New packing method in somewhat homomorphic encryption and its applications

Abstract

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. Copyright © 2015 John Wiley & Sons, Ltd.

Efficient Secure Matrix Multiplication Over LWE-Based Homomorphic Encryption

“…Over the SHE scheme, L a u t e r et al [5] proposed a method to pack an integer of large size into a single ciphertext so that it enables to efficiently compute secure sums and products over the integers. After that, Y a s u d a et al [9] proposed a new packing method for secure multiple inner products, which can be applied to secure Hamming distance and pattern matching computations. While their packing method is efficient only for vectors with small size entries, they modified their method for large size entries [10].…”

“…In this paper, we propose several packing methods for secure matrix multiplication, using the idea of Y a s u d a et al's methods [9], [10]. More specifically, for matrices with binary entries, our method is based on [9], and for non-binary entries, it is based on [10].…”

“…In this paper, we propose several packing methods for secure matrix multiplication, using the idea of Y a s u d a et al's methods [9], [10]. More specifically, for matrices with binary entries, our method is based on [9], and for non-binary entries, it is based on [10]. Our main ingredient for packing a matrix A is to deploy the entries of A into a single polynomial by using the packing methods of [9], [10], and then encrypt the polynomial over the SHE scheme.…”

“…More specifically, for matrices with binary entries, our method is based on [9], and for non-binary entries, it is based on [10]. Our main ingredient for packing a matrix A is to deploy the entries of A into a single polynomial by using the packing methods of [9], [10], and then encrypt the polynomial over the SHE scheme. Our matrix packing method requires only one homomorphic multiplication over our packed ciphertexts for secure matrix multiplication.…”

Fingerprint code authentication protocol on cloud

“…The design is a robust key to protect the original biometrics from being shared, copied or distributed across a network [5] [6] [7] [8] [9]. This turns out to be the reason behind their second name, as helper data methods.…”