Secure brightness/contrast filter using fully homomorphic encryption

Performing signal processing via a distributed method while maintaining data privacy has great uses. We focus on this problem to a two party situation where the first one (client) has a signal needing to be processed and is computationally bounded and the second (server) has computational resources. As a client, revealing the signal unencrypted causes a violation of privacy. One solution to this problem is to process the signal while encrypted. Problems of this type have been attracting attention recently; particularly with the growing capabilities of cloud computing. This paper contributes to solving this type of problem by processing the signals in an encrypted form, using fully homomorphic encryption (FHE). Realization of this type of application was performed using a brightness/contrast filter as a simple form of signal processing. 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).