1. A biometric authentication apparatus comprising: a vein image extraction unit for emitting a light having a predetermined wavelength to a finger portion and extracting a vein image showing positions of veins from an image including veins in the obtained finger portion; a vein image dividing unit for dividing the vein image extracted by the vein image extraction unit into a plurality of partial regions; a vein pixel counting unit for counting the number of pixels corresponding to the veins in each of the partial regions divided by the vein image dividing unit; a vector generation unit for arranging, in a predetermined order, count results of the respective partial regions provided by the vein pixel counting unit, and generating a vein distribution vector, which is a numerical sequence representing a degree of distribution of the veins in the vein image; and an authentication unit for authenticating the vein distribution vector generated by the vector generation unit, based on a registered vein distribution vector, which is a vein distribution vector registered in advance.