Secure signal processing using fully Homomorphic Encryption

Abstract

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 pr(brightness/contrast filter).