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We propose a novel deeply learnt convolutional neural network architecture for supervised hashing of medical images through residual learning, coined as Deep Residual Hashing (DRH). It offers maximal separability of classes in hashing space while preserving semantic similarities in local embedding neighborhoods. We also introduce a new optimization formulation comprising of complementary loss terms and regularizations that suit hashing objectives the best by controlling over quantization errors. We conduct extensive validations on 2,599 Chest X-ray images with co-morbidities against eight state-of-the-art hashing techniques and demonstrate improved performance and computational benefits of the proposed algorithm for fast and scalable retrieval.