Commit to KZG Polynomial

WHAT IT DOES

Commit to KZG Polynomial enables you to generate KZG (Kate-Zaverucha-Goldberg) polynomial commitments, a fundamental building block of modern cryptographic proof systems. KZG commitments are used extensively in PLONK, Groth16, and other zk-SNARK proof systems, as well as in Ethereum's Danksharding and various blockchain scalability solutions. The tool takes polynomial coefficients (as a JSON array or text), trusted setup parameters (powers of tau, SRS), and a curve selection (bn128 or BLS12-381), and generates a KZG commitment to the polynomial. The commitment is a single elliptic curve point that binds the prover to the polynomial without revealing it. KZG commitments support efficient evaluation proofs, making them ideal for verification in smart contracts. The tool uses the standard KZG commitment scheme with support for both bn128 (BN254) and BLS12-381 curves.

HOW TO USE

Connect your wallet using the BGWallet connector (required for context). Select your curve: bn128 (BN254, Ethereum-compatible) or BLS12-381 (used in newer systems). Select the input format: "JSON" for structured coefficients (recommended, highest degree first) or "Text" for space/comma-separated values. Enter the polynomial coefficients in the text area—for JSON, provide an array of field elements (e.g., ["1", "2", "3"] representing 1 + 2x + 3x^2). Paste the trusted setup parameters as a hex string with 0x prefix (the SRS containing the powers of tau). Click "Generate Commitment" to compute the KZG commitment. The tool displays the curve, format, polynomial degree, and the generated commitment as a hex string. You can copy the commitment to your clipboard for use in proof systems, verification contracts, or polynomial evaluation protocols.

TECHNICAL MECHANISM

This tool implements the KZG (Kate-Zaverucha-Goldberg) polynomial commitment scheme. Given a polynomial f(x) = Σ c_i * x^i of degree d, the KZG commitment is computed as C = Σ c_i * [tau^i] * G1, where [tau^i] are the powers of tau from the trusted setup (SRS) in the G1 group. The commitment is a single point on the chosen elliptic curve (bn128 or BLS12-381). The trusted setup parameters consist of the powers of tau: [tau^0], [tau^1], ..., [tau^d] for the G1 group and optionally the G2 group. The commitment is computed using scalar multiplication and point addition over the elliptic curve. The commitment is binding (the prover cannot change the polynomial without being detected) and hiding (the polynomial remains private). KZG commitments support efficient opening proofs: to prove f(z) = y, the prover computes the quotient polynomial q(x) = (f(x) - y) / (x - z) and provides a commitment to q(x). The verifier checks the pairing equation. The tool uses the bn128 curve for Ethereum compatibility and BLS12-381 for newer protocols. All computation is performed locally in the browser with no data sent to external servers.

WHAT IT CANNOT SEE

This tool cannot verify that the polynomial or commitment corresponds to actual on-chain state or values—you must ensure the coefficients are correct for your application. It does not support all polynomial commitment schemes (only KZG). The tool cannot generate commitments without the circuit-specific trusted setup parameters; the SRS must be provided and match the polynomial degree. It does not support hardware acceleration for commitment generation; all computation is done in software in the browser. The tool cannot verify the correctness of the trusted setup without additional trust assumptions; you must trust the setup ceremony. It does not support commitment generation for polynomials with degree larger than browser memory limits; very high-degree polynomials may cause performance issues. The tool cannot guarantee the security of the generated commitment if the trusted setup is compromised; setup integrity is essential. It does not support batch commitments or multi-polynomial commitments; it only commits to a single polynomial. The tool cannot generate commitments for polynomials with mutable or dynamic coefficients; the coefficients must be fixed. It requires a trusted setup for security guarantees, which is inherent to KZG commitments. The tool cannot recover the polynomial from the commitment—the commitment is one-way and hiding.

PLEASE NOTE

This tool is designed for developers working with KZG polynomial commitments, which are fundamental to modern zk-SNARK proof systems and blockchain scalability solutions. The bn128 curve is the standard for Ethereum, used in Groth16 and PLONK on Ethereum. BLS12-381 is used in newer protocols like Danksharding and various zk-rollup implementations. The trusted setup parameters (SRS, powers of tau) must be generated in a multi-party computation ceremony and must have enough powers to cover the polynomial degree. The commitment is a single point in the G1 group, represented as a hex string. Always verify the generated commitment using a standard KZG verification library before using it in production systems. The commitment is deterministic for a given polynomial and trusted setup. The tool is read-only and does not broadcast to the chain; it is intended for offline commitment generation and testing.