Cloud computing is an important part of today's world because offloading computations is a method to reduce costs. In this paper, we investigate computing the Speeded Up Robust Features (SURF) using Fully Homomorphic Encryption (FHE). Performing SURF in FHE enables a method to offload the computations while maintaining security and privacy of the original data. In support of this research, we developed a framework to compute SURF via a rational number based compatible with FHE. Although floating point (R) to rational numbers (Q) conversion introduces error, our research provides tight bounds on the magnitude of error in terms of parameters of FHE. We empirically verified the proposed method against a set of images at different sizes and showed that our framework accurately computes most of the SURF keypoints in FHE.
Over the past decade growing interest in privacy has increased interest in secure signal processing. Troncoso-Pastoriza and Perez-Gonzalez have an excellent survey of the problems and solution techniques for privacy in cloud computing @cite_15 . There are many other examples among varying fields; secure signal processing @cite_5 , biometrics @cite_7 , and @cite_11 . Many specific examples exist that use the Paillier encryption scheme (see @cite_10 for scheme definition). This scheme is not an FHE scheme as it provides only additive homomorphic operations (i.e. no ciphertext-ciphertext multiplication). FHE schemes provide both additive and multiplicative operations over ciphertexts. Hsu, Lu, and Pei used Paillier to implement a privacy preserving SIFT @cite_10 . An encrypted version of SURF also exists using the Paillier scheme @cite_0 . The main difference here is that we use FHE instead of Paillier. A few other examples of using Paillier exist in signal processing @cite_16 @cite_14 . Other encryption techniques also exist; particularly with two party computations while hiding data from both sides, ex. @cite_2 .
@cite_14 @cite_7 @cite_0 @cite_2 @cite_5 @cite_15 @cite_16 @cite_10 @cite_11
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Signal processing in the encrypted domain has become a hot research topic, which enable signal processing tasks in a secure and privacy-preserving manner. Taken the fact that SURF (Speeded Up Robust Feature) has been widely utilized in various applications into account, SURF feature extraction method in the encrypted domain has been proposed in this paper. Because all steps must be implemented in the encrypted domain, Paillier homomorphic encryption method is adopted. Experimental results demonstrate that the number and location of SURF features extracted from the encrypted data are the same as those from the plaintext data. And the error between the descriptors obtained from the plaintext data and the encrypted data is only 0.0002932 . We also provide security analysis and complexity analysis. The proposed method can be used in the encrypted domain based applications, such as secure image processing and image retrieval. This paper investigates the problem of performing signal processing via remote execution methods while maintaining the privacy of the data. Primary focus on this problem is a situation where there are two parties; a client with data or a signal that needs to be processed and a server with computational resources. Revealing the signal unencrypted causes a violation of privacy for the client. One solution to this problem is to process the data or signal while encrypted. Problems of this type have been attracting attention recently; particularly with the growing capabilities of cloud computing. We contribute to solving this type of problem by processing the signals in an encrypted form, using fully homomorphic encryption FHE. Three additional contributions of this manuscript includes 1 extending FHE to real numbers, 2 bounding the error related to the FHE process against the unencrypted variation of the process, and 3 increasing the practicality of FHE as a tool by using graphical processing units GPU. We demonstrate our contributions by applying these ideas to two classical problems: natural logarithm calculation and signal prbrightness contrast filter. We present a novel approach to fully homomorphic encryption (FHE) that dramatically improves performance and bases security on weaker assumptions. A central conceptual contribution in our work is a new way of constructing leveled fully homomorphic encryption schemes (capable of evaluating arbitrary polynomial-size circuits), without Gentry's bootstrapping procedure. Specifically, we offer a choice of FHE schemes based on the learning with error (LWE) or ring-LWE (RLWE) problems that have 2λ security against known attacks. For RLWE, we have: • A leveled FHE scheme that can evaluate L-level arithmetic circuits with O(λ · L3) per-gate computation -- i.e., computation quasi-linear in the security parameter. Security is based on RLWE for an approximation factor exponential in L. This construction does not use the bootstrapping procedure. • A leveled FHE scheme that uses bootstrapping as an optimization, where the per-gate computation (which includes the bootstrapping procedure) is O(λ2), independent of L. Security is based on the hardness of RLWE for quasi-polynomial factors (as opposed to the sub-exponential factors needed in previous schemes). We obtain similar results to the above for LWE, but with worse performance. Based on the Ring LWE assumption, we introduce a number of further optimizations to our schemes. As an example, for circuits of large width -- e.g., where a constant fraction of levels have width at least λ -- we can reduce the per-gate computation of the bootstrapped version to O(λ), independent of L, by batching the bootstrapping operation. Previous FHE schemes all required Ω(λ3.5) computation per gate. At the core of our construction is a much more effective approach for managing the noise level of lattice-based ciphertexts as homomorphic operations are performed, using some new techniques recently introduced by Brakerski and Vaikuntanathan (FOCS 2011). In the setting of secure two-party computation, two parties wish to securely compute a joint function of their private inputs, while revealing only the output. One of the primary techniques for achieving efficient secure two-party computation is that of Yao’s garbled circuits (FOCS 1986). In the semi-honest model, where just one garbled circuit is constructed and evaluated, Yao’s protocol has proven itself to be very efficient. However, a malicious adversary who constructs the garbled circuit may construct a garbling of a different circuit computing a different function, and this cannot be detected (due to the garbling). In order to solve this problem, many circuits are sent and some of them are opened to check that they are correct while the others are evaluated. This methodology, called cut-and-choose, introduces significant overhead, both in computation and in communication, and is mainly due to the number of circuits that must be used in order to prevent cheating.