New packing method in somewhat homomorphic encryption and its applications

Somewhat homomorphic encryption is public key encryption supporting a limited number of additions and multiplications on encrypted data. This encryption gives a powerful tool in performing meaningful computations with protecting data confidentiality, whose property is suitable mainly in cloud computing. In this paper, we focus on the scheme proposed by Brakerski and Vaikuntanathan, and present two types of packed ciphertexts in order to improve performance and reduce size of the encrypted data. One type of our packed ciphertexts is based on the message encoding technique proposed by Lauter, Naehrig and Vaikuntanathan. While their technique empowers efficient secure computation of sums and products over the integers, our second type of packed ciphertexts enables efficient secure computation of more complex functionalities such as multiple inner products and multiple Hamming distances. We apply our packing method to construct several protocols for secure biometric authentication and secure pattern matching computations. Our implementation shows that our method gives faster performance than the state-of-the-art work in such applications.