Round-Optimal Secure Two-Party Computation

13 years 9 months ago

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Abstract. We consider the central cryptographic task of secure twoparty computation, where two parties wish to compute some function of their private inputs (each receiving possibly diﬀerent outputs) and security should hold with respect to arbitrarily-malicious behavior of either of the participants. Despite extensive research in this area, the exact round-complexity of this fundamental problem (i.e., the number of rounds required to compute an arbitrary poly-time functionality) was not previously known. Here, we establish the exact round complexity of secure two-party computation with respect to black-box proofs of security. We ﬁrst show a lower bound establishing (unconditionally) that four rounds are not sufﬁcient to securely compute the coin-tossing functionality for any superlogarithmic number of coins; this rules out 4-round protocols for other natural functionalities as well. Next, we construct protocols for securely computing any (randomized) functionality using only ﬁ...

Jonathan Katz, Rafail Ostrovsky

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