Single Secret Leader Election (SSLE) protocols allow a set of users to elect a leader among them so that the identity of the winner remains secret until she decides to reveal herself. This notion was formalized and implemented in a recent result by Boneh, et al. (ACM Advances on Financial Technology 2020) and finds important applications in the area of Proof of Stake blockchains. In this paper we propose new solutions to the problem that advance the state of the art both from a theoretical and a practical perspective. On the theoretical front, we propose a definition of SSLE in the uni- versal composability framework. We believe this to be the right setting for highly concurrent contexts such as those of many blockchain-related applications. Next, we propose a UC-realization of SSLE from public key encryption with keyword search (PEKS) and based on the ability of dis- tributing the PEKS key generation and encryption algorithms. Finally, we present an efficient MPC-friendly PEKS that allows us to efficiently instantiate the abstract scheme. Our concrete construction compares favorably with previous work (both in terms of computational costs and in terms of overall communication overhead) while guaranteeing much stronger composability guarantees.