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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→Trustless Setup

→Cryptographic Primitive

→Universal Setup

Lattice Commitments Secure Transparent Post-Quantum Zero-Knowledge Proofs

A new lattice-based polynomial commitment scheme secures zero-knowledge proofs against quantum attacks, eliminating the need for a trusted setup.

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→Cryptographic Primitive

→Fiat-Shamir Transformation

→Verifiable Computation

Lattice Polynomial Commitments Achieve Post-Quantum Transparent SNARKs

This research delivers the first efficient lattice-based polynomial commitment scheme, securing succinct arguments against quantum adversaries without a trusted setup.

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→Transparent Setup

→Constant Size Proofs

→Group of Unknown Order

Transparent Polynomial Commitments Achieve Practical Constant-Size Proofs

New aggregation techniques slash transparent polynomial commitment proof size by 85%, enabling practical, trustless, constant-sized ZK-SNARKs.

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→Class Group Cryptography

→Algebraic Framework

→Polynomial Commitment Scheme

Transparent Constant-Sized Polynomial Commitments Enable Practical Trustless zk-SNARKs

Dew introduces the first transparent polynomial commitment scheme with constant proof size and logarithmic verification, eliminating the trusted setup barrier for succinct verifiable computation.

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→Module-SIS

→Succinct Proof Size

→Cryptographic Primitive

Greyhound Achieves Post-Quantum Polynomial Commitments with Unprecedented Efficiency

A new lattice-based polynomial commitment scheme, Greyhound, delivers post-quantum security and 8000X smaller proofs, unlocking scalable verifiable computation.

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→Commitment Scheme

→Cryptographic Security

→Succinct Non-Interactive Argument

Vector-Code Commitments Unlock Transparent Logarithmic-Time Zero-Knowledge Proof Verification

A new Vector-Code Commitment scheme uses algebraic codes to create transparent, logarithmic-time verifiable proofs, radically improving ZKP scalability.

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→Succinct Arguments

→Interactive Oracle Proof

→Proof Verification Time

Efficient Transparent Zero-Knowledge Proofs Eliminate Trusted Setup for Scalability

A new recursive polynomial commitment scheme, LUMEN, achieves the efficiency of trusted-setup SNARKs while maintaining full transparency, unlocking truly scalable and trustless rollups.

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→Rollup Scalability

→Cryptographic Primitive

→Proof Verification Time

Sublinear Transparent Commitment Scheme Unlocks Efficient Data Availability Sampling

A new transparent polynomial commitment scheme with sublinear proof size radically optimizes data availability for stateless clients, resolving a core rollup bottleneck.

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→Succinct Non-Interactive Argument

→ZK Rollup Scaling

→Accumulation Scheme

New Folding Scheme Enables Logarithmic Recursive Proof Verification

This new folding scheme aggregates multiple zero-knowledge instances into a single, compact proof, achieving logarithmic-time recursive verification for unprecedented rollup scalability.

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→Decentralized Proving

→Rollup Architecture

→Data Availability Sampling

Cryptographic Oracle Decouples Data Availability from Execution for Scalable Rollups

The Data Availability Oracle (DAO) uses polynomial commitments and game theory to cryptographically enforce off-chain data publication, unlocking trustless, massive L2 scalability.

Polynomial Commitment Scheme

Lattice Commitments Secure Transparent Post-Quantum Zero-Knowledge Proofs

Lattice Polynomial Commitments Achieve Post-Quantum Transparent SNARKs

Transparent Polynomial Commitments Achieve Practical Constant-Size Proofs

Transparent Constant-Sized Polynomial Commitments Enable Practical Trustless zk-SNARKs

Greyhound Achieves Post-Quantum Polynomial Commitments with Unprecedented Efficiency

Vector-Code Commitments Unlock Transparent Logarithmic-Time Zero-Knowledge Proof Verification

Efficient Transparent Zero-Knowledge Proofs Eliminate Trusted Setup for Scalability

Sublinear Transparent Commitment Scheme Unlocks Efficient Data Availability Sampling

New Folding Scheme Enables Logarithmic Recursive Proof Verification

Cryptographic Oracle Decouples Data Availability from Execution for Scalable Rollups

Incrypthos

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