Pseudonyms are often used by nodes to anonymously communicate in ad hoc networks. However, in exiting anonymous routing protocols for ad hoc networks, most pseudonym schemes have side effects that diminish the anonymity of protocols, and authentication protocols based on them are inefficient as to scarce communication resources. Classical pseudonym systems are applicable for center-controlled networks which require an organization management center to act as an administrator, and not desirable in ad hoc networks. To resolve above problems, this paper proposes a pseudonym-based signature scheme where pseudonyms can be self-generated and used as public keys for signatures. At the same time, the credential can be selective revoked or full revoked in the signature scheme. Because the pseudonyms are self-updated and not directly bound to real identities or certificates, the signature scheme based on them must satisfy some new requirements. Hence, we formalize a security model for pseudonym-based signature schemes. Using pseudonym-based signature schemes as authenticators, authentication protocols can be easily constructed and achieve anonymity and non-interaction. Finally, the security of our scheme is analyzed and proved in the random oracle model.