Abstract: Disclosed embodiments include methods and apparatuses for secure iterative processing of encrypted signals based on implementing a secure iterative processing protocol that avoids cipher blowup, and applying an iterative algorithm directly on the encrypted signals to generate an encrypted processed output signal. In a particular embodiment, the protocol comprises applying homomorphic linear processing, preparing and applying a rescaling module to avoid cypher blowup, and homomorphically adapting the encrypted signals. Specific embodiments implement iterative adaptive filtering algorithms in the encrypted domain including non-collaborative secure filtering and two-party filtering based on homomorphic encryption, interactive secure protocols, garbled circuits, or a combination thereof.