Secure Testing for Genetic Diseases on Encrypted Genomes with Homomorphic Encryption Scheme

The decline in genome sequencing costs has widened the population that can afford its cost and has also raised concerns about genetic privacy. Kim et al. present a practical solution to the scenario of secure searching of gene data on a semitrusted business cloud. However, there are three errors in their scheme. We have made three improvements to solve these three errors. (1) They truncate the variation encodings of gene to 21 bits, which causes LPCE error and more than 5% of the entries in the database cannot be queried integrally. We decompose these large encodings by 44 bits and deal with the components, respectively, to avoid LPCE error. (2) We abandon the hash function used in Kim’s scheme, which may cause HCE error with a probability of 2-22 and decompose the position encoding of gene into three parts with the basis 211 to avoid HCE error. (3) We analyze the relationship between the parameters and the CCE error and specify the condition that parameters need to satisfy to avoid the CCE error. Experiments show that our scheme can search all entries, and the probability of searching error is reduced to less than 2-37.4.