A private key generation apparatus for generating a private key corresponding to a user ID using the user ID as a public key is disclosed. When a user ID is input, an ID conversion unit outputs a specific element value of a discrete logarithm cyclic group having a one-to-one correspondence relationship with an input user ID. A private key calculation unit calculates a discrete logarithm result value based on the output specific element value of the discrete logarithm cyclic group and calculates a private key having a one-to-one correspondence relationship with the user ID. According to the present invention, it is possible to concretely propose a method of calculating a secret key, capable of guaranteeing a one-to-one correspondence relationship between the ID and the private key by applying a method of calculating a discrete logarithm using the pre-computation table in an ID-based encryption system.