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Lossy trapdoor functions (LTFs), introduced by Peiker and Waters in STOC'08, are functions that may be working in another injective mode or a lossy mode. Given such a function key, it is impossible to distinguish an injective key from a lossy key for any (probabilistic) polynomial-time adversary. This paper studies lossy trapdoor functions with tight security. First, we give a formal definition for tightly secure LTFs. Loosely speaking, a collection of LTFs is tightly secure if the advantage todoi:10.1155/2019/3636759 fatcat:dtms3uvuo5fj3mypbusmq6lm3i