TPM remote attestation allows to verify the integrity of the boot sequence of a remote device. Deep Attestation extends that concept to virtualized platforms by allowing to attest virtual components, the hypervisor, and the link between them. In multi-tenant environments, deep attestation solution offer security and/or efficiency, but no privacy. In this paper, we propose a privacy preserving TPM-based deep attestation solution in multi-tenant environments, which provably guarantees: (i) Inter-tenant privacy: a tenant is cannot know whether other VMs outside its own are hosted on the same machine; (ii) Configuration hiding: the hypervisor's configuration, used during attestation, remains hidden from the tenants; and (iii) Layer linking: tenants can link hypervisors with the VMs, thus obtaining a guarantee that the VMs are running on specific hardware. We also implement our scheme and show that it is efficient despite the use of complex cryptographic tools.