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This paper presents a novel coprime blurred pair (CBP) model to improve data security in camera surveillance. While most previous approaches have focused on completely encrypting the video stream, we introduce a spatial encryption scheme by strategically blurring the image/video contents. Specifically, we form a public stream and a private stream by blurring the original video data using two different kernels. Each blurred stream will provide the user who has lower clearance less access to personally identifiable details while still allowing behavior to be monitored. If the behavior is recognized as suspicious, a supervisor can use both streams to deblur the contents. Our approach is based on a new CBP theory where the two kernels are coprime when mapped to bivariate polynomials in the z domain. We show that coprimality can be derived in terms of the rank of Bézout matrix formed by sampled polynomials, and we present an efficient algorithm to factor the Bézout matrix for recovering the latent image. To make our solution practical, we implement our decryption scheme on a graphics processing unit (GPU) to achieve real-time performance. Extensive experiments demonstrate that our new scheme can effectively protect sensitive identity information in surveillance videos and faithfully reconstruct the unblurred video stream when both CBP sequences are available.