1. An apparatus comprising: a touchscreen having a touch sensor array comprising a capacitive wire grid providing a touch sensor output at each of a plurality of grid intersection points, a spacing between grid intersection points being greater than a spacing between ridges and valleys of a user's fingerprint terrain; a touchscreen controller, connected to the touchscreen and to sample the touch sensor outputs so that each sampled touch sensor output is representative of a difference in mutual capacitance between ridges and valleys of a portion of the fingerprint terrain of a finger of the user as that user's finger moves with respect to the grid intersection point, such that the touch sensor outputs, detected over time, provide a set of one-dimensional time-varying user profile signals representative of a portion of the user's fingerprint terrain; a memory, for storing the set of user profile signals; a processor, for reading the set of user profile signals and executing code to continuously authenticate the user, the code for: authorizing the user via a user authorization task, by determining if the user is an authorized user by comparing the user profile signals against stored authorized user information representative of a fingerprint of an authorized user; detecting, over time, additional user profile signals received from the touch sensor outputs as a result of the user interacting with the touchscreen while the user is performing tasks other than the user authorization task, each additional user profile signal comprising a one-dimensional time-varying signal representative of a difference in mutual capacitance between ridges and valleys of a different portion of the fingerprint terrain of the user, produced as the user's finger makes subsequent movements with respect to the grid intersection points; and further determining if the user is an authorized user by comparing the stored authorized user information and the additional user profile signals.