A \(universal thresholdizer \) ( \(\textsf{UT}\) ), constructed from a threshold fully homomorphic encryption by Boneh et. al , Crypto 2018, is a general framework for universally thresholdizing many cryptographic schemes. However, their framework is insufficient to construct strongly secure threshold schemes, such as threshold signatures and threshold public-key encryption, etc. In this paper, we strengthen the security definition for a universal thresholdizer and propose a scheme which satisfies our stronger security notion. Our \(\textsf{UT}\) scheme is an improvement of Boneh et. al ’s construction at the level of threshold fully homomorphic encryption using a key homomorphic pseudorandom function. We apply our strongly secure \(\textsf{UT}\) scheme to construct strongly secure threshold signatures and threshold public-key encryption.