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The field of Signal Processing in the Encrypted Domain (SPED) has emerged in order to provide efficient and secure solutions for pre serving privacy of signals that are processed by untrusted agents. In this work, we study the privacy problem of adaptive filtering, one of the most important and ubiquitous blocks in signal processing nowadays. We examine several use cases along with their privacy characteristics, constraints and requirements, that differ in several aspects from those of the already tackled linear filtering and classification problems. Due to the impossibility of using a strategy based solely on current homomorphic encryption systems, we pro pose novel secure protocols for a privacy-preserving execution of the BLMS (Block Least Mean Squares) algorithm, combining different SPED techniques, and paying special attention to the trade-off between computational complexity, bandwidth, and the error produced due to finite-precision implementations.