Privacy-preserving string search for genome sequences with FHE bootstrapping optimization

Privacy-preserving string search is a crucial task for analyzing genomics-driven big data. In this work, we propose a cryptographic protocol that uses Fully Homomorphic Encryption (FHE) to enable a client to search on a genome sequence database without leaking his/her query to the server. Though FHE supports both addition and multiplication over encrypted data, random noise inside ciphertexts grows with every arithmetic operation especially multiplication, which results in incorrect decryption when the noise amount exceeds its threshold called level. There are two approaches to avoid the incorrect decryption: one is setting the sufficient level that assures correct decryption within the limited number of operations, and the other is resetting the noise by the method called bootstrapping. It is important to find an optimal balance between overhead caused by the level and overhead caused by the bootstrapping, since using higher level deteriorates the performance of all the arithmetic operations, while the more number of bootstrappings causes more expensive overhead. In this study, we propose an efficient approach to minimize the number of bootstrappings while reducing the level as much as possible. Our experimental result shows that it runs at most 10 times faster than a naïve approach.