Arithmetic Circuit

Definition ∞ An arithmetic circuit is a computational model that performs mathematical operations on inputs. In cryptography, it represents a sequence of addition and multiplication gates used to define a computation for zero-knowledge proofs. These circuits transform a computational problem into a form verifiable without revealing the inputs themselves. Their structure is fundamental for proving the correctness of complex calculations privately.
Context ∞ Arithmetic circuits are central to advancements in zero-knowledge proof systems like zk-SNARKs and zk-STARKs, which are critical for scaling blockchain networks and enhancing transaction privacy. Ongoing research focuses on optimizing circuit size and proof generation time to improve the practical application of these cryptographic primitives. Their efficiency directly impacts the viability of privacy-preserving technologies in digital asset transactions.

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→Recursive Proof Composition

→Incremental Verifiable Computation

→Constant Verifier Circuit

Folding Schemes Enable Linear-Time Recursive Zero-Knowledge Computation

Nova's folding scheme fundamentally solves recursive proof composition by accumulating instances instead of verifying SNARKs, unlocking infinite verifiable computation.

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→Succinct Argument

→Recursive Proof

→Multi Client Rollup

Statement Hiders Enable Privacy Preserving Folding Schemes for Verifiable Computation

The Statement Hider primitive blinds zero-knowledge statements before folding, resolving privacy leakage during selective verification for multi-client computation.

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→Linear Prover Time

→Zero-Knowledge Argument

→Expander Graph

Linear Prover Time Unlocks Practical Zero-Knowledge Proof Scalability

A new ZKP argument system achieves optimal linear prover time, dramatically lowering the cost barrier for large-scale verifiable computation.

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→Discrete Logarithm Assumption

→Computational Soundness

→Cryptographic Primitive

Logarithmic Zero-Knowledge Proofs Eliminate Trusted Setup for Private Computation

Bulletproofs introduce non-interactive zero-knowledge proofs with logarithmic size and no trusted setup, fundamentally solving the proof-size bottleneck for on-chain privacy.