Efficient homomorphic encryption on integer vectors and its applications

Abstract

Abstract-Homomorphic encryption, aimed at enabling computation in the encrypted domain, is becoming important to a wide and growing range of applications, from cloud computing to distributed sensing. In recent years, a number of approaches to fully (or nearly fully) homomorphic encryption have been proposed, but to date the space and time complexity of the associated schemes has precluded their use in practice. In this work, we demonstrate that more practical homomorphic encryption schemes are possible when we require that not all encrypted computations be supported, but rather only those of interest to the target application. More specifically, we develop a homomorphic encryption scheme operating directly on integer vectors that supports three operations of fundamental interest in signal processing applications: addition, linear transformation, and weighted inner products. Moreover, when used in combination, these primatives allow us to efficiently and securely compute arbitrary polynomials. Some practically relevant examples of the computations supported by this framework are described, including feature extraction, recognition, classification, and data aggregation.

Protection Cloud via Homomorphic Encryption

“…APPLICATIONS We first portray the distinctive however more conventional situation that has been the concentration of a significant part of the homomorphic encryption writing to date [2]. As portrayed in Fig.…”

Cryptanalysis of a homomorphic encryption scheme

“…The encryption scheme proposed in [20] is a homomorphic encryption scheme that supports three operations: addition, linear transformation and weighted inner products. Moreover, based on the three fundamental operations, the scheme enables to compute arbitrary polynomials.…”

“…Moreover, based on the three fundamental operations, the scheme enables to compute arbitrary polynomials. As stated in [20], these operations can be useful in applications where tasks as feature extraction, recognition, classification, and data aggregation are needed. This scheme is a natural generalization of the PVW scheme [13] from binary vectors to integer vectors where techniques as ciphertext packing [1] and key switching [3] are employed to optimize the scheme.…”

“…In this article, we first formalize the homomorphic encryption scheme from [20]. The presentation in the original paper is not very intuitive nor easy to follow.…”

“…In Section 2, we formalize the encryption scheme from [20] and describe the operations which are possible in the encrypted domain. In Section 3, we present three attacks against this encryption scheme.…”