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Although biometrics is more reliable, robust and convenient than traditional methods, security and privacy concerns are growing. Biometric templates stored in databases are vulnerable to attacks if they are not protected. To solve this problem, a biometric cryptosystem approach that combines cryptography and biometrics has been proposed. Under this approach, helper data is stored in a database rather than the original reference biometric templates. The helper data is generated from the original reference biometric templates and a cryptographic key with error-correcting coding schemes. During decoding, the same cryptographic key can be released from the helper data if and only if the input query data is close enough to the reference. It is assumed that the helper data does not reveal any information about the original reference biometric templates. Thus, the biometric cryptosystem approach can protect the original reference templates. However, error-correcting coding algorithms (e.g., the fuzzy commitment scheme and fuzzy vault) normally require finite input. As most face templates are real-valued templates, a binarization scheme transforming the original real-valued face templates into binary templates is required. Most existing binarization schemes are performed in an ad hoc manner and do not consider the discriminability of the binary template. The recognition accuracy based on the binary templates is thus degraded. In view of this limitation, we propose a new binarization scheme by optimizing binary template discriminability. A novel binary discriminant analysis is developed to transform a real-valued template into a binary template. Differentiation is hard to perform in binary space and direct optimization is difficult. To solve this problem, we construct a continuous function based on the perceptron to optimize binary template discriminability. Our experimental results show that the proposed algorithm improves binary template discriminability.