Proof Generation

Achronyme generates zero-knowledge proofs natively — no external tools required. Both backends produce real, verifiable proofs using standard cryptographic protocols.

Two Proving Systems

	R1CS + Groth16	Plonkish + KZG-PlonK
Library	ark-groth16	PSE halo2
Curve	BN254	BN254
Proof size	~128 bytes (constant)	Larger (scales with circuit)
Setup	Per-circuit trusted setup	Universal KZG params (reusable)
Verification	Constant time	Logarithmic

The Pipeline

Whether using the CLI or inline prove {} blocks, the proof pipeline follows the same steps:

Source → Parse → AST → IR → Optimize → Compile → Witness → Verify → Prove

1. Parse: source code to AST
2. IR Lowering: AST to SSA intermediate representation, extracting public/witness declarations
3. Optimize: const_fold, dce, bool_prop passes reduce constraint count
4. Compile: IR instructions become R1CS constraints or Plonkish table rows
5. Witness: concrete input values fill the witness vector/table
6. Verify: constraints are checked against the witness (catches bugs before proving)
7. Prove: cryptographic proof is generated

CLI: circuit Command

The circuit command compiles a standalone .ach file:

# R1CS (default): compile + witness + export .r1cs/.wtns
achronyme circuit multiply.ach --inputs "x=6,y=7,out=42"

# Plonkish: compile + verify
achronyme circuit multiply.ach --backend plonkish --inputs "x=6,y=7,out=42"

# Plonkish with proof generation
achronyme circuit multiply.ach --backend plonkish --inputs "x=6,y=7,out=42" --prove

R1CS Output Files

With the R1CS backend, the CLI exports two binary files:

• circuit.r1cs: the constraint system in iden3 format (snarkjs-compatible)
• circuit.wtns: the witness vector in iden3 format

These can be used directly with snarkjs for Groth16 proof generation:

# Using snarkjs (external)
snarkjs r1cs info circuit.r1cs
snarkjs wtns check circuit.r1cs circuit.wtns
snarkjs groth16 setup circuit.r1cs pot_final.ptau circuit.zkey
snarkjs groth16 prove circuit.zkey circuit.wtns proof.json public.json
snarkjs groth16 verify vkey.json public.json proof.json

Or let Achronyme handle it natively — see the prove {} block section below.

Plonkish Output

With --prove, the Plonkish backend generates:

• proof.json: the KZG-PlonK proof (hex-encoded bytes)
• public.json: public input values
• vkey.json: the verifying key (hex-encoded)

Solidity Verifier

For R1CS/Groth16, you can generate an on-chain verifier:

achronyme circuit multiply.ach --inputs "x=6,y=7,out=42" --solidity Verifier.sol

This produces a Solidity contract that verifies Groth16 proofs for the specific circuit.

Inline: prove {} Blocks

Prove blocks let you generate proofs inline within regular Achronyme programs:

let secret = 42
let hash = 0p18569430475105882...

let p = prove(hash: Public) {
    assert_eq(poseidon(secret, 0), hash)
}

// p is a proof object
print(proof_json(p))
print(proof_public(p))
print(proof_vkey(p))

How Prove Blocks Work

1. The VM encounters the prove {} block
2. Variables from the outer scope are captured — secret and hash become circuit inputs
3. Int values are automatically converted to field elements (the only place this happens implicitly)
4. The block is compiled as a circuit, a witness is generated from captured values, and a proof is produced
5. The result is a ProofObject on the heap, accessible via native functions

ProveResult

A prove block returns one of:

• Proof: contains proof_json, public_json, and vkey_json strings
• VerifiedOnly: constraints were verified but no proof was generated (verify-only mode)

Proof Object Natives

Function	Returns	Description
proof_json(p)	String	The proof data (Groth16 or PlonK format)
proof_public(p)	String	Public inputs as a JSON array of decimal strings
proof_vkey(p)	String	The verification key

Backend Selection

Prove blocks support both backends:

• R1CS + Groth16 (default): native via ark-groth16
• Plonkish + KZG-PlonK: native via halo2

Key Caching

Proof generation requires cryptographic keys (proving key + verifying key). These are expensive to compute, so Achronyme caches them:

• Location: ~/.achronyme/cache/
• R1CS (Groth16): cached by a SHA256 hash of the constraint system structure. Same circuit = same keys, even across runs.
• Plonkish (KZG): universal params cached by k (the log2 of table size). Reusable across different circuits of the same size.

On first run for a new circuit, key generation may take a few seconds. Subsequent runs with the same circuit structure are near-instant.

Witness Generation

The witness is the complete assignment of values to all circuit wires — inputs, intermediates, and outputs. The compiler builds it in three passes:

1. Evaluate: runs the IR with concrete inputs for early validation. Catches assertion failures, division by zero, and missing inputs before emitting any constraints.
2. Compile: lowers IR to constraints, recording a trace of WitnessOp instructions as a side effect.
3. Replay: fills the witness vector by replaying the ops trace with concrete values.

Witness Operations

Each intermediate wire is computed by a recorded operation:

Op	Description
AssignLC	Evaluate a linear combination
Multiply	Multiply two LCs
Inverse	Compute modular inverse
BitExtract	Extract the n-th bit from a field element
IsZero	IsZero gadget: set result and inverse
PoseidonHash	Compute Poseidon permutation (fills ~360 internal wires)

Error Handling

The pipeline reports errors at the earliest possible stage:

Stage	Error	Example
IR Lowering	Parse/declaration errors	variable 'x' not declared
Evaluation	Assertion/arithmetic errors	assert_eq failed: 5 != 6
Compilation	Constraint errors	division by zero
Verification	Unsatisfied constraints	constraint 3 failed
Proof Generation	Cryptographic errors	Groth16 setup failed

The early evaluation pass is intentional: it catches logical errors before spending time on constraint generation and proving.

Further Reading

• R1CS — how constraints work in the R1CS backend
• Plonkish — how the Plonkish backend works
• Circuit Overview — writing circuits in Achronyme
• Builtins — built-in circuit functions and their costs