Tor is a famous routing overlay network based on the Onion multi-layered encryption to support communication anonymity in a threat model in which some network nodes are malicious. However, Tor does not provide any protection against the global passive adversary. In this threat model, an idea to obtain recipient anonymity, which is enough to have relationship anonymity, is to hide the recipient among a sufficiently large anonymity set. However, this would lead to high latency both in the set-up phase (which has a quadratic cost in the number of involved nodes) and in the successive communication. In this paper, we propose a way to arrange a Tor circuit with a tree-like topology, in which the anonymity set consists of all its nodes, whereas set-up and communication latency depends on the number of the sole branch nodes (which is a small fraction of all the nodes). Basically, the cost goes down from quadratic to linear. Anonymity is obtained by applying a broadcast-based technique for the forward message, and cover traffic (generated by the terminal-chain nodes) plus mixing over branch nodes, for the response.
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