Efficient linear filtering of encrypted signals via composite representation

Signal processing tools working on encrypted data provide an efficient solution when sensitive signals must be protected from an untrusted processing device. In this paper, we investigate an issue usually neglected in the proposed solutions for secure signal processing, that is the huge size augmentation from the plaintext to the sample-wise encrypted representation of signals, due to the use of cryptosystems operating on very large algebraic structures. A composite signal representation is proposed that allows to speed up linear filtering on encrypted signals via parallel processing and to reduce the size of encrypted signals. A case study is proposed and discussed.