In this paper, we propose the use of non-negative matrix factorization (NMF) for robust image hashing. In particular, we view images as matrices and the goal of hashing as a randomized dimensionality reduction that retains the essence of the original image matrix while preventing against intentional attacks of guessing and forgery. Our work is motivated by the fact that standard-rank reduction techniques such as the QR, and Singular Value Decomposition (SVD), produce low rank bases which do not respect the structure (i.e. non-negativity for images) of the original data. We observe that NMFs have two very desirable properties for secure image hashing applications: 1.) The additivity property resulting from the non-negativity constraints results in bases that capture local characteristics of the image, thereby significantly reducing misclassification, and 2.) the effect of geometric attacks on images in the spatial domain manifests (approximately) as independent identically distributed noise on NMF vectors, allowing design of detectors that are both computationally simple and at the same time optimal in the sense of minimizing error probabilities. ROC (receiver operating characteristics) analysis over a large image database reveals that the proposed algorithms significantly outperform existing approaches for robust image hashing.