Multikey homomorphic encryption (MKHE) supports arbitrary homomorphic evaluation on the ciphertext of different users and thus can be applied to scenarios involving multiusers (e.g., cloud computing and artificial intelligence) to protect user privacy. CDKS19 is the current most efficient MKHE scheme, and its relinearization process consumes most of the time of homomorphic evaluation. In this study, an optimized relinearization algorithm of CDKS19 is proposed. This algorithm reorganizes the evaluation key during the key generation process, decreases the complexity of relinearization, and reduces the error growth rate during homomorphic evaluation. First, we reduce the scale of the evaluation key by increasing its modulus instead of using a gadget vector to decompose the user’s public key and extend the ciphertext of homomorphic multiplication. Second, we use rescaling technology to optimize the relinearization algorithm; thus, the error bound of the ciphertext is reduced, and the homomorphic operation efficiency is improved. Lastly, the average-case error estimation on the variances of polynomial coefficients and the upper bound of the canonical embedding map are provided. Results show that our scheme reduces the scale of the evaluation key, the error variance, and the computational cost of the relinearization process. Our scheme can effectively perform the homomorphic multiplication of ciphertexts.

Genes have great significance for the prevention and treatment of some diseases. A vital consideration is the need to find a way to locate pathogenic genes by analyzing the genetic data obtained from different medical institutions while protecting the privacy of patients’ genetic data. In this paper, we present a secure scheme for locating disease-causing genes based on Multi-Key Homomorphic Encryption (MKHE), which reduces the risk of leaking genetic data. First, we combine MKHE with a frequency-based pathogenic gene location function. The medical institutions use MKHE to encrypt their genetic data. The cloud then homomorphically evaluates specific gene-locating circuits on the encrypted genetic data. Second, whereas most location circuits are designed only for locating monogenic diseases, we propose two location circuits (TH-intersection and Top-q) that can locate the disease-causing genes of polygenic diseases. Third, we construct a directed decryption protocol in which the users involved in the homomorphic evaluation can appoint a target user who can obtain the final decryption result. Our experimental results show that compared to the JWB+17 scheme published in the journal Science, our scheme can be used to diagnose polygenic diseases, and the participants only need to upload their encrypted genetic data once, which reduces the communication traffic by a few hundred-fold.