Abstract In this paper, we present generic transformations, which allow us to be able to convert any signature scheme satisfying the weak existential unforgeability property into one satisfying the strong existential unforgeability property. Different from the previous researches, we consider this kind of transformations in the bounded leakage model, in which part of the secret information could be learned by the adversary. To achieve such transformations, we define a new cryptographic primitive called leakage resilient chameleon hash function and give an instantiation of it based on leakage resilient hard relation. By making use of this new variant of chameleon hash function, we improve the technique proposed by Steinfeld, Pieprzk, and Wang to obtain a generic transformation that works well in the bounded leakage model. Furthermore, we follow the construction of strong one‐time signature by Mohassel to give an instantiation of fully leakage resilient strong one‐time signature based on leakage resilient chameleon hash function. We prove that by combining the fully leakage resilient strong one‐time signature scheme with the transformation proposed by Huang, Wong, and Zhao, we can obtain another transformation that can convert any fully leakage resilient signature scheme that is weakly existentially unforgeable into one that is strongly existentially unforgeable without changing the signing key. Copyright © 2016 John Wiley & Sons, Ltd.