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.