Abstract: The computer-implemented method for authenticating secret information according to an aspect of the present disclosure, comprises receiving, by an authentication server, Q{right arrow over (X)} from a terminal for registering secret information; storing, by the authentication server, the received Q{right arrow over (X)}; receiving, by the authentication server, a vector {right arrow over (Z)} from a terminal for requesting authentication of secret information; calculating, by the authentication server, the inner product of Q{right arrow over (X)} and {right arrow over (Z)}; calculating, by the authentication server, ½(n?the inner product); and determining, by the authentication server, that the authentication is successful if ½(n?the inner product) is within a predetermined value and that the authentication fails otherwise.