Proximity services discovery using LTE-based Device-to-Device (D2D) communications has been recently in the heart of the discussions about the advent of 5G networks. Meanwhile, their related security aspects are of a major concern especially when dealing with direct radio communications and large-scale deployment of D2D. Yet, existing security algorithms and solutions are not adapted to these emerging new types of communications. This paper is focused on D2D communications' security issues in both discovery and communication phases. First, we address the global security stakes and challenges in D2D. Then, a solution based on the Identity-Based Encryption (IBE) mechanism is proposed to secure the exchanged D2D messages during the discovery and communication phases. The proposed solution is discussed under two D2D use cases and is further used to introduce an efficient key management system for group communication. Finally, a security requirements analysis is presented in order to evaluate the scalability and efficiency levels of the proposed solution