In this paper, we propose a secure biometric based authentication scheme which fundamentally relies on the use of a robust hash function. The robust hash function is a one-way transformation tailored specifically for each user based on their biometrics. The function is designed as a sum of properly weighted and shifted Gaussian functions to ensure the security and privacy of biometric data. We discuss various design issues such as scalability, collision-freeness and security. We also provide test results obtained by applying the proposed scheme to ORL face database by designating the biometrics as singular values of face images.