In this paper we considered the problem of security analysis of robust perceptual hashing in authentication application. The main goal of our analysis was to estimate the amount of trial efforts of the attacker, who is acting within the Kerckhoffs security principle, to reveal a secret key. For this purpose, we proposed to use Shannon equivocation that provides an estimate of complexity of the key search performed based on all available prior information and presented its application to security evaluation of particular robust perceptual hashing algorithms.