PURPOSE: A method for a digital signature and the certification based on an ID on the decisional Diffie-Hellman groups is provided to simplify a key management process and to realize a safe certification model by using because an user ID is used as a key necessary for the digital signature by creating a signature sentence written the digital signature using the user ID. CONSTITUTION: A key and system variable creating part selects the fourth element for the system variable, the first Hash function, and the second Hash function(S10). The key and system variable creating part creates a personal secrete key and a public key by applying the second Hash function and the user ID(S20). A signature part finds out a digital signature value by using a random value, the system variable, a personal secrete key and the public key(S30), and creates the signature sentence by encrypting a plain sentence with a digital signature value(S40).
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