KZG Polynomial Commitment Visualizer

🔗 Live Demo: https://adamsonja-kzg-visualizer-vizapp-streamlit-jwn8bg.streamlit.app/

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Overview

This project is an educational and research-oriented implementation of the KZG (Kate–Zaverucha–Goldberg) polynomial commitment scheme over the BLS12-381 elliptic curve. It is designed to help build deep intuition about how polynomial commitments work internally, how opening proofs are constructed, and how pairing-based verification enforces correctness.

The project intentionally separates:

• Toy algebraic intuition (finite-field polynomials)
• Real cryptographic implementation (pairings on BLS12-381)

This separation follows standard cryptographic pedagogy and research practice.

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What This Project Demonstrates

1. Polynomial Commitments (KZG)

• Commitment to a polynomial using a Structured Reference String (SRS)
• Opening the commitment at a point z
• Verification using bilinear pairings

Mathematically:

• Commit: ( C = \sum_i f_i (\tau^i G_1) = g^{f(\tau)} )

• Open at z: ( q(x) = (f(x) - f(z)) / (x - z) ), witness ( \pi = Commit(q) )

• Verify: [ e(C - yG_1, H) = e(\pi, H_\tau - zH) ]

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2. Toy Finite-Field Polynomial Visualization (Intuition Layer)

A toy visualization is included to build intuition about:

• Polynomial evaluation over finite fields
• Why division by (x - z) yields the witness polynomial

This uses small finite fields to make behavior observable and is not cryptographic.

⚠️ Important:

This toy visualization is purely algebraic and does not represent elliptic curve geometry or cryptographic security.

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3. Pairing-Based Verification (Cryptographic Layer)

• Real elliptic curve operations over BLS12-381
• Bilinear pairing checks using py-ecc
• Explicit construction of both sides of the pairing equation

The UI shows:

• The pairing equation
• Equality / inequality results
• Optional raw pairing element inspection

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This project is educational + research-oriented, not security-hardened.

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Threat Model & Assumptions

Assumptions

• Trusted setup is assumed to be honest
• The secret parameter ( \tau ) is unknown to adversaries
• No toxic waste leakage
• Correctness of elliptic curve and pairing operations

Adversary Capabilities

• May choose arbitrary polynomials and evaluation points
• May attempt to forge incorrect openings

Security Goals

• Binding: Commitments bind to a single polynomial
• Correctness: Valid openings always verify
• Soundness: Invalid openings are rejected

Out of Scope

• Malicious trusted setup
• Batch or multi-point openings
• Aggregated proofs
• Side-channel attacks

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Implementation Breakdown (Clarifying Ownership)

This project uses external libraries only for low-level cryptographic primitives.

Libraries Used

• py-ecc: elliptic curve & pairing primitives
• numpy, matplotlib: toy visualization
• streamlit: UI

Implemented From Scratch

• Polynomial arithmetic over finite fields
• Synthetic division for witness construction
• Commitment logic (MSM over SRS)
• Opening proof generation
• Pairing equation assembly for verification
• Educational and visualization tooling

No existing KZG or SNARK library is used.

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Project Structure

KZG-Visualizer/
├── kzg/
│   ├── commit.py        # Commit, open, verify logic
│   ├── field_poly.py    # Polynomial arithmetic
│   └── srs.py           # Trusted setup (SRS)
│
├── viz/
│   ├── app_streamlit.py # Streamlit application entry point
│   └── pairing_visuals.py
│
├── requirements.txt
└── README.md

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Running Locally

Requirements

• Python 3.10+ (or Python 3.8+ with Optional[int] typing)

Install dependencies

pip install -r requirements.txt

Run the app

streamlit run viz/app_streamlit.py

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Live Deployment

The project is deployed using Streamlit Cloud:

🔗 Live App: https://adamsonja-kzg-visualizer-vizapp-streamlit-jwn8bg.streamlit.app/

This demonstrates:

• Reproducibility
• End-to-end correctness
• Practical engineering maturity

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Limitations & Future Work

Current Limitations

• Only single-point openings
• No batching or aggregation
• Trusted setup assumed
• No prover/verifier optimizations
• No comparison with other commitment schemes

Possible Extensions

• Batch openings
• Proof aggregation
• Comparison with IPA / FRI
• Performance optimization & benchmarking

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Research Context

Polynomial commitments are a foundational primitive in modern cryptography and zero-knowledge proofs, including:

• Plonk-style SNARKs
• Ethereum’s EIP-4844 (data availability)

This project serves as a conceptual bridge between algebraic intuition and real pairing-based cryptographic systems.

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Author

Sunny B.Tech CSE | Cryptography & Zero-Knowledge Proofs Enthusiast

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