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 S A and S B , respectively, such that with probability 1+ε/2 these bits are equal. Further assume that conditioned on the event S A =n S B no polynomial time bounded algorithm can predict the bit better than with probability 1-δ/2. Is it possible to obtain key agreement from such a primitive? We show that for constant δ and ε the answer is yes if and only if δ > 1-ε/1+ε, 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.

Authors

• Thomas Holenstein

Keywords

• cryptography
• hard-core sets
• key agreement