1. A bill discriminating apparatus that performs bill discrimination, comprising: a storage unit that stores in advance reference thickness distribution data that shows the thickness distribution of an authentic note; a thickness detection unit that detects the thickness distribution of a bill that is subject to discrimination; and a discrimination unit that references the storage unit and performs a specified discrimination based on the reference thickness distribution data and the detected detection thickness distribution data, wherein the discrimination unit performs authenticity discrimination of the bill based on the reference thickness distribution data and the detected thickness distribution data for areas for which the absolute value of the difference between the detected thickness distribution data and the reference thickness distribution data is less than a specified threshold value.