Boneh and Franklin introduced one of the earliest constructions of the elegant concept of identity-based encryption (IBE) about two decades ago. Despite significant research advancements and numerous potential applications, IBE has yet to see widespread real-world adoption. A primary challenge is the excessive trust placed in the key derivation server, which inherently possesses the ability to decrypt all ciphertexts. Recent work proposed approaches to reduce server trust in IBE schemes by using a server, called a key curator, that only helps update the public parameters and holds no secret key. In this paper, we present, in the key-curator model, the first IBE scheme that, via a black-box reduction, preserves sender efficiency of a class of IBE schemes (for which we show that there are already well-known and efficient instantiations in the literature), works in the public-random string model (and in particular not requiring extra secret information kept by the key curator) and satisfies ‘sender-efficiency’ performance requirements demanded by many applications (e.g., Internet of Things). All previously proposed IBE schemes with reduced server trust either did not preserve IBE functionality or were subject to server-collusion attacks or only focused on ‘receiver-efficiency’ performance requirements.