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We analyze physical-layer security based on the premise that the coding mechanism for secrecy over noisy channels is tied to the notion of channel resolvability. Instead of considering capacity-based constructions, which associate to each message a subcode that operates just below the capacity of the eavesdropper's channel, we consider channel-resolvability-based constructions, which associate to each message a subcode that operates just above the resolvability of the eavesdropper's channel. Building upon the work of Csiszár and Hayashi, we provide further evidence that channel resolvability is a powerful and versatile coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels. Specifically, we show that at least for symmetric wiretap channels, random capacity-based constructions fail to achieve the strong secrecy capacity, while channel-resolvability-based constructions achieve it. We then leverage channel resolvability to establish the secrecy-capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics. Finally, we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information (CSI), mixed channels, and compound channels with receiver CSI, as well as the secret-key capacity of source models for secret-key agreement. By tying secrecy to channel resolvability, we obtain achievable rates for strong secrecy metrics with simple proofs.