1. A system for fingerprint authentication, which comprises: which stores, regenerates, or matches shape of curves, by using a specified group of data in length and/or angle and/or position to express a shape of curve, in said system using sequence of several measure points on the curve, which are determined so as to make the same distances between those adjacent measure points, the data of lengths of arcs being between starting measure point and ending measure points among every 3 consecutive measure points on the curve.