Arithmetics of Ciphertexts under Homomorphic Encryption

Abstract

Privacy homomorphism is an important concept for encrypting clear data while allowing one to perform operations on encrypted data without decryption. Although the use of fully homomorphic encryption schemes theoretically allows for the secure evaluation of any function, the evaluation cost is still far from being practical for many functions and no secure solutions have been developed to satisfy the efficiency requirements.

In this thesis, the foundation of our simple framework is a set of optimized circuits for the following operations: equality, greater-than comparison and integer addition. We first focus on the applications of homomorphic encryption for private query processing on encrypted databases. In particular, we construct a unied framework to eciently and privately process queries with search and compute operations by applying the underlying circuit primitives.

Since genomic data contains numerous distinguishing features and sensitive personal information, a privacy-preserving genome analysis in a cloud computing environment becomes the major issue in bioinformatics. We present a method to perform the exact edit distance algorithm on encrypted data to obtain an encrypted result. We also describe how to privately compute the approximate edit distance between encrypted DNA sequences. Finally we create a homomorphic security system for searching a set of biomarkers to encrypted genomes. We propose an efficient method to securely search a matching position with biomarker and extract the information of DNA sequences at the position without complicated computation such as comparison.