1. An authentication method comprising: receiving data for authentication; extracting a feature vector indicating features of the received data; first moving positions of a plurality of particles on a unit sphere in a multidimensional space according to a value of a probability density function, the probability density function indicating a probability of existence of a particle on the unit sphere, by a processor; converting the feature vector to a binary string, using a normal vector of a hyperplane that divides the multidimensional space, by the processor; and authenticating the data based on the converted feature vector, the first moving including: calculating a positional vector of the particle on the unit sphere as the normal vector of the hyperplane, obtaining an evaluation function configured to evaluate the hyperplane as the probability density function, extracting a movement destination candidate of the particle, calculating a value obtained by dividing a value of the evaluation function according to a positional vector of the particle moved to the movement destination candidate by a value of the evaluation function according to a current positional vector of the particle, and second moving the particle to an extracted movement destination candidate, upon obtaining the calculated value larger than a random number of not less than 0 and not more than 1, or preventing movement of the particle, upon obtaining the calculated value not larger than the random number.