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S

ETH Series in Information Security and Cryptography
edited by Ueli Maurer
Volume 7
Thomas Holenstein
Strengthening Key Agreement
using HardCore Sets
1^{st}
edition/ 1. Auflage 2006, 168 pages/Seiten,
€ 65,00. ISBN 3866280882
Given an
authentic communication channel, a key agreement protocol enables two parties
to obtain a common bit string, such that a computationally bounded eavesdropper
does not get any information about it, even if he observes the whole
communication. Many such protocols are used in practice today, and they all
base their security on an unproven assumption.
The goal of this thesis is to base such a protocol on an assumption which is as
weak as possible. The assumption we use is the existence of a weak key agreement
protocol. Such a protocol works partially: in some executions the honest
parties get the same key, but sometimes their respective keys differ.
Furthermore, in some cases the resulting key is secret, while sometimes
information about the key is leaked. We then strengthen such a protocol; i.e.,
we make it both secret and correct.
Our proof relies on a powerful lemma about hardcore sets. Roughly speaking,
the lemma shows that any computational problem which is mildly hard has a set
of instances for which it is very hard. In our setting this implies that for a
weak key agreement protocol, if the randomness of Alice and Bob is restricted
to a certain subset, finding the key from the communication is a very hard
problem.
Keywords: Cryptograhpy, Keyagreement, HardCore
Sets.
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ETH Series in Information Security and Cryptography