Secure Rate-Distortion-Perception Trade-off Over Channels: A Randomized Distributed Function Computation (RDFC) Application

Secure rate-distortion-perception (RDP) trade-offs arise in critical applications, such as semantic compression and privacy-preserving generative coding, where preserving perceptual quality while minimizing distortion is vital. This paper studies a framework for secure RDP over noiseless and noisy broadcast channels under strong secrecy constraints. We first characterize the exact secure RDP region for noiseless transmission channels. We then develop an inner bound on the secure RDP region for a memoryless broadcast channel with correlated noise components at the receivers' observations and prove its tightness under a more capable broadcast channel assumption. Our results demonstrate how optimized binning schemes simultaneously achieve high perceptual quality, low distortion, and strong secrecy, illuminating fundamental information-theoretic limits for next-generation trustworthy computation systems.