Direct Anonymous Attestation (DAA) is an anonymous digital signature scheme that aims to provide both signer authentication and privacy. One of the properties that makes DAA an attractive choice in practice is the split signer role. In short, a principal signer (a Trusted Platform Module (TPM)) signs messages in collaboration with an assistant signer (the host, a standard computing platform into which the TPM is embedded). This split aims to harness the high level of security offered by the TPM, and augment it using the high level of computational and storage ability offered by the host. Our contribution in this paper is a modification to an existing pairing-based DAA scheme that significantly improves efficiency, and a comparison with the original RSA-based DAA scheme via a concrete implementation.