Deep attestation is a particular case of remote attestation, i.e., verifying the integrity of a platform with a remote verification server. We focus on the remote attestation of hypervisors and their hosted virtual machines (VM), for which two solutions are currently supported by ETSI. The first is single-channel attestation, requiring for each VM an attestation of that VM and the underlying hypervisor through the physical TPM. The second, multi-channel attestation, allows to attest VMs via virtual TPMs and separately from the hypervisor-this is faster and requires less overall attestations, but the server cannot verify the link between VM and hypervisor attestations, which comes for free for single-channel attestation. We design a new approach to provide linked remote attestation which achieves the best of both worlds: we benefit from the efficiency of multichannel attestation while simultaneously allowing attestations to be linked. Moreover, we formalize a security model for deep attestation and prove the security of our approach. Our contribution is agnostic of the precise underlying secure component (which could be instantiated as a TPM or something equivalent) and can be of independent interest. Finally, we implement our proposal using TPM 2.0 and vTPM (KVM/QEMU), and show that it is practical and efficient.