In some systems, users might want to identify themselves by their pseudonyms. If access control is necessary, then a certificate of authorized access employing pseudonyms must be unforgeable. We call a certificate of authorized access a credential. If different pseudonyms which identify a user are to be unlinkable, the user must be able to choose his pseudonyms at random and to transfer the credential issued on one pseudonym to another pseudonym untraceably. However, in order to prevent forgery of the certificate, pseudonyms must be formed in a specific way. This work presents a pseudonym validation process based on discrete logarithms without using cut-and-choose. The certificates issued with pseudonyms are unforgeable. The privacy of users is protected unconditionally. This pseudonym system has the novel feature that each user has a validated public key relevant to each pseudonym, so that signatures can be made by pseudonyms.