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In this letter, we analyze the security of a perceptual image hashing technique based on non-negative matrix factorization which was recently proposed and reported in the literature. We theoretically demonstrate that, although the technique uses different secret keys in subsequent stages, the first key plays an essential role to secure the hashing system. We next act as an attacker and propose a technique to estimate the secret key. Extensive experiments support our theoretical analysis and validate the proposed key estimation technique.