Polynomial Commitment Scheme

Definition ∞ A polynomial commitment scheme is a cryptographic primitive that allows a prover to commit to a polynomial in a way that later permits opening the commitment at specific points, proving the polynomial’s evaluation at those points without revealing the entire polynomial. This scheme is a foundational building block for many advanced zero-knowledge proof systems, enabling efficient and compact proofs of computation. It plays a vital role in constructing scalable and privacy-preserving blockchain solutions. The integrity of the commitment is secured by cryptographic assumptions.
Context ∞ Polynomial commitment schemes are a subject of intensive research in cryptography and are frequently mentioned in technical discussions about blockchain scaling and privacy protocols. Different schemes, such as KZG and FRI, are being developed and optimized to improve prover efficiency and verifier succinctness. The selection and implementation of a particular polynomial commitment scheme significantly influence the performance and security characteristics of zero-knowledge rollups and other layer-2 solutions, impacting the future of decentralized applications.

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→Post-Quantum Cryptography

→Sublinear Verification

→Lattice-Based ZK

Lattice-Based Polynomial Commitments Achieve Post-Quantum Succinct Zero-Knowledge Proofs

A new lattice-based Polynomial Commitment Scheme secures zero-knowledge proofs against quantum threats while achieving sublinear verification and minimal proof size.

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→Data Availability Solutions

→Standard Lattice Assumptions

→Post-Quantum Security

Post-Quantum Polynomial Commitments Enable Scalable, Quantum-Resistant Blockchain Architectures

This lattice-based polynomial commitment scheme achieves post-quantum security and succinct proof size, fundamentally unlocking quantum-resistant ZK-rollups and data availability.

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→Hidden Order Groups

→Cryptographic Primitive

→Verifiable Computation

Transparent Recursive Polynomial Commitment Scheme Achieves Efficient Setup-Free ZK-SNARKs

Novel recursive commitment eliminates trusted setup risk, achieving transparent ZK-SNARK efficiency on par with non-transparent schemes.

→Cryptographic Primitive

→Interactive Oracle Proof

→Arithmetic Circuit

Constraint-Reduced Circuits Accelerate Zero-Knowledge Verifiable Computation

Introducing Constraint-Reduced Polynomial Circuits, a novel zk-SNARK construction that minimizes arithmetic constraints for complex operations, unlocking practical, scalable verifiable computation.

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→Polynomial Commitment Scheme

→Post-Quantum Security

→Succinct Proof

Zero-Knowledge Auditing Secures AI Compliance without Revealing Models

ZKMLOps leverages polynomial commitments to cryptographically prove AI model compliance, resolving the fundamental conflict between privacy and regulatory transparency.

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→Transparent Setup

→Post-Quantum Security

→FRI Protocol

FRIDA Enables Transparent Data Availability Sampling with Poly-Logarithmic Proofs

FRIDA uses a novel FRI-based commitment to achieve non-trusted setup data availability sampling, fundamentally improving scalability.

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→R1CS Arithmetization

→Expander Graph Sampling

→Quantum Security

Linear Prover Time Unlocks Scalable Zero-Knowledge Proof Generation

Orion achieves optimal linear prover time and polylogarithmic proof size, resolving the ZKP scalability bottleneck for complex on-chain computation.

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→zkVM Instruction Set

→Zero-Knowledge Virtual Machine

→Arithmetization Technique

Lookup-Only zkVM Architecture Fundamentally Simplifies and Accelerates Verifiable Computation

Lasso lookup arguments enable Jolt, a zkVM that shifts proving complexity from circuit constraints to efficient table lookups, unlocking new performance ceilings.

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→Verifier Complexity

→Trustless Scaling

→Modular Blockchain Scaling

HyperCommit Achieves Constant-Time Verifiable Data Availability Sampling

A novel polynomial commitment scheme enables light clients to verify massive data availability with constant-time cryptographic proofs, securing modular scaling.

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→Univariate Polynomials

→Multilinear Polynomials

→Succinct Non-Interactive Argument

Equifficient Polynomial Commitments Achieve Smallest Proof Size and Fastest SNARKs

Equifficient Polynomial Commitments are a new primitive that enforces polynomial basis representation, enabling SNARKs with 160-byte proofs and triple-speed proving.

Polynomial Commitment Scheme

Lattice-Based Polynomial Commitments Achieve Post-Quantum Succinct Zero-Knowledge Proofs

Post-Quantum Polynomial Commitments Enable Scalable, Quantum-Resistant Blockchain Architectures

Transparent Recursive Polynomial Commitment Scheme Achieves Efficient Setup-Free ZK-SNARKs

Constraint-Reduced Circuits Accelerate Zero-Knowledge Verifiable Computation

Zero-Knowledge Auditing Secures AI Compliance without Revealing Models

FRIDA Enables Transparent Data Availability Sampling with Poly-Logarithmic Proofs

Linear Prover Time Unlocks Scalable Zero-Knowledge Proof Generation

Lookup-Only zkVM Architecture Fundamentally Simplifies and Accelerates Verifiable Computation

HyperCommit Achieves Constant-Time Verifiable Data Availability Sampling

Equifficient Polynomial Commitments Achieve Smallest Proof Size and Fastest SNARKs

Incrypthos

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