IACR News item: 20 November 2015
Ivan Damg{\\aa}rd, Jesper Buus Nielsen, Rafail Ostovsky, Adi Rosen
ePrint ReportNext, we consider round complexity. It is a long-standing open problem to determine whether all efficiently computable functions can also be efficiently computed in constant-round with unconditional security. Motivated by this, we consider the question of whether we can compute any function securely, while minimizing the interaction of some of the players? And if so, how many players can this apply to? Note that we still want the standard security guarantees (correctness, privacy, termi- nation) and we consider the standard communication model with secure point-to-point channels. We answer the questions as follows: for passive security, with n = 2t + 1 players and t corruptions, up to t players can have minimal interaction, i.e., they send 1 message in the first round to each of the t + 1 remaining players and receive one message from each of them in the last round. Using our result on message complexity, we show that this is (unconditionally) optimal. For malicious security with n = 3t + 1 players and t corruptions, up to t players can have minimal interaction, and we show that this is also optimal.
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