  Multimedia contents are inherently sensitive signals that must be protected
whenever they are outsourced to an untrusted environment. This problem becomes
a challenge when the untrusted environment must perform some processing on the
sensitive signals; a paradigmatic example is Cloud-based signal processing
services. Approaches based on Secure Signal Processing (SSP) address this
challenge by proposing novel mechanisms for signal processing in the encrypted
domain and interactive secure protocols to achieve the goal of protecting
signals without disclosing the sensitive information they convey.
  This work presents a novel and comprehensive set of approaches and primitives
to efficiently process signals in an encrypted form, by using Number Theoretic
Transforms (NTTs) in innovative ways. This usage of NTTs paired with
appropriate signal pre- and post-coding enables a whole range of easily
composable signal processing operations comprising, among others, filtering,
generalized convolutions, matrix-based processing or error correcting codes.
The main focus is on unattended processing, in which no interaction from the
client is needed; for implementation purposes, efficient lattice-based somewhat
homomorphic cryptosystems are used. We exemplify these approaches and evaluate
their performance and accuracy, proving that the proposed framework opens up a
wide variety of new applications for secured outsourced-processing of
multimedia contents.
