Proof System Efficiency

∞Argument Consistency

New Linear PCP Simplifies NIZK Arguments, Significantly Improving Prover Efficiency

Researchers unveil a linear PCP for Circuit-SAT, leveraging error-correcting codes to simplify argument construction and boost SNARK prover efficiency.

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∞Cryptographic Primitive

∞Cryptographic Commitment

∞Linearly Homomorphic Commitments

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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∞System Efficiency

∞Expander Graphs

∞Commitment Scheme

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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∞Constant Time Proving

∞zkVM Architecture

Zero-Knowledge Bag Unlocks Constant-Time Verifiable General Computation

Introducing the Zero-Knowledge Bag, a new cryptographic primitive enabling constant computational and communication complexity for zkVM execution.

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∞Proof Generation

∞Modular Remainder

∞Succinct Arguments

ZNARKs Enable Efficient Verifiable Computation over Integers

A new polynomial commitment with modular remainder fundamentally simplifies creating succinct arguments for real-world integer arithmetic.

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∞Universal Trusted Setup

∞Cryptographic Primitives

Distributed Zero-Knowledge Proofs Achieve Optimal Prover Computational Efficiency

Distributed proving protocols dramatically reduce ZKP generation time, transforming verifiable computation from a theoretical ideal to a scalable, practical primitive.

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∞Polynomial Commitment

∞Cryptoeconomic Security

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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∞Finite Field Operations

∞Transparent Setup

Linear-Time Post-Quantum SNARKs Achieve Optimal Prover Efficiency

Brakedown introduces the first built linear-time SNARK, achieving optimal O(N) prover complexity for large computations while eliminating trusted setup.

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∞Polynomial Commitment

∞Scalable Verification

∞Set Membership Proofs

Universal Vector Commitments Enable Efficient Proofs of Non-Membership and Data Integrity

Introducing Universal Vector Commitments, a new primitive that securely proves element non-membership, fundamentally enhancing stateless client and ZK-rollup data verification.

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∞Linear Memory Bottleneck

∞Square-Root Scaling

Sublinear Space Zero-Knowledge Proofs Democratize Verifiable Computation on Constrained Devices

New sublinear memory ZKPs shift resource constraints from linear to square-root complexity, unlocking verifiable computation on mobile and edge devices.

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∞Trustless Security

∞Scalable Verification

∞Recursive Proof System

Novel Recursive Commitment Scheme Achieves Transparent, Efficient Zero-Knowledge Proofs

LUMEN introduces a recursive polynomial commitment scheme and PIOP protocol, eliminating the trusted setup while maintaining zk-SNARK efficiency, securing rollup scalability.

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∞Arithmetic Circuit

Plonky2 Proves SHA-256 Integrity for Scalable Zero-Knowledge Blockchains

A new Plonky2-based methodology efficiently generates zero-knowledge proofs for SHA-256, solving a core computational integrity bottleneck for scaling ZK-Rollups.

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∞Block Processing

∞Proof Generation Time

Sublinear Zero-Knowledge Proofs Unlock Ubiquitous Private Computation

A new proof system eliminates ZKP memory bottlenecks by achieving square-root scaling, enabling verifiable computation on all devices.

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∞Polynomial Commitments

∞Prover Complexity

Fractal Commitments Enable Universal Logarithmic-Size Verifiable Computation

This new fractal commitment scheme recursively compresses polynomial proofs, achieving truly logarithmic verification costs for universal computation without a trusted setup.

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∞Post-Quantum Security

∞Black-Box Framework

Post-Quantum Zero-Knowledge Proofs Achieve Shorter, Faster Verification

Lantern introduces a direct polynomial product proof for vector norms, slashing post-quantum ZKP size for practical privacy applications.

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∞Trustless Verification

∞Verifiable Computation Scaling

Distributed zkVM Architecture Slashes Verification Costs and Latency

A modular, distributed zkVM architecture dramatically cuts hardware costs and latency, making real-time zero-knowledge verification economically feasible for all validators.

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∞Succinct Proof Systems

Recursive Proof Composition Achieves Logarithmic-Time Zero-Knowledge Verification

A novel folding scheme reduces the verification of long computations to a logarithmic function, fundamentally decoupling security from computational scale.

∞Secret Shared Data

∞Batch Verification

Constant-Cost Batch Verification with Silently Verifiable Proofs

Silently Verifiable Proofs introduce a new zero-knowledge primitive that achieves constant verifier-to-verifier communication for arbitrarily large proof batches, drastically cutting overhead for private computation.

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∞Evaluation Proof

∞Post-Quantum Ledger

∞Cryptographic Binding

Lattice-Based Polynomial Commitments Achieve Post-Quantum Succinctness and Sublinear Verification

Greyhound is the first concretely efficient lattice-based polynomial commitment scheme, enabling post-quantum secure zero-knowledge proofs with sublinear verifier time.

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∞Logarithmic Complexity

∞Transparent Security

Recursive Inner Product Arguments Enable Universal Transparent Polynomial Commitments

A novel recursive folding of polynomial commitments into Inner Product Arguments yields universal, transparent proof systems for highly scalable verifiable computation.

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∞Constant Proof Size