| name | implementing-zero-knowledge-proof-for-authentication |
| description | Implements the Schnorr identification protocol and a simplified Zero-Knowledge Password Proof (ZKPP) over the discrete logarithm problem, letting a prover authenticate by demonstrating knowledge of a secret without ever revealing it to the server. Use when designing or building password-less or password-secret-free authentication, or when a server must verify a user's credential without learning or storing the underlying secret. |
| domain | cybersecurity |
| subdomain | cryptography |
| tags | ["cryptography","zero-knowledge-proof","authentication","privacy","zkp"] |
| version | 1.0 |
| author | mahipal |
| license | Apache-2.0 |
| nist_csf | ["PR.DS-01","PR.DS-02","PR.DS-10"] |
| mitre_attack | ["T1600","T1573","T1553"] |
Implementing Zero-Knowledge Proof for Authentication
Overview
Zero-Knowledge Proofs (ZKPs) allow a prover to demonstrate knowledge of a secret (such as a password or private key) without revealing the secret itself. This skill implements the Schnorr identification protocol and a simplified ZKPP (Zero-Knowledge Password Proof) using the discrete logarithm problem, enabling authentication where the server never learns the user's password.
When to Use
- When deploying or configuring implementing zero knowledge proof for authentication capabilities in your environment
- When establishing security controls aligned to compliance requirements
- When building or improving security architecture for this domain
- When conducting security assessments that require this implementation
Prerequisites
- Familiarity with cryptography concepts and tools
- Access to a test or lab environment for safe execution
- Python 3.8+ with required dependencies installed
- Appropriate authorization for any testing activities
Objectives
- Implement Schnorr's identification protocol for ZKP authentication
- Build a non-interactive ZKP using Fiat-Shamir heuristic
- Implement zero-knowledge password proof (ZKPP)
- Demonstrate completeness, soundness, and zero-knowledge properties
- Compare ZKP authentication with traditional password verification
Key Concepts
ZKP Properties
| Property | Description |
|---|
| Completeness | Honest prover always convinces honest verifier |
| Soundness | Dishonest prover cannot convince verifier (except negligible probability) |
| Zero-Knowledge | Verifier learns nothing beyond the statement's truth |
Schnorr Protocol
- Setup: Public generator g, prime p, q (order of g)
- Registration: Prover computes y = g^x mod p (public key from secret x)
- Commitment: Prover sends t = g^r mod p (random r)
- Challenge: Verifier sends random c
- Response: Prover sends s = r + c*x mod q
- Verify: Check g^s == t * y^c mod p
Security Considerations
- Use cryptographically secure random number generators
- Challenge must be unpredictable (from verifier's perspective)
