The next generation of cellular networks will be characterized by openness, intelligence, virtualization, and distributed computing. The Open Radio Access Network (Open RAN) framework represents a significant leap toward realizing these ideals, with prototype deployments taking place in both academic and industrial domains. While it holds the potential to disrupt the established vendor lock-ins, Open RAN's disaggregated nature raises critical security concerns. Safeguarding data and securing interfaces must be integral to Open RAN's design, demanding meticulous analysis of cost/benefit tradeoffs. In this paper, we embark on the first comprehensive investigation into the impact of encryption on two pivotal Open RAN interfaces: the E2 interface, connecting the base station with a near-real-time RAN Intelligent Controller, and the Open Fronthaul, connecting the Radio Unit to the Distributed Unit. Our study leverages a full-stack O-RAN ALLIANCE compliant implementation within the Colosseum network emulator and a production-ready Open RAN and 5G-compliant private cellular network. This research contributes quantitative insights into the latency introduced and throughput reduction stemming from using various encryption protocols. Furthermore, we present four fundamental principles for constructing security by design within Open RAN systems, offering a roadmap for navigating the intricate landscape of Open RAN security.