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IEEE International Symposium on Information Theory (ISIT)

Secret key agreement under sampling attack

Jun Muramatsu, Kazuyuki Yoshimura, Kenichi Arai, Peter Davis

Published Jan 1, 2005• 1 citation
Publisher

Abstract

This paper considers the capacity for secret key agreement under a sampling attack. Given the number of the eavesdropper's sources, we evaluate the secret key capacity bound which is defined as the supremum of the secret key capacity divided by the description length of the alphabet, where the supremum is taken over a set of probability distributions corresponding to the correlated sources. In particular, we consider symmetric sources and permutation-invariant sources. We derive inequalities which show the scaling of the secret key capacity bound with the number of the eavesdropper's sources

DOI
10.1109/isit.2005.1523726

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This paper considers the capacity for secret key agreement under a sampling attack. Given the number of the eavesdropper's sources, we evaluate the secret key capacity bound which is defined as the supremum of the secret key capacity divided by the description length of the alphabet, where the supremum is taken over a set of probability distributions corresponding to the correlated sources. In particular, we consider symmetric sources and permutation-invariant sources. We derive inequalities which show the scaling of the secret key capacity bound with the number of the eavesdropper's sources
The capacity for secret key agreement for permutation-invariant and symmetric sources under a sampling attack is investigated. The supremum of the normalized secret key capacity is introduced, where the supremum is taken over all permutation-invariant sources or all symmetric sources and the normalized secret key capacity is the secret key capacity divided by the description length of the symbol. It is proved that the supremum of the normalized secret key capacity bound under a sampling attack is close to 1/m for permutation-invariant sources and O(1/m) for symmetric sources, where and m is the number of Eve's sources
Secret key agreement is a procedure for agreeing on a secret key by exchanging messages over a public channel when a sender, a legitimate receiver (henceforth referred to as a receiver), and an eavesdropper have access to correlated sources. Maurer [6] defined secret key capacity, which is the least upper bound of the key generation rate of the secret key agreement, and presented an upper and a lower bound for the secret key capacity. The advantage distillation capacity is introduced and it is shown that this quantity equals to the secret key capacity. Naive information theoretical expressions of the secret key capacity and the advantage distillation capacity are also presented. An example of correlated sources, for which an analytic expression of the secret key capacity can be obtained, is also presented.
A secret key agreement setup between three users is considered in which each of the users 1 and 2 intends to share a secret key with user 3 and users 1 and 2 are eavesdroppers with respect to each other. The three users observe i.i.d. outputs of correlated sources and there is a generalized discrete memoryless multiple access channel (GDMMAC) from users 1 and 2 to user 3 for communication between the users. The secret key agreement is established using the correlated sources and the GDMMAC. In this setup, inner and outer bounds of the secret key capacity region are investigated. Moreover, for a special case where the channel inputs and outputs and the sources form Markov chains in some order, the secret key capacity region is derived. Also a Gaussian case is considered in this setup.
Secret key agreement is a procedure for agreeing on a secret key by exchanging messages over a public channel when a sender, a legitimate receiver and an eavesdropper have access to correlated sources. Maurer, IEEE Trans. Inf. Theory 1993 defined secret key capacity, which is the least upper bound of the key generation rate of the secret key agreement, and presented an upper and a lower bound for the secret key capacity. In this paper, the advantage distillation capacity is introduced and it is shown that this quantity equals to the secret key capacity. A naive information theoretical expression of the secret key capacity and the advantage distillation capacity is also presented. An example of correlated sources, for which an analytic expression of the secret key capacity can be obtained, is also presented
A secret key agreement setup between three users is considered in which each pair of them wishes to agree on a secret key hidden from the remaining user. The three users observe i.i.d. outputs of correlated sources and there is a noiseless public channel from each user for communication to the others. In this setup, inner and outer bounds of the secret key capacity region is derived. Moreover, some special cases are obtained in which the inner bound coincides the explicit outer bound. Also a binary-erasure example is presented through which the results are examined.
We study the problem of information-theoretically secure secret key agreement under the well-known source model and channel model. In both of these models, multiple terminals wish to create a shared secret key that is secure from a passive eavesdropper. The terminals have access to a noiseless public communication channel and an additional resource that depends on the model. In the source model, the resource is an external source that repeatedly beams correlated randomness to the terminals; whereas in the channel model, the resource is a secure but noisy discrete memoryless broadcast channel. We derive new lower and upper bounds on the secret key capacity under both the source model and the channel model. The technique used for deriving our bound for the source model is to find certain properties of functions of joint probability distributions which, applied to the joint distribution of the source, will imply that they dominate the secret key capacity, and then prove the bound by a verification argument. A similar technique is used for the channel model. Finally, we also define a problem of communication for omniscience by a neutral observer and establish the equivalence between this new problem and the problem of secret key agreement. This generalizes an earlier result of Csiszár and Narayan.