Anonymous credential systems provide privacy-preserving authentication solutions for accessing services and resources. In these systems, copying and sharing credentials can be a serious issue. As this cannot be prevented in software alone, these problems form a major obstacle for the use of fully anonymous authentication systems in practice. In this paper, we propose a solution for anonymous authentication that is based on a hardware security module to prevent sharing of credentials. Our protocols are based on the standard protocols Transport Layer Security (TLS) and Direct Anonymous Attestation (DAA). We present a detailed description and a reference implementation of our approach based on a Trusted Platform Module (TPM) as hardware security module. Moreover, we discuss drawbacks and alternatives, and provide a pure software implementation to compare with our TPM-based approach.