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In the context of sharing video surveillance data, a significant threat to privacy is face recognition software, which can automatically identify known people, such as from a database of drivers' license photos, and thereby track people regardless of suspicion. This paper introduces an algorithm to protect the privacy of individuals in video surveillance data by deidentifying faces such that many facial characteristics remain but the face cannot be reliably recognized. A trivial solution to deidentifying faces involves blacking out each face. This thwarts any possible face recognition, but because all facial details are obscured, the result is of limited use. Many ad hoc attempts, such as covering eyes, fail to thwart face recognition because of the robustness of face recognition methods. This work presents a new privacy-enabling algorithm, named k-Same, that guarantees face recognition software cannot reliably recognize deidentified faces, even though many facial details are preserved. The algorithm determines similarity between faces based on a distance metric and creates new faces by averaging image components, which may be the original image pixels (k-Same-Pixel) or eigenvectors (k-Same-Eigen). Results are presented on a standard collection of real face images with varying k.