Impostors are attackers who take over a smartphone and gain access to the legitimate user's confidential and private information. This paper proposes a defense-in-depth mechanism to detect impostors quickly with simple Deep Learning algorithms, which can achieve better detection accuracy than the best prior work which used Machine Learning algorithms requiring computation of multiple features. Different from previous work, we then consider protecting the privacy of a user's behavioral (sensor) data by not exposing it outside the smartphone. For this scenario, we propose a Recurrent Neural Network (RNN) based Deep Learning algorithm that uses only the legitimate user's sensor data to learn his/her normal behavior. We propose to use Prediction Error Distribution (PED) to enhance the detection accuracy. We also show how a minimalist hardware module, dubbed SID for Smartphone Impostor Detector, can be designed and integrated into smartphones for self-contained impostor detection. Experimental results show that SID can support real-time impostor detection, at a very low hardware cost and energy consumption, compared to other RNN accelerators.