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In recent years there has been exponential growth in the use of biometrics for user authentication applications because biometricsbased authentication offers several advantages over knowledge and possession-based methods such as password/PIN-based systems. However, it is important that biometrics-based authentication systems be designed to withstand different sources of attacks on the system when employed in security-critical applications. This is even more important for unattended remote applications such as e-commerce. In this paper we outline the potential security holes in a biometrics-based authentication scheme, quantify the numerical strength of one method of fingerprint matching, then discuss how to combat some of the remaining weaknesses.