Complex domain approach for reversible data hiding and homomorphic encryption: General framework and application to dispersed data
Ensuring the trustworthiness of data from distributed and resource-constrained environments, such as Wireless Sensor Networks or IoT devices, is critical. Existing Reversible Data Hiding (RDH) methods for scalar data suffer from low embedding capacity and poor intrinsic entanglement between host data and watermark. This paper introduces Hiding in the Imaginary Domain with Data Encryption (H[$i$]dden), a novel framework based on complex number arithmetic for simultaneous information embedding and encryption. The H[$i$]dden framework offers perfect reversibility, highly scalable watermark capacity decoupled from the host data's range, and intrinsic data-watermark entanglement. The paper further introduces two protocols: H[$i$]dden-EG, for joint reversible data hiding and encryption, and H[$i$]dden-AggP, for privacy-preserving aggregation of watermarked data, based on partially homomorphic encryption. Rigorous comparative evaluation against recent state-of-the-art baselines demonstrates that the framework significantly expands embedding capacity and achieves an exponential improvement in False Data Injection (FDI) resilience ---ranging from $10^5$ to $10^{19}$ under standard configurations--- effectively neutralizing targeted structural vulnerabilities such as homomorphic injection attacks. Furthermore, empirical performance analysis ---encompassing hardware-agnostic cryptographic metrics and direct IoT edge hardware emulation (ESP32)--- confirms the practical deployment feasibility of the framework within standard sensor duty cycles. Ultimately, these protocols provide efficient and resilient solutions for data integrity, provenance (or group-level integrity in the aggregated case), and confidentiality, serving as a foundation for new schemes based on the algebraic properties of the complex domain.work and application to dispersed data