An authentication server according to embodiments performs statistical processing on a plurality of pieces of ID data acquired from an electronic device including a PUF circuit generating the pieces of ID data (S1052 to S1071), determines whether the plurality of pieces of ID data are physical random numbers based on a result of the statistical processing (S1072), and when the plurality of pieces of ID data are determined to be physical random numbers, recognizes the result of authentication of the electronic device as a success of authentication (S1073), and when the plurality of pieces of ID data are determined not to be physical random numbers, recognizes a result of authentication of the electronic device as a failure of authentication (S1074).