Collusion-free (CF) and collusion-preserving (CP) protocols enrich the standard security offered by multi-party computation (MPC), to tackle settings where subliminal communication is undesirable. However, all existing solutions make arguably unrealistic assumptions on setups, such as physical presence of the parties, access to physical envelopes, or extreme isolation, where the only means of communication is a star-topology network. The above state of affairs remained a limitation of such protocols, which was even reinforced by impossibility results. Thus, for years, it has been unclear if and how the above setup assumptions could be relaxed towards more realistic scenarios. Motivated also by the increasing interest in using hardware tokens for cryptographic applications, in this work we provide the first solution to collusion preserving computation which uses weaker and more common assumptions than the state of the art, i.e., an authenticated broadcast functionality and access to honestly generated trusted hardware tokens. We prove that our protocol is collusion-preserving (in short, CP) secure as long as no parties abort. In the case of an aborting adversary, our protocol still achieves standard (G)UC security with identifiable (and unanimous) abort.

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