Vector Commitment

Definition ∞ A vector commitment is a cryptographic primitive that allows a party to commit to an ordered list of values and later reveal individual elements or subsets with proofs. This commitment scheme provides the properties of both hiding and binding for each element within the vector, while also enabling efficient opening of specific positions without disclosing the entire list. It is particularly useful in scenarios where verifiable access to specific data points within a larger dataset is required without revealing the complete dataset. Vector commitments are foundational for constructing efficient zero-knowledge proofs and verifiable data structures.
Context ∞ Vector commitments are a subject of ongoing research and development in advanced cryptography, frequently appearing in news related to scaling blockchains and enhancing data privacy. Their application in succinct proofs and verifiable computation is a key area of focus. Future developments aim to improve the efficiency and security of these schemes, making them more practical for widespread use in decentralized applications and confidential transactions.

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→Polynomial Commitment

→Proof System

→Stateless Client

FRI Protocol Enables Poly-Logarithmic Data Availability Sampling without Trusted Setup

FRIDA, a new primitive, leverages the FRI proximity test to construct a vector commitment, enabling non-trusted-setup DAS with $O(log^2 N)$ communication overhead.

→Vector Commitment

→Constant Proof Size

→Proof System Efficiency

Hierarchical Vector Commitment Enables Constant-Time Stateless Blockchain Verification

A new Hierarchical Polynomial Vector Commitment achieves constant-size state proofs, drastically lowering node hardware requirements and securing decentralization.

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→Vector Commitment

→On-The-Fly Coding

→Cryptographic Assurance

Decoupling Coding and Commitment Strengthens Data Availability Sampling Assurance

A new Data Availability Sampling paradigm uses Random Linear Network Coding to generate coded samples on-the-fly, achieving significantly stronger security assurance for light clients.

A sleek, silver and black hardware module showcases intricate internal mechanisms through a transparent blue chassis. Visible components include a central control button and a precision-engineered balance wheel, reminiscent of a cryptographic primitive operating within a secure enclave. This design visually interprets the robust engineering of a dedicated node validator or a cold storage device, emphasizing the immutability and transparent execution inherent in distributed ledger technology. The visible mechanics symbolize the underlying consensus mechanism securing digital assets.

→State Management

→Dynamic Updates

→Succinct Global State

Asymptotically Optimal Vector Commitments Enable True Stateless Clients

New cryptographic vector commitment achieves sublinear update complexity, fundamentally solving state bloat for scalable decentralized architectures.

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→ZK Rollup Finality

→Verifiable Computation

→Zero-Knowledge Proofs

Vector-SNARK Achieves Constant-Time Verification for Recursive Zero-Knowledge Proofs

Introducing Vector-SNARK, a hash-based commitment scheme that decouples verifier cost from recursion depth, enabling instant ZK-Rollup finality.

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→Client-Side Validation

→Logarithmic Proof Size

→Fixed Size Commitment

Vector Accumulators Enable Logarithmic Stateless Client Verification without Trusted Setup

This new Vector Accumulator primitive decouples state size from client verification cost, achieving logarithmic-time proofs for truly scalable stateless nodes.

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→Quasi-Linear Time

→Batch Updatable

→Stateless Blockchain

Batch-Updatable Vector Commitments Enable Efficient Stateless Blockchain Architecture

Cauchyproofs introduces a quasi-linear batch-updatable vector commitment, solving the critical state proof maintenance bottleneck for practical stateless chains.

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→Reed-Solomon Codes

→Zero-Knowledge Proofs

→Distributed Systems

FRI Proximity Tests Enable Transparent Logarithmic Data Availability Sampling

FRI-based Data Availability Sampling provides a transparent, post-quantum path to scalable light client verification with logarithmic communication overhead.