A directed acyclic graph of addition and multiplication gates representing a computation over a finite field. Used as the intermediate representation for compiling programs into zero-knowledge proofs. The circuit maps inputs to outputs through a series of field operations, with circuit size (number of gates) determining proof generation cost.
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A directed acyclic graph of addition and multiplication gates representing a computation over a finite field. Used as the intermediate representation for compiling programs into zero-knowledge proofs. The circuit maps inputs to outputs through a series of field operations, with circuit size (number of gates) determining proof generation cost.
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Arithmetic Circuit (arithmetic-circuit) Category: ZK Compression Definition: A directed acyclic graph of addition and multiplication gates representing a computation over a finite field. Used as the intermediate representation for compiling programs into zero-knowledge proofs. The circuit maps inputs to outputs through a series of field operations, with circuit size (number of gates) determining proof generation cost. Related: R1CS (Rank-1 Constraint System), Zero-Knowledge Proofs (ZKP), Groth16
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An arithmetic constraint format used to represent computations as systems of equations for zero-knowledge proof generation. Programs are compiled into R1CS constraints of the form A * B = C, where A, B, C are linear combinations of variables. Groth16 and other SNARKs use R1CS as their computation representation layer.
A zero-knowledge proof is a cryptographic protocol by which a prover convinces a verifier that a statement is true — for example, that a state transition is valid — without revealing any information beyond the truth of the statement itself, satisfying the properties of completeness, soundness, and zero-knowledge. In Solana's ecosystem, ZKPs are used by ZK Compression (via Groth16 SNARKs) to prove correct state transitions for compressed accounts without storing full account state on-chain, and by the Token-2022 Confidential Transfers extension (via ElGamal encryption and range proofs) to prove token balances are non-negative without revealing the actual amounts. Solana's BPF VM exposes the alt_bn128 elliptic curve syscall to make on-chain Groth16 proof verification computationally feasible within the 1.4M compute unit budget.
Groth16 is a highly efficient zk-SNARK proving system introduced by Jens Groth in 2016 that produces constant-size proofs (128 bytes: two G1 points and one G2 point on a pairing-friendly elliptic curve) with constant-time verification regardless of circuit complexity, making it the preferred proof system for on-chain verification where calldata and compute costs are constrained. Light Protocol uses Groth16 proofs over the BN254 curve (known as alt_bn128 in Ethereum tooling) to verify compressed account state transitions on Solana, leveraging the native alt_bn128 pairing and point-addition syscalls added to the SVM to keep verification within the per-transaction compute unit limit. The trade-off is that Groth16 requires a trusted setup ceremony per circuit, producing a structured reference string (SRS) whose security relies on participants honestly discarding their toxic waste.
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An arithmetic constraint format used to represent computations as systems of equations for zero-knowledge proof generation. Programs are compiled into R1CS constraints of the form A * B = C, where A, B, C are linear combinations of variables. Groth16 and other SNARKs use R1CS as their computation representation layer.
A zero-knowledge proof is a cryptographic protocol by which a prover convinces a verifier that a statement is true — for example, that a state transition is valid — without revealing any information beyond the truth of the statement itself, satisfying the properties of completeness, soundness, and zero-knowledge. In Solana's ecosystem, ZKPs are used by ZK Compression (via Groth16 SNARKs) to prove correct state transitions for compressed accounts without storing full account state on-chain, and by the Token-2022 Confidential Transfers extension (via ElGamal encryption and range proofs) to prove token balances are non-negative without revealing the actual amounts. Solana's BPF VM exposes the alt_bn128 elliptic curve syscall to make on-chain Groth16 proof verification computationally feasible within the 1.4M compute unit budget.
Groth16 is a highly efficient zk-SNARK proving system introduced by Jens Groth in 2016 that produces constant-size proofs (128 bytes: two G1 points and one G2 point on a pairing-friendly elliptic curve) with constant-time verification regardless of circuit complexity, making it the preferred proof system for on-chain verification where calldata and compute costs are constrained. Light Protocol uses Groth16 proofs over the BN254 curve (known as alt_bn128 in Ethereum tooling) to verify compressed account state transitions on Solana, leveraging the native alt_bn128 pairing and point-addition syscalls added to the SVM to keep verification within the per-transaction compute unit limit. The trade-off is that Groth16 requires a trusted setup ceremony per circuit, producing a structured reference string (SRS) whose security relies on participants honestly discarding their toxic waste.
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State Compression is Solana's technique for storing the cryptographic fingerprint (root hash) of a Merkle tree on-chain while keeping the actual leaf data off-chain in the Solana ledger's account data logs, reducing the cost of storing large datasets by orders of magnitude. A compressed NFT collection of 1 million items costs roughly 50 SOL to mint versus ~12,000 SOL with standard SPL accounts, because only a single Concurrent Merkle Tree account occupies on-chain storage. Any data change requires updating the root hash and supplying a Merkle proof to the on-chain program, which verifies inclusion without reading the full dataset.
ZK Compression, pioneered by Light Protocol, extends Solana's state compression model beyond NFTs to general-purpose compressed accounts by using zero-knowledge proofs (specifically Groth16 SNARKs verified via the alt_bn128 syscall) to prove the validity of state transitions without storing full account state on-chain. Compressed accounts live in on-chain Merkle trees but their data is reconstructed from the Solana ledger by indexers like Photon, enabling developers to build applications that use thousands of accounts at a fraction of the normal rent cost — often 1,000x to 5,000x cheaper than regular accounts. The protocol introduces compressed tokens, compressed PDAs, and a system of nullifiers to prevent double-spends while maintaining Solana's throughput.
A compressed account is a Solana account whose state is stored as a leaf in an on-chain Concurrent Merkle Tree rather than as a dedicated on-chain account, making it 100–1,000x cheaper to create and maintain because no rent-exempt lamport balance is required per account. Compressed accounts are identified by a hash of their data and position in the tree; to interact with one, a client must supply a Merkle proof (or rely on the canopy) showing the leaf is part of the current tree root, which the on-chain program verifies before processing the state change. Light Protocol's compressed account model supports arbitrary data, discriminators, and owner programs, making it a general-purpose replacement for expensive on-chain accounts in high-volume use cases.
A Concurrent Merkle Tree (CMT) is a specialized on-chain Solana data structure that allows multiple state updates to the same Merkle tree within a single block without conflicting, by recording a changelog buffer of recent root transitions that validators use to reconcile parallel proof submissions. A CMT is parameterized by its maximum depth (max_depth, determining tree capacity of 2^max_depth leaves), max_buffer_size (number of concurrent changes the changelog can track, directly controlling how many operations per slot the tree can safely absorb), and an optional canopy_depth. The SPL Account Compression program manages CMTs, and they are the foundational storage primitive for both Metaplex compressed NFTs and Light Protocol compressed accounts.