Certificateless universal designated-verifier signature proofs for carbon-footprint verification

Carbon-footprint audits require organizations to verify signed electricity and production evidence while limiting unnecessary disclosure. We study a certificateless signature-proof construction that combines a partial key issued by a key-generation center (KGC), an independent user secret, signature transformation and an interactive proof of the transformation factor. A canonical message binds the report and evidence digests to the signer identity, key epoch and accounting context; detailed records remain off chain. For validated nonidentity statements, we establish correctness, two-transcript signature extraction and honest-verifier transcript simulation. These properties are distinguished from the additional unforgeability requirements of the underlying signature. Reproducible analytical calculations describe communication size, group-operation counts, queueing and ledger-dependent workflow latency. Under explicitly selected delay inputs, an asynchronous online decision is calculated at 385.2 ms, compared with 2570.2 ms when commitment blocks the same path. These values are model outputs, not measured cryptographic or deployment performance. Source attestation, endpoint key protection, revocation and constrained-device verification are discussed as deployment measures. The result is a bounded design and analytical assessment; a complete underlying-signature security proof and implementation measurements remain necessary for deployment.