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Existing integrity verification approaches for deep models are designed for private verification (i.e., assuming the service provider is honest, with white-box access to model parameters). However, private verification approaches do not allow model users to verify the model at run-time. Instead, they must trust the service provider, who may tamper with the verification results. In contrast, a public verification approach that considers the possibility of dishonest service providers can benefit a wider range of users. In this paper, we propose PublicCheck, a practical public integrity verification solution for services of run-time deep models. PublicCheck considers dishonest service providers, and overcomes public verification challenges of being lightweight, providing anti-counterfeiting protection, and having fingerprinting samples that appear smooth. To capture and fingerprint the inherent prediction behaviors of a run-time model, PublicCheck generates smoothly transformed and augmented encysted samples that are enclosed around the model's decision boundary while ensuring that the verification queries are indistinguishable from normal queries. PublicCheck is also applicable when knowledge of the target model is limited (e.g., with no knowledge of gradients or model parameters). A thorough evaluation of PublicCheck demonstrates the strong capability for model integrity breach detection (100% detection accuracy with less than 10 black-box API queries) against various model integrity attacks and model compression attacks. PublicCheck also demonstrates the smooth appearance, feasibility, and efficiency of generating a plethora of encysted samples for fingerprinting.