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.

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

Schnorr Protocol

1. Setup: Public generator g, prime p, q (order of g)
2. Registration: Prover computes y = g^x mod p (public key from secret x)
3. Commitment: Prover sends t = g^r mod p (random r)
4. Challenge: Verifier sends random c
5. Response: Prover sends s = r + c*x mod q
6. 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)
• For non-interactive proofs, use Fiat-Shamir with collision-resistant hash
• ZKP alone does not provide forward secrecy; combine with TLS

Validation Criteria

• Honest prover always verifies successfully (completeness)
• Random response without secret does not verify (soundness)
• Server never receives the secret value
• Non-interactive proof is verifiable offline
• Multiple authentications produce different transcripts
• Protocol resists replay attacks