We present a theory for constructing linear, black box approximations to face recognition algorithms and empirically demonstrate that a surprisingly diverse set of face recognition approaches can be approximated well using a linear model. The construction of the linear model to a face recognition algorithm involves embedding of a training set of face images constrained by the distances between them, as computed by the face recognition algorithm being approximated. We accomplish this embedding by iterative majorization, initialized by classical multi-dimensional scaling (MDS). We empirically demonstrate the adequacy of the linear model using six face recognition algorithms, spanning both template based and feature based approaches on standard face recognition benchmarks such as the Facial Recognition Technology (FERET) and Face Recognition Grand Challenge (FRGC) data sets. The experimental results show that the average Error in Modeling for six algorithms is 6.3% at 0.001 False Acceptance Rate (FAR), for FERET fafb probe set which contains maximum number of subjects among all the probe sets. We demonstrate the usefulness of the linear model for algorithm dependent indexing of face databases and find that it results in more than 20 times reduction in face comparisons for Bayesian Intra/Extra-class person classifier (BAY), Elastic Bunch Graph Matching algorithm (EBGM), and the commercial face recognition algorithms. We also propose a novel paradigm to reconstruct face templates from match scores using the linear model and use the reconstructed templates to explore the security breach in a face recognition system. We evaluate the proposed template reconstruction scheme using three, fundamentally different, face recognition algorithms: Principal Component Analysis (PCA), Bayesian Intra/Extra-class person classifier (BAY), and a feature based commercial algorithm. With an operational point set at 1% False Acceptance Rate (FAR) and 99% True Acceptance Rate (TAR) for 1196 enrollments (FERET gallery), we show that at most 600 attempts (score computations) are required to achieve 73%, 72% and 100% chance of breaking in as a randomly chosen target subject for the commercial, BAY and PCA based face recognition system, respectively. We also show that the proposed reconstruction scheme has 47% more probability of breaking in as a randomly chosen target subject for the commercial system as compared to a hill climbing approach with the same number of attempts.