Abstract: An approach is provided for a method for authentication with dynamic and random passwords, which comprises acts of obtaining a code equation initially from a person through an register page of a system, generating a starting code set and a result value, obtaining a password from the person through an authentication page of the system, determining the identity of the result value and the password, and granting the person for the authentication when the password and the result value are the same. The code equation is formed by at least one mathematical equation. The result value is the calculation result of the starting code set and the code equation. The starting code set is a set of number randomly generated by the system. Therefore, the present invention is able to prevent password cracking or recovering from data that has been stored in or transmitted by an apparatus.