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Security is still a relatively unexplored issue in image hashing. In this paper, we address this problem and present a new metric, called minimum distortion estimation (MDE), by demonstrating its appropriateness over entropy for secure hashing evaluation. We investigate the relationship between bit changing rate and content distortion via statistical analyses of MDE. This provides a guideline for our design of a new secure image hashing method. The feasibility of our method is further demonstrated via comparisons with two known image hashing methods.