Key agreement from weak bit agreement

Assume that Alice and Bob, given an authentic channel, have a protocol where they end up with a bit SA and SB, respectively, such that with probability 1+ 2 these bits are equal. Further assume that conditioned on the event SA = SB no polynomial time bounded algorithm can predict the bit better than with probability 1 2 . Is it possible to obtain key agreement from such a primitive? We show that for constant and the answer is yes if and only if > 11+ , both for uniform and non-uniform adversaries. The main computational technique used in this paper is a strengthening of Impagliazzo's hard-core lemma to the uniform case and to a set size parameter which is tight (i.e., twice the original size). This may be of independent interest. Categories and Subject Descriptors F.2.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity--Nonnumerical Algorithms and Problems; E.3 [Data]: Data Encryption General Terms Algorithms, Theory Keywords Cryptography, Hard-core Set...

• Type: Conference
• Year: 2005
• Where: STOC
• Authors: Thomas Holenstein
• Keywords: Algorithms, General Terms Algorithms, Hard-core Lemma, Key Agreement, STOC 2005