1. An authentication system comprising: a physical device that includes a ring oscillator, which outputs a data sequence along a time series, a value of each bit of the data sequence being correlated with a value of another bit in the data sequence; a measurement unit that obtains a plurality of data sequences by performing measurements of the data sequence of the ring oscillator, the measurements of the data sequence of the ring oscillator being performed two or more times immediately after an activation of the ring oscillator when the ring oscillator is in an unstable state; a generator that generates an identification (ID) for the physical device from the plurality of data sequences using a statistical method; a calculator that, using a hidden Markov model, performs a probability calculation on the ID; and an authenticator that authenticates the physical device based on a calculation result of the calculator.