Blockchain-based identity services let applications across administrative domains verify biometric authentication results without sharing a trusted biometric server. BioZero evaluates how to protect private templates while limiting on-chain execution and submitted transaction-data costs under explicit cryptographic assumptions. FullCheck provides knowledge soundness for the modular distance relation, but exhaustive coordinate checks cost 22.1 million gas at N=128 in a threshold-stand-in benchmark. SpotCheck tests a natural optimization: sampling checks within the same homomorphic structure. Checking seven coordinates saves 81.3% gas, reducing it to 4.1 million, but retains 127,844 bytes of calldata. We prove that changing one product commitment can shift the reconstructed distance to any chosen residue and evade a uniform sample of t among N coordinates with probability 1-t/N. Negligible attack success therefore requires nearly exhaustive checking, limiting the scope for coordinate-check savings. CircuitCheck changes the verification structure, proving commitment openings, coordinate ranges, and the integer distance threshold in one circuit. Its complete reference transaction costs 255 thousand gas with 356 bytes of calldata. At N=128, median proving time and process peak memory are 0.63 s and 822 MiB on the evaluated workstation. On two face datasets, every tested width of at least 6 bits stays within 0.46 percentage points of float accuracy, supporting the shared integer-input front end. These results favor CircuitCheck for the evaluated integer matching task in blockchain-backed cross-domain identity services, provided that committed probes are separately bound to authenticated live captures.

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