Linear Time Prover

Definition ∞ A linear time prover is a component within a zero-knowledge proof system that generates a proof in time proportional to the size of the computation it is verifying. This means the time taken to create the proof scales linearly with the complexity of the statement being proven. Such provers are highly efficient for certain types of cryptographic proofs. Their performance is critical for the practical scalability of privacy-preserving technologies.
Context ∞ The concept of a linear time prover is highly relevant in the ongoing research and development of zero-knowledge proofs (ZKPs), particularly for scaling blockchain transactions. Achieving linear prover time is a significant goal for systems aiming to process large batches of transactions off-chain and then submit a single, compact proof to the main chain. Advances in linear time provers directly impact the throughput and cost-effectiveness of zk-rollups and other layer-2 scaling solutions, often discussed in technical crypto news.

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→Arithmetic Circuit

→Succinct Non-Interactive Arguments

→Distributed Proving

Optimal Prover Complexity Unlocks Linear-Time Zero-Knowledge Proof Generation

This breakthrough achieves optimal $O(N)$ prover time for SNARKs, fundamentally solving the quasi-linear bottleneck and enabling practical, scalable verifiable computation.

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→Polylogarithmic Verification

→Verifier Complexity

→Universal Setup

Universal Commitment Schemes Achieve Optimal Prover Efficiency

A new polynomial commitment scheme enables optimal linear-time prover complexity with a universal, updatable setup, finally resolving the ZK-SNARK trust-efficiency paradox.

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→Finite Field Operations

→Proof System Efficiency

→Non-Interactive

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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→Zero-Knowledge Proofs

→Succinctness Parameter

→Cryptographic Primitive

Constant-Size Polynomial Commitments Unlock Scalable Zero-Knowledge Proof Systems

This cryptographic primitive allows a constant-size commitment to any polynomial, fundamentally decoupling proof size from computation complexity.

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→RAM Programs

→Constant Complexity

→ZK-VM Architecture

ZKBag Cryptographic Primitive Solves RAM Program Zero-Knowledge Expressiveness Tradeoff

The ZKBag primitive, built on homomorphic commitments, fundamentally resolves the expressiveness-performance dilemma for verifiable computation, unlocking scalable ZK-VMs.

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→ZK Rollup Scalability

→Succinct Non-Interactive Argument

→Circuit Arithmetization

HyperPlonk’s Multilinear Arithmetization Unlocks Linear Prover Time for ZK-SNARKs

HyperPlonk eliminates the FFT bottleneck in Plonk by using multilinear polynomials over the boolean hypercube, enabling linear-time ZK-proof generation for massive circuits.

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→Proof Aggregation

→Linear Time Prover

→Cryptographic Primitive

Vanishing Polynomial Commitments Enable Post-Quantum Succinct Arguments and Recursive Folding

A novel commitment scheme utilizing vanishing polynomials unlocks the first lattice-based linear-time prover and polylogarithmic verifier succinct arguments.

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→Cryptography Research

→GKR Protocol

→Theoretical Computer Science

Optimal ZKP Prover Time Unlocks Practical Succinct Verifiable Computation

Libra achieves the theoretical optimum for ZKP prover efficiency, utilizing a linear-time GKR algorithm to finally scale zero-knowledge proofs.

→Zero-Knowledge Proofs

→Cryptographic Primitive

→Optimal Complexity Profile

Linear-Time Prover SNARK with Constant Proof Size Achieves ZKP Optimality

Samaritan introduces a multilinear polynomial commitment scheme that achieves the theoretical optimum: linear prover time and constant proof size for scalable verifiable computation.

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→Verifier Complexity

→Cryptographic Primitive

→Prover Complexity

WARP: Linear Accumulation Unlocks Post-Quantum Scalable Verifiable Computation

Introducing WARP, a hash-based accumulation scheme achieving linear prover time and logarithmic verification, radically accelerating recursive proof systems.