For solving the questions of complexities, high computation-consumings and applications limited for the direct anonymous attestation (DAA), a new DAA scheme is proposed based on bilinear maps under the assumption of q strong Diffie-Hellman and decisional Diffie-Hellman so as to match the limited computational resource of trusted platform module (TPM). It is shown that the secured scheme can efficiently relieve the computation bottleneck of trusted platform and enable TPM to be used in embedded and other resource-constrained environments.