Secure word-level sorting based on fully homomorphic encryption

Abstract

Fully homomorphic encryption enables to perform arbitrary computations over encrypted data opening a new avenue for the secure outsourced computation in cloud computing. Data sorting is a classical computational problem in computer science. Previously, all the secure sorting algorithms based on fully homomorphic encryption made use of the bit-level encryption, which requires that each bit of the input data is encrypted separately. However, the bit-level encryption incurs expensive computational overheads and a large ciphertext expansion. In this paper, we propose a secure word-level sorting scheme based on fully homomorphic encryption. We introduce a set of novel techniques to design an efficient word-level sorting algorithm. These include a new technique to compare two encrypted integers, a constant extraction technique to postprocess the output ciphertext of the comparison algorithm, an equality test method to check whether two ciphertexts encrypt the same integer and the single instruction multiple data technique to reduce the ciphertext sizes and improve the computational performance. The experimental results show that our word-level sorting algorithm outperforms the state-of-the-art bit-level sorting algorithm by more than 10 times.