Processing in the encrypted domain using a composite signal representation: Pros and cons

The current solutions for secure processing in the encrypted domain are usually based on homomorphic cryptosystems operating on very large algebraic structures. Recently, a composite signal representation has been proposed that allows to speed up linear operations on encrypted signals via parallel processing and to reduce the size of the encrypted signals. Though many of the most common signal processing operations can be applied to composite signals, some operations require to process the signal samples independently from each other, thus requiring an unpacking of the composite signals. In this paper, we will address the above issues, showing both merits and limits of the composite signal representation when applied in practical scenarios. A secure protocol for converting an encrypted composite representation into the encryptions of the single signal samples will be introduced. A case study clearly highlights pros and cons of using the composite signal representation in the proposed scenarios.