Abstract: An objective of the present invention is to obtain a mutual authentication method in which mutual authentication is carried out securely and conveniently. In order to achieve the above objective, in the mutual authentication process, a private key K0, being an initial value, is stored in a client and a server (Pc0, Ps0). The client generates a random number R, calculates secret data C and authentication data A, and transmits the data items to the server (Pc1). The server receives the authentication data A and the secret data C from the client, and generates a random number Q, calculates secret data S, and authentication data B and returns the data items, as well as updating the private key K0 with a private key K1 (Ps1). The client receives from the server the authentication data B and the secret data S, generates the random number R, calculates secret data C2, authentication data A2, and returns the data items to the server, and updates the private key K0 with the private key K1(Pc2).