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A trusted execution environment (TEE) such as Intel Software Guard Extension (SGX) runs a remote attestation to prove to a data owner the integrity of the initial state of an enclave, including the program to operate on her data. For this purpose, the data-processing program is supposed to be open to the owner, so its functionality can be evaluated before trust can be established. However, increasingly there are application scenarios in which the program itself needs to be protected. So its compliance with privacy policies as expected by the data owner should be verified without exposing its code. To this end, this paper presents CAT, a new model for TEE-based confidential attestation. Our model is inspired by Proof-Carrying Code, where a code generator produces proof together with the code and a code consumer verifies the proof against the code on its compliance with security policies. Given that the conventional solutions do not work well under the resource-limited and TCB-frugal TEE, we propose a new design that allows an untrusted out-enclave generator to analyze the source code of a program when compiling it into binary and a trusted in-enclave consumer efficiently verifies the correctness of the instrumentation and the presence of other protection before running the binary. Our design strategically moves most of the workload to the code generator, which is responsible for producing well-formatted and easy-to-check code, while keeping the consumer simple. Also, the whole consumer can be made public and verified through a conventional attestation. We implemented this model on Intel SGX and demonstrate that it introduces a very small part of TCB. We also thoroughly evaluated its performance on micro- and macro- benchmarks and real-world applications, showing that the new design only incurs a small overhead when enforcing several categories of security policies.