Parameterized Symmetric Homomorphic Encryption for Exact Computation on Encrypted Data

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Abstract
The increasing use of cloud and collaborative computing creates a growing need to process sensitive data while keeping them encrypted. Existing encryption mechanisms either prevent direct computation or rely on general-purpose homomorphic constructions whose parameters and computational cost may exceed the requirements of structured applications with known operations and bounded computation depth. We address this problem by introducing a workload-driven computable symmetric encryption scheme whose parameters are derived directly from the structure of the data, the required operations, the numerical precision, and the targeted computation depth. The construction organizes text and numerical data into semantic coordinates and combines them through a hierarchical Chinese Remainder Theorem (CRT) representation. The main challenges are to preserve exact computation across the CRT hierarchy, prevent modular overflow, remove deterministic algebraic relations between stages, and introduce randomization without destroying the supported operations. To address them, we derive explicit capacity bounds, introduce inter-stage decorrelation, and develop two complementary protection profiles: a PRF-masked profile and a secret-lifting profile supporting bounded encrypted arithmetic. The resulting scheme enables targeted encrypted-text substitutions, matrix aggregation, Hadamard products, and collaborative or federated computations. We evaluate the construction through correctness, leakage-oriented security experiments, comparative benchmarks, and parameter-growth studies. The results confirm exact recovery within the prescribed bounds, effective suppression of the targeted structural leakages, efficient encrypted aggregation, and predictable cost growth with precision, data dimension, and computation depth.

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