Polynomial Commitment

Definition ∞ Polynomial commitment is a cryptographic primitive that allows a prover to commit to a polynomial in a concise manner. This commitment permits the prover to later open the polynomial at specific points, proving its value without revealing the entire polynomial. It forms a fundamental building block for advanced zero-knowledge proof systems, enabling efficient verification of complex computations. Such schemes ensure data integrity and privacy in various cryptographic protocols.
Context ∞ Polynomial commitment schemes are central to ongoing research and development in scalable blockchain solutions, particularly for rollups and other layer-2 protocols that rely on zero-knowledge proofs. Discussions frequently involve comparing different commitment schemes, such as KZG or FRI, based on their efficiency, security assumptions, and proof size. The continuous refinement of these cryptographic tools is vital for enhancing the performance and privacy features of decentralized applications.

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→Polynomial Commitment

→Circuit Size

→Linear Computation

Optimal Prover Time Unlocks Scalable Linear-Time Zero-Knowledge Proofs

Libra is the first ZKP system to achieve optimal linear prover time $O(C)$ while maintaining succinct proof size, enabling practical large-scale verifiable computation.

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→Groups of Unknown Order

→Proof System Design

→Non-Interactive Argument

Transparent Constant-Size Zero-Knowledge Proofs Eliminate Trusted Setup

This breakthrough cryptographic primitive, based on Groups of Unknown Order, yields a truly succinct zk-SNARK without a trusted setup, unlocking scalable, trustless computation.

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→Polynomial Commitment

→Transparent Setup

→Succinct Arguments

Isogeny-Based Commitments Enable Transparent Post-Quantum ZK Arguments

Isogeny-based polynomial commitments deliver the first transparent, quantum-resistant ZK-SNARK, securing all verifiable computation.

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→Proof Systems

→Trustless Systems

→Verification Time

Inner Product Arguments Eliminate Trusted Setup for Data Availability Sampling

Inner Product Arguments enable trustless data availability sampling by replacing complex trusted setups with a transparent, discrete log-based commitment scheme.

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→Zero-Knowledge Proof Systems

→Verifiable Security

→Polynomial Commitment

Verifiable Fine-Tuning Secures Large Language Models with Zero-Knowledge Proofs

zkLoRA is a new framework that cryptographically verifies LLM fine-tuning correctness without revealing model weights, unlocking private, auditable AI.

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→Efficient Verification

→Polynomial Commitment

→Stateless Client

Dynamic Vector Commitments Enable Sublinear State Updates and Stateless Clients

A new algebraic commitment primitive achieves sublinear state updates, fundamentally solving the efficiency bottleneck for large-scale stateless blockchain architecture.

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→Trustless Setup

→Data Availability

→Rollup Security

Erasure Code Commitments Enable Efficient Trustless Data Availability Sampling

This new cryptographic primitive formally guarantees committed data is a valid code word, enabling poly-logarithmic Data Availability Sampling without a trusted setup.

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→Polylogarithmic Proof

→Blockchain Scaling

→Computational Integrity

Efficient Post-Quantum Polynomial Commitments Fortify Zero-Knowledge Scalability

Greyhound introduces the first concretely efficient lattice-based polynomial commitment scheme, unlocking post-quantum security for zk-SNARKs and blockchain scaling primitives.

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→Black Box Cryptography

→Minimal Assumptions

→Succinct Arguments

Black-Box Succinct Proofs Achieve Statistical Zero-Knowledge Security

A new polynomial commitment scheme enables succinct zero-knowledge proofs from minimal assumptions, establishing a theoretically optimal foundation for verifiable computation.

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→Relaxed R1CS

→Recursive Proof Systems

→Computational Integrity

Nova Folding Scheme Enables Efficient Recursive Proof Accumulation

Nova's non-interactive folding scheme compresses arbitrary computation histories into a single, logarithmic-size proof, finally enabling practical IVC.