We propose a protocol for converting the encryption function of a ciphertext into another encryption function while keeping the corresponding message secret. The proposed protocol allows conversions of the El Gamal and Paillier cryptosystems and has the potential to design an efficient multiparty protocol intended for circuits consisting of arithmetic and logical operations. We clarify the condition of circuits such that the multiparty protocol based on the proposed protocol provides better performance than previous approaches. In addition, we introduce some privacy-preserving statistical computations as an effective application of the proposed protocol.

We propose a multiparty protocol for comparator networks which are used to compute various functions in statistical analysis, such as the maximum, minimum, median, and quartiles, for example, through sorting and searching. In the protocol, all values which are inputted to a comparator network and all intermediate outputs are kept secret assuming the presence of an honest majority. We also introduce an application of the protocol for a secure (M+1)-st price auction.