Sublinear Proof Size

Definition ∞ Sublinear Proof Size is a desirable property of cryptographic proof systems where the size of the proof generated is smaller than linear with respect to the size of the computation being proven. This means that as the computation becomes larger, the proof size grows at a slower rate, such as logarithmically or as a constant. It is crucial for scalability in blockchain applications.
Context ∞ Sublinear proof size is a key technical metric in the ongoing development of scalable blockchain solutions, particularly for zero-knowledge rollups and other Layer 2 technologies. News often highlights breakthroughs in cryptographic research that achieve smaller proof sizes, as this directly reduces on-chain verification costs and improves network throughput. This advancement is vital for broader adoption of decentralized systems.

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→Sublinear Proof Size

→Polynomial Commitment Scheme

→Cryptographic Primitive

Optimal Linear Prover Complexity Revolutionizes Polynomial Commitment Schemes

New PolyFRIM polynomial commitment scheme achieves optimal linear prover complexity, accelerating verifiable computation and distributed consensus.

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→Hash Based Commitment

→Prover Efficiency

→Linear Time Prover

Linear-Time Post-Quantum SNARKs Revolutionize Verifiable Computation Efficiency

Brakedown introduces a post-quantum, linear-time SNARK by engineering a novel polynomial commitment scheme using linear codes, fundamentally accelerating verifiable computation.

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→Reed-Solomon Codes

→Post-Quantum Cryptography

→Symmetric Key Primitives

Brakedown Achieves Post-Quantum Sublinear Polynomial Commitment without Trusted Setup

This new polynomial commitment scheme combines Reed-Solomon codes with Merkle trees, enabling post-quantum security and sublinear proof size.

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→Aggregate Signature Scheme

→Transaction Efficiency

→Post-Quantum Cryptography

Logarithmic-Size Lattice Signatures Achieve Post-Quantum Blockchain Scalability

This new lattice-based aggregate signature achieves logarithmic size growth, providing post-quantum security while radically compressing blockchain transaction data.

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→Efficient Update Process

→Succinct Commitment Scheme

→Communication Bandwidth Reduction

Partition Vector Commitment Minimizes Proof Size for Scalable Blockchain Data

Partition Vector Commitment introduces data partitioning to significantly reduce cryptographic proof size, directly addressing the critical bandwidth bottleneck for scalable data verification.

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→Witness Reduction

→Scalable Verification

→Module-SIS Assumption

Lattice-Based Recursion Enables Transparent Post-Quantum Zero-Knowledge Proofs

LaBRADOR introduces a post-quantum, lattice-based ZK primitive that achieves sublinear proof size via recursive folding, securing future computation.

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→Proof Verification Time

→Rollup Scalability

→Theoretical Cryptography

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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→Sharded Blockchain Architecture

→Efficient State Management

→Merkle Tree Optimization

Vector Commitments Enable Constant-Time Data Availability Proofs for Stateless Clients

This new Vector Commitment primitive achieves $O(1)$ data availability proof verification, fundamentally decoupling light client security from network throughput limits.

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→Data Availability Sampling

→Elliptic Curve Pairing

→Scalable Blockchain Architecture

Sublinear Vector Commitments Enable Constant-Time Verification for Scalable Systems

A new vector commitment scheme achieves constant verification time with logarithmic proof size, fundamentally enabling efficient stateless clients and scalable data availability.

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→Interactive Oracle Proof

→R1CS Circuit Satisfiability