© 2016 IEEE. Smartphones have ubiquitously integrated into our home and work environments. It is now a common practice for people to store their sensitive and confidential information on their phones. This has made it extremely important to authenticate legitimate users of a phone and block imposters. In this paper, we demonstrate that the motion dynamics of smartphones, captured using their built in accelerometers, can be used for accurate user identification. We call this mechanism gait fingerprinting. To this end, we first collected the acceleration data from multiple users as they walked with a smartphone placed freely in their pants pockets. Next, we studied the application of different feature extraction, feature selection and classification techniques from the machine learning literature on these data. Through extensive experimentation, demonstrated is that simple time domain features extracted from these data, which are further optimized using stepwise linear discrimination analysis, can be used to train artificial neural networks to identify legitimate user and block imposter with an average accuracy of 95%.