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In social networks, revealing the structure of communities can expose sensitive groups to detection. Traditional approaches, such as DICE, attempt to hide these communities by randomly rewiring links, but this strategy is often inefficient and insecure. We propose an efficient heuristic method called CRIME (Community Rewiring for Influence and Masking Entities) to address this challenge. CRIME removes the most influential internal links, measured by edge-betweenness centrality, and adds external links with the least betweenness centrality. Experiments on real-world networks demonstrate that CRIME hides targeted communities more effectively than DICE, and also achieves faster execution and improves hiding effectiveness by up to 99.8%.