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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

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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

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