This thesis studies the requirements and processes involved in building an authentication system using the fingerprint biometric, where the fingerprint template is protected during storage and during comparison. The principles developed in this thesis can be easily extended to authentication systems using other biometric modalities. Most existing biometric authentication systems store their template securely using an encryption function. However, in order to perform matching, the enrolled template must be decrypted. It is at this point that the authentication system is most vulnerable as the entire enrolled template is exposed. A biometric is irreplaceable if compromised and can also reveal sensitive information about an individual. If biometric systems are taken up widely, the template could also be used as an individual's digital identifier. Compromise in that case, violates an individual's right to privacy as their transactions in all systems where they used that compromised biometric can be tracked. Therefore securing a biometric template during comparison as well as storage in an authentication system is imperative. Eight different fingerprint template representation techniques, where templates were treated as a set of elements derived from the locations and orientations of fingerprint minutiae, were studied. Four main steps to build any biometric based authentication system were identified and each of the eight fingerprint template representations was inducted through the four steps. Two distinct Error Tolerant Cryptographic Constructs based on the set difference metric, were studied for their ability to securely store and compare each of the template types in an authentication system. The first construct was found to be unsuitable for a fundamental reason that would apply to all the template types considered in the research. The second construct did not have the limitation of the first and three algorithms to build authentication systems using the second construct were proposed. It was determined that minutiae-based templates had significant intra sample variation as a result of which a very relaxed matching threshold had to be set in the authentication system. The relaxed threshold caused the authentication systems built using the first two algorithms to reveal enough information about the stored templates to render them insecure. It was found that in cases of such large intra-sample variation, a commonality based match decision was more appropriate. One solution to building a secure authentication system using minutiae-based templates was demonstrated by the third algorithm which used a two stage matching process involving the second cryptographic construct and a commonality based similarity measure in the two stages respectively. This implementation was successful in securing the fingerprint template during comparison as well as storage, with minimal reduction in accuracy when compared to the matching performance without the cryptographic construct. Another solution is to use an efficient commonality based error tolerant cryptographic construct. This thesis lists the desirable characteristics of such a construct as existence of any is unknown to date. This thesis concludes by presenting good guidelines to evaluate the suitability of different cryptographic constructs to protect biometric templates of other modalities in an authentication system.