1. A biometric authentication device, comprising: a storage unit to store data indicating an initial-element generation probability of a blood vessel image, data indicating a branch probability of an element and data indicating a change coefficient or a change probability of the element, which are obtained by dividing a plurality of sets of a registration image and a verification image which indicate the blood vessel image of a living body into a plurality of respective elements; a verification-image generation probability calculation unit to calculate an element generation probability of a focused-on element of a verification image to be authenticated, using the data indicating the generation probability of the initial element and the data indicating the branch probability which are stored in the storage unit and calculating a value obtained by multiplying the element generation probabilities of respective focused-on elements as a verification-image generation probability of the verification image to be authenticated; a change probability calculation unit to calculate change probability of the change between the focused-on element of the verification image and the element of a registration image for a person to be authenticated, using the data indicating the change coefficient or the change probability which are stored in the storage unit and calculating a value obtained by multiplying the change probabilities of respective focused-on elements as a change probability of the verification image; a dissimilarity or similarity calculation unit to calculate a degree of similarity or dissimilarity using the verification image generation probability and the change probability; and an authentication unit to determine whether the verification image to be authenticated belongs to a registered person, in accordance with whether the degree of dissimilarity or similarity is more or less than a threshold.