Individual privacy is becoming a more prioritized issue in the modern world, because the world is becoming increasingly more digitized and citizens are starting to feel monitored. Private information could furthermore be misused in the wrong hands. Many control systems rely on data that often contain privacy sensitive information. These are systems such as the power grid, water network, and smart house where data contain individual consumption profiles and daily schedules. The systems use the data to compute optimized solutions; hence, the data is valuable but it contains private information. To this end, it is desirable to achieve algorithms able to calculate optimized solutions while keeping the data secret. As a step towards this goal, we propose a privacy preserving recursive least squares protocol that computes a least squares estimate of the parameters of a linear system based on observations of input and outputs. This estimate is calculated while ensuring no leakage of information about observations.