An Efficient NTRU-Type MPHE Scheme for Sensitive Data in Cloud Computing

The development of cloud computing has heightened demand for sensitive data privacy. Multi party homomorphic encryption (MPHE) enables ho momorphicevaluation on encrypted data from multiple users, providing a crucial solution for secure multi-user computation in cloud computing models. NTRU-type MPHEschemes are particularly promising due to their simplicity and efficiency; however, existing solutions face three key limitations: a lack of threshold decryption (t-out-of-N), reliance on trusted third parties, and vulnerability to subfield lattice attacks. In this paper, we propose GTS, a novel NTRU-type MPHE scheme. Compared to existing schemes, GTS offers several advantages. On the one hand, we design a t-out-of-N threshold access structure, allowing GTS to facilitate threshold decryption with predefined participants. On the other hand, we combine distributed key generation and Lagrange interpolation, enabling GTS to operate without relying on trusted third parties and enhancing its resistance to subfield lattice attacks. These features effectively address the aforementioned challenges. We provide the correctness and security proofs for GTS, along with comprehensive analyses of computational and communication overheads. Experimental evaluations demonstrate significant efficiency improvements: compared to state-of-the-art methods, GTS achieves total execution time speedups of up to 2.4× and 3.7× at 128-bit security with N = 20 parties.