H‐ SPDZ ‐Cloud: A Formal Prototype for Hierarchical Authenticated MPC in Edge–Fog–Cloud Architectures

Abstract

ABSTRACT Hierarchical Edge–Fog–Cloud infrastructures increasingly support distributed sensing, analytics, and collaborative computation over sensitive data. Their multi‐tier structure creates systems challenges for secure orchestration: resources are heterogeneous, communication costs vary sharply across layers, and trust assumptions are often bounded by administrative domains. This paper presents H‐SPDZ‐Cloud, a formal prototype for hierarchical authenticated secure multi‐party computation over Edge–Fog–Cloud architectures. The design organizes computation into cryptographically isolated levels, each using an independent message authentication code key, and introduces a verified inter‐level resharing mechanism that keeps secrets in shared form during normal‐case upward transitions. The prototype also includes localized fault handling under a per‐level honest‐majority assumption suited to bounded hierarchical deployments. The H‐SPDZ‐Cloud prototype is evaluated in a controlled single‐host reproducibility testbed configured with the 127‐bit Mersenne prime field , represented using 16‐byte field‐element encodings. Prototype measurements show communication‐locality behavior relative to an internal flat SPDZ‐style Python baseline, with a 31.4% reduction in measured online communication and a 42.4% reduction in total communication for the tested workload. The prototype also evaluates secure fixed‐point inference on the public Wisconsin Diagnostic Breast Cancer dataset, with secret‐shared test features and 100% agreement between the secure and quantized plaintext predictions on the secured subset. The implemented 127‐bit‐prime‐field pipeline uses fixed‐base precomputation for the BN254/Pedersen transition evidence, the corrected masked batch MAC check, and a prototype Sigma/Schnorr dispute‐proof fallback, yielding a measured local‐pipeline latency of 696.2 ms and an fault‐localization latency of 3066.8 ms as reproducible prototype timings. TCP validation with independent party servers further exercises socket serialization and process‐isolated Edge/Fog transition workers; a subsequent authenticated multi‐region three‐VPS validation executes the external‐endpoint path from an independent Cloud controller to Edge and Fog VPS workers over TLS 1.3, reporting 229.2 ms mean TCP/TLS latency, 93.5 ms transition‐fault detection with 30/30 detections, and 264.3 ms/sample secure‐inference latency. A separate local MP‐SPDZ MASCOT reference execution confirms that the three reference arithmetic workloads also run in a standard MPC framework, while H‐SPDZ‐Cloud measurements use the Python prototype pipeline. The manuscript implements and measures an optimistic verification and pessimistic privacy‐preserving dispute path, with plaintext audit opening reserved for a separate administrative debug mode.