Secure wavelet matrix: Alphabet-friendly privacy-preserving string search for bioinformatics

Biomedical data often includes personal information, and the technology is demanded that enables the searching of such sensitive data while protecting privacy. We consider a case in which a server has a text database and a user searches the database to find substring matches. The user wants to conceal his/her query and the server wants to conceal the database except for the search results. The previous approach for this problem is based on a linear-time algorithm in terms of alphabet size $\mathbf{|\Sigma |}$||, and it cannot search on the database of large alphabet such as biomedical documents. We present a novel algorithm that can search a string in logarithmic time of $\mathbf{|\Sigma |}$||. In our algorithm, named secure wavelet matrix sWM, we use an additively homomorphic encryption to build an efficient data structure called a wavelet matrix. In an experiment using a simulated string of length 10,000 whose alphabet size ranges from 4 to 1024, the run time of the sWM was up to around two orders of magnitude faster than that of the previous method. sWM enables the searching of a private database efficiently and thus it will facilitate utilizing sensitive biomedical information.