provided
• Implementation not audited by third parties
• Performance characteristics for research only
• Security levels not formally validated

Code Quality:

• TypeScript with strict type checking
• Comprehensive error handling
• Input validation and sanitization
• Secure random number generation

Security Features:

• No hardcoded cryptographic material
• Proper memory management
• Secure buffer handling
• Comprehensive logging

1. Start with Hash-Based: Understand basic ZKP concepts
2. Progress to Lattice-Based: Study quantum resistance
3. Explore Multivariate: Research polynomial cryptography
4. Consider Hybrid: Implement defense-in-depth

1. Use Established Primitives: SHA-256, HMAC, etc.
2. Implement Proper Randomness: Use crypto.randomBytes()
3. Validate All Inputs: Check parameters and data
4. Handle Errors Securely: Don't leak sensitive information

1. Consult Cryptographic Experts: Get professional review
2. Use Audited Implementations: Choose established libraries
3. Implement Formal Security: Undergo security analysis
4. Follow Industry Standards: Adhere to NIST guidelines

For security-related questions or vulnerabilities:

• Security Issues: GitHub Security
• Consulting: Contact NeaByteLab
• Research Support: GitHub Discussions

Note: This security analysis is provided for research and educational purposes. For production use, consult with qualified cryptographic experts and use formally audited implementations.