DAA schemes are generally employed with the hardware of TPM to realize anonymous authentication. Basically, DAA schemes are based on group signatures. We propose a new DAA scheme based on a short group signature without encryption which departs from the traditional sign-encrypt-prove paradigm, and only adopts an anonymous signature and non-interactive zero-knowledge(NIZK) proofs. Compared to other DAA schemes at present, our scheme is approximately the most efficient and computation cost-saving with shorter signature length and easier signature generation. Our scheme also satisfies anonymity, trace ability and non-frame ability requirements.