1. A fingerprint authentication device comprising: a sweep fingerprint sensor that acquires a plurality of images of a fingerprint on a finger in a single scan for the same area of the fingerprint at each of sensitivity levels including low sensitivity level and high sensitivity level; and a counterfeit-finger determining unit that determines whether the finger is counterfeit by comparing among the plurality of images acquired by the sweep fingerprint sensor, the counterfeit-finger determining unit determining that the finger is counterfeit when a difference in a parameter relating to two images among the plurality of images is less than a threshold and the plurality of images do not include a sweat pattern, the counterfeit-finger determining unit determining that the finger is living when the difference in the parameter relating to two images among the plurality of images is greater than or equal to the threshold or the plurality of images include a sweat pattern, the difference in the parameter including a difference in luminance between corresponding pixels of the two images.