Constant-Rate Oblivious Transfer from Noisy Channels

A binary symmetric channel (BSC) is a noisy communication channel that flips each bit independently with some fixed error probability 0 < p < 1/2. Crépeau and Kilian (FOCS 1988) showed that oblivious transfer, and hence general secure two-party computation, can be unconditionally realized by communicating over a BSC. There has been a long line of works on improving the efficiency and generality of this construction. However, all known constructions that achieve security against malicious parties require the parties to communicate poly(k) bits over the channel for each instance of oblivious transfer (more precisely, ( 2 1 ) bit-OT) being realized, where k is a statistical security parameter. The question of achieving a constant (positive) rate was left open, even in the easier case of realizing a single oblivious transfer of a long string. We settle this question in the affirmative by showing how to realize n independent instances of oblivious transfer, with statistical error that vanishes with n, by communicating just O(n) bits over a BSC. As a corollary, any boolean circuit of size s can be securely evaluated by two parties with O(s)+poly(k) bits of communication over a BSC, improving over the O(s) · poly(k) complexity of previous constructions. ? Work done in part while visiting UCLA. Supported by ERC Starting Grant 259426, ISF grant 1361/10, and BSF grant 2008411. [email protected] ?? Work done in part while visiting UCLA. Supported by ISF grant 1361/10 and BSF grant 2008411. [email protected] ? ? ? Research supported in part by DARPA, IBM Faculty Award, Xerox Innovation Group Award, the Okawa Foundation Award, Intel, Teradata, NSF grants 0830803, 0916574, BSF grant 2008411 and U.C. MICRO grant. [email protected] † Supported by NSF grant CNS 07-47027. [email protected] ‡ Research supported in part from a DARPA/ONR PROCEED award, NSF grants 0916574 and 0830803, a Xerox Foundation Award, a Google Faculty Research Award, an equipment grant from Intel, and an Okawa Foundation Research Grant. [email protected] § Research supported by the Canada-France NSERC-ANR project FREQUENCY.