Toward this end we combinatorially characterize the classes of functions that can be computed IT securely in the authenticated channels model in presence of passive, semi-honest, active, and quantum adversaries (our results for quantum adversaries and in part for active adversaries are limited to the 2-party setting). In particular we obtain results on the fair computability of functions in the IT setting along the lines of the work of Gordon et al.~[STOC'08] for the computational setting. Our treatment is constructive in the sense that if a function is computable in a given setting, then we exhibit a protocol.
We show that the class of functions computable with long-term security in a very practical setting where the adversary may be active and insecure channels and a public-key infrastructure are provided is precisely the class of functions computable with IT security in the authenticated channels model in presence of a semi-honest adversary.
Finally, from our results and the work of Kushilevitz [SIAM Journal on Discrete Mathematics '92] and Kraschewski and Müller-Quade we can derive a complete combinatorial classification of functions, by secure computability and completeness under passive, semi-honest, active, and quantum adversaries.Category / Keywords: long-term security, information-theoretic security, corrupted majority, secure function evaluation Date: received 11 Jun 2008, last revised 6 Nov 2008 Contact author: d raub at inf ethz ch Available format(s): PDF | BibTeX Citation Note: We added many new results for the multi-party case. Version: 20081106:152814 (All versions of this report) Discussion forum: Show discussion | Start new discussion