Key Reduction in Multi-Key and Threshold Multi-Key Homomorphic Encryptions by Reusing Error

As cloud computing and AI as a Service are provided, it is increasingly necessary to deal with privacy sensitive data. To the data, there two cases of outsourcing process: i) many clients participate dynamically ii) pre-determined. The solutions for protecting data in both multi-key homomorphic encryption (MKHE) scheme threshold (TMKHE) scheme. However, these schemes may be difficult limited resources perform MKHE TMKHE. In addition, due large size evaluation keys, particular multiplication rotation communication between server that provide service increases. Also, keys must hold tremendous, particular, which essential bootstrapping operation. this paper, we propose variant TMKHE reduced keys. reduce ring learning errors (RLWE), called RLWE reusing (ReRLWE). ReRLWE generates other components by error used when generating an sample. We prove can modified under assumption, For MKHE, 66% 25%, respectively. TMKHE, 50%