Propagate DirectSNARK synthesis errors and enforce the step circuit arity contract

[somasoil]

Summary

DirectSNARK swallowed every error raised while synthesizing the step circuit, and never
checked that the circuit honors the arity it declares. setup / prove now return a proper
NovaError in all of those cases.

Changes

• src/spartan/direct.rs
  • DirectCircuit no longer discards the two inputize results; they are propagated with ?.
  • Added DirectCircuit::synthesize_inner, which returns NovaError and enforces the
    StepCircuit arity contract:
    • supplied inputs must have exactly arity() elements, otherwise NovaError::InvalidInputLength;
    • the step circuit must return exactly arity() outputs, otherwise
      NovaError::InvalidStepOutputLength.
  • DirectSNARK::setup and DirectSNARK::prove call synthesize_inner(&mut cs)? instead of
    let _ = circuit.synthesize(&mut cs);, so synthesis failures are surfaced as
    NovaError::SynthesisError { .. } through the existing From<SynthesisError> impl.
  • The Circuit impl is kept and is now a thin wrapper over synthesize_inner, so there are no
    public API changes and the existing call sites in src/neutron/{nifs,relation}.rs keep working.

Why a private synthesize_inner

Circuit::synthesize must return SynthesisError, so a check placed inside it cannot surface the
existing typed NovaError::InvalidInputLength / NovaError::InvalidStepOutputLength.
synthesize_inner returns NovaError and is what setup / prove call, which makes each failure
mode directly assertable in tests (same style as the existing
assert_eq!(pp.err(), Some(NovaError::InvalidStepCircuitIO)) in src/nova/mod.rs).

Tests

Added to src/spartan/direct.rs:

• FailingCircuit — a step circuit whose synthesize always returns
  Err(SynthesisError::Unsatisfiable(..)). Both setup and prove now return
  Err(NovaError::SynthesisError { .. }).
• WrongOutputArityCircuit — declares arity() == 2 but returns a single output. setup returns
  Err(NovaError::InvalidStepOutputLength).
• prove with an input that is too long (2 elements for arity() == 1) returns
  Err(NovaError::InvalidInputLength); with an empty input it returns the same error instead of
  panicking (previously an index-out-of-bounds panic).

Verified:

• cargo test --release --lib spartan::direct — 3 passed
• cargo test --release --features experimental neutron — 10 passed (DirectCircuit is also used there)
• cargo clippy --all-targets -- -D warnings — clean
• cargo fmt --all -- --check — clean

Checklist

• cargo fmt --all -- --check
• cargo clippy --all-targets -- -D warnings
• cargo test --release

[somasoil]

@microsoft-github-policy-service agree

[somasoil]

Srinath Setty (@srinathsetty) Could you please take a look when you have a chance? Thanks!