Split manufacturing was introduced as an effective countermeasure against hardware-level threats such as IP piracy, overbuilding, and insertion of hardware Trojans. Nevertheless, the security promise of split manufacturing has been challenged by various attacks, which exploit the well-known working principles of physical design tools to infer the missing BEOL interconnects. In this work, we advocate a new paradigm to enhance the security for split manufacturing. Based on Kerckhoff's principle, we protect the FEOL layout in a formal and secure manner, by embedding keys. These keys are purposefully implemented and routed through the BEOL in such a way that they become indecipherable to the state-of-the-art FEOL-centric attacks. We provide our secure physical design flow to the community. We also define the security of split manufacturing formally and provide the associated proofs. At the same time, our technique is competitive with current schemes in terms of layout overhead, especially for practical, large-scale designs (ITC'99 benchmarks).