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IEEE Military Communications Conference (MILCOM)

An LDPC-based key-agreement scheme over the fast-fading wiretap channel

Chan Wong Wong, Tan F. Wong, John M. Shea

Published Nov 1, 2011• 0 citations
Publisher

Abstract

This paper considers the design of practical schemes that enable two terminals, namely a source and a destination, to agree on a secret key in the presence of an eavesdropper (wire-tapper). The channel model considered is a fast Rayleigh fading wiretap channel with the constraints of quadrature phase-shift-keyed source symbols and hard-decision destination quantization. It is assumed that there exists a public feedback channel between the source and destination to facilitate the key-agreement process, however, any communication over the public channel is perfectly observed by the wiretapper. A key-agreement scheme employing irregular low-density parity-check (LDPC) codes is proposed, and its secrecy performance is measured in terms of the key rate between the source and destination and the leakage rate about the secret key at the wiretapper. A code search algorithm is also developed to design irregular LDPC codes to achieve good secrecy performance under various channel conditions.

DOI
10.1109/milcom.2011.6127689

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This paper considers the design of practical schemes that enable two terminals, namely a source and a destination, to agree on a secret key in the presence of an eavesdropper (wire-tapper). The channel model considered is a fast Rayleigh fading wiretap channel with the constraints of quadrature phase-shift-keyed source symbols and hard-decision destination quantization. It is assumed that there exists a public feedback channel between the source and destination to facilitate the key-agreement process, however, any communication over the public channel is perfectly observed by the wiretapper. A key-agreement scheme employing irregular low-density parity-check (LDPC) codes is proposed, and its secrecy performance is measured in terms of the key rate between the source and destination and the leakage rate about the secret key at the wiretapper. A code search algorithm is also developed to design irregular LDPC codes to achieve good secrecy performance under various channel conditions.
Secret sharing over the fast-fading MIMO wiretap channel is considered. A source and a destination try to share secret information over a fast-fading MIMO channel in the presence of an eavesdropper who also makes channel observations that are different from but correlated to those made by the destination. An interactive, authenticated public channel with unlimited capacity is available to the source and destination for the secret sharing process. This situation is a special case of the "channel model with wiretapper" considered by Ahlswede and Csiszár. An extension of their result to continuous channel alphabets is employed to evaluate the key capacity of the fast-fading MIMO wiretap channel. The effects of spatial dimensionality provided by the use of multiple antennas at the source, destination, and eavesdropper are then investigated.
A wiretap channel I is one of the channel models that was proved to achieve unconditional security. However, it has been an open problem in realizing such a channel model in a practical network environment. The paper is committed to solve the open problem by introducing a novel approach for building wiretap channel I in which the eavesdropper sees a binary symmetric channel (BSC) with error probability p while the main channel is error free. By taking advantage of the feedback and low density parity check (LDPC) codes, our scheme adds randomness to the feedback signals from the destination for keeping an eavesdropper ignorant; on the other hand, redundancy is added and encoded by the LDPC codes such that a legitimate receiver can correctly receive and decode the signals. With the proposed approach, unconditionally-secure communication can be achieved through interactive communications, in which the legitimate partner can realize the secret information transmission without a pre-shared secret key even if the eavesdropper has better channel from the beginning.
Secret sharing over the fast-fading MIMO wiretap channel is considered. A source and a destination try to share secret information over a fast-fading MIMO channel in the presence of a wiretapper who also makes channel observations that are different from but correlated to those made by the destination. An interactive authenticated unrestricted public channel is also available for use by the source and destination in the secret sharing process. This falls under the "channel-type model with wiretapper" considered by Ahlswede and Csiszar. A minor extension of their result (to continuous channel alphabets) is employed to evaluate the key capacity of the fast-fading MIMO wiretap channel. The effects of spatial dimensionality provided by the use of multiple antennas at the source, destination, and wiretapper are then investigated.
We study secret-key agreement protocols over a wiretap channel controlled by a state parameter. The secret-key capacity is established when the wiretap channel is discrete and memoryless, the sender and receiver are both revealed the underlying state parameter, and no public discussion is allowed. An optimal coding scheme involves a two step approach — (i) design a wiretap codebook assuming that the state parameter is also known to the eavesdropper (ii) generate an additional secret key by exploiting the uncertainty of the state parameter at the eavesdropper. When unlimited public discussion is allowed between the legitimate terminals, we provide an upper bound on the secret-key capacity and establish its tightness when the channel outputs of the legitimate receiver and eavesdropper satisfy a conditional independence property. Numerical results for an on-off fading model suggest that the proposed coding schemes significantly outperform naive schemes that either disregard the contribution of the common state sequence or the contribution of the underlying channel.
Information-theoretic secret-key agreement is perhaps the most practically feasible mechanism that provides unconditional security at the physical layer to date. In this paper, we consider the problem of secret-key agreement by sharing randomness at low power over an orthogonal frequency division multiplexing (OFDM) link, in the presence of an eavesdropper. The low power assumption greatly simplifies the design of the randomness sharing scheme, even in a fading channel scenario. We assess the performance of the proposed system in terms of secrecy key rate and show that a practical approach to key sharing is obtained by using low-density parity check (LDPC) codes for information reconciliation. Numerical results confirm the merits of the proposed approach as a feasible and practical solution. Moreover, the outage formulation allows to implement secret-key agreement even when only statistical knowledge of the eavesdropper channel is available.
Information-theoretic secret-key agreement is perhaps the most practically feasible mechanism that provides unconditional security at the physical layer to date. In this paper, we consider the problem of secret-key agreement by sharing randomness at low power over an orthogonal frequency division multiplexing (OFDM) link, in the presence of an eavesdropper. The low power assumption greatly simplifies the design of the randomness sharing scheme, even in a fading channel scenario. We assess the performance of the proposed system in terms of secrecy key rate and show that a practical approach to key sharing is obtained by using low-density parity check (LDPC) codes for information reconciliation. Numerical results confirm the merits of the proposed approach as a feasible and practical solution. Moreover, the outage formulation allows to implement secret-key agreement even when only statistical knowledge of the eavesdropper channel is available.