Secure signal processing is becoming a de facto model for preserving privacy. We propose a model based on the Fully Homomorphic Encryption (FHE) technique to mitigate security breaches. Our framework provides a method to perform a Fast Fourier Transform (FFT) on a user-specified signal. Using encryption of individual binary values and FHE operations over addition and multiplication, we enable a user to perform the FFT in a fixed point fractional representation in binary. Our approach bounds the error of the implementation to enable user-selectable parameters based on the specific application. We verified our framework against test cases for one dimensional signals and images (two dimensional signals).
Research in secure signal processing has received increasing attention over the past decade. Troncoso-Pastoriza and Perez-Gonzalez @cite_9 examined secure signal processing in the cloud very similar to the concept we use in our work. They focused on privacy issues that occur with cloud computing which is ideally what a Fully Homomorphic Encryption scheme can provide. Wang et. al. @cite_6 also considered privacy issues with secure signal processing. Their focus was on biometrics and protecting authentication and privacy. This paper is similar in keeping confidentiality of private data in a cloud computing environment.
@cite_9 @cite_6
2007470995 2032001704
In recent years, the paradigm of cloud computing has gained an increasing interest from the academic community as well as from the commercial point of view. The cloud is a very appealing concept both for the providers (who can benefit from hiring out their extra computation and storage resources) and for the users (who can avoid the initial investment on resources by outsourcing their processes and data to a cloud). We present a theoretical framework for the analysis of privacy and security trade-offs in secure biometric authentication systems. We use this framework to conduct a comparative information-theoretic analysis of two biometric systems that are based on linear error correction codes, namely fuzzy commitment and secure sketches. We derive upper bounds for the probability of false rejection (PFR) and false acceptance (PFA) for these systems. We use mutual information to quantify the information leaked about a user's biometric identity, in the scenario where one or multiple biometric enrollments of the user are fully or partially compromised. We also quantify the probability of successful attack (PSA) based on the compromised information. Our analysis reveals that fuzzy commitment and secure sketch systems have identical PFR, PFA, PSA, and information leakage, but secure sketch systems have lower storage requirements. We analyze both single-factor (keyless) and two-factor (key-based) variants of secure biometrics, and consider the most general scenarios in which a single user may provide noisy biometric enrollments at several access control devices, some of which may be subsequently compromised by an attacker. Our analysis highlights the revocability and reusability properties of key-based systems and exposes a subtle design trade-off between reducing information leakage from compromised systems and preventing successful attacks on systems whose data have not been compromised.