1. A blood vessel authentication apparatus comprising: an inputted image acquiring section configured to acquire an inputted image; a transforming section configured to transform the inputted image to transformed information indicating image points in the inputted image based on a distance from a reference position to a closest point on a straight line passing through each image point; a proper information acquiring section configured to acquire proper information indicating image points in the proper image based on a distance from a reference position to a closest point on a straight line passing through each image point; a matching section configured to match the transformed information and the proper information; and an authentication section configured to authenticate the inputted image according to the result of matching by the matching section, wherein the matching section performs a Fourier transformation for the inputted and proper images and performs the matching of the inputted and proper image on the basis of correlated values responsive to phase components of the resultant Fourier transformation processed values.