Security of biometric templates stored in a system is important because a stolen template can compromise system security as well as user privacy. Therefore, a number of secure biometrics schemes have been proposed that facilitate matching of feature templates without the need for a stored biometric sample. However, most of these schemes suffer from poor matching performance owing to the difficulty of designing biometric features that remain robust over repeated biometric measurements. This paper describes a scheme to extract binary features from fingerprints using minutia points and fingerprint ridges. The features are amenable to direct matching based on binary Hamming distance, but are especially suitable for use in secure biometric cryptosystems that use standard error correcting codes. Given all binary features, a method for retaining only the most discriminable features is presented which improves the Genuine Accept Rate (GAR) from 82% to 90% at a False Accept Rate (FAR) of 0.1% on a well-known public database. Additionally, incorporating singular points such as a core or delta feature is shown to improve the matching tradeoff.