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IEEE International Symposium on Information Theory (ISIT)

LDPC-based secret key agreement over the Gaussian wiretap channel

Matthieu R. Bloch, Andrew Thangaraj, Steven McLaughlin, Jean-Marc Mérolla

Published Jul 1, 2006• 44 citations
Publisher

Abstract

This paper investigates a practical secret key agreement protocol over the Gaussian wire-tap channel. The protocol is based on an efficient information reconciliation method which allows two parties having access to correlated continuous random variables to agree on a common bit string. We describe an explicit reconciliation method based on LDPC codes optimized with EXIT charts and density evolution. When used in conjunction with existing privacy amplification techniques our method allows secret key agreement over the Gaussian wire-tap channel close to the secrecy capacity

DOI
10.1109/isit.2006.261991

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This paper investigates a practical secret key agreement protocol over the Gaussian wire-tap channel. The protocol is based on an efficient information reconciliation method which allows two parties having access to correlated continuous random variables to agree on a common bit string. We describe an explicit reconciliation method based on LDPC codes optimized with EXIT charts and density evolution. When used in conjunction with existing privacy amplification techniques our method allows secret key agreement over the Gaussian wire-tap channel close to the secrecy capacity
This paper investigates an efficient and practical information reconciliation method in the case where two parties have access to correlated continuous random variables. We show that reconciliation is a special case of channel coding and that existing coded modulation techniques can be adapted for reconciliation. We describe an explicit reconciliation method based on LDPC codes in the case of correlated Gaussian variables. We believe that the proposed method can improve the efficiency of quantum key distribution protocols based on continuous-spectrum quantum states.
Reconciliation is an essential part of any secret-key agreement protocol and hence of a quantum key distribution (QKD) protocol, where two legitimate parties are given correlated data and want to agree on a common string in the presence of an adversary, while revealing a minimum amount of information. In this paper, we show that for discrete-variable QKD protocols, this problem can be advantageously solved with low density parity check (LDPC) codes optimized for the binary symmetric channel (BSC). In particular, we demonstrate that our method leads to a significant improvement of the achievable secret key rate, with respect to earlier interactive reconciliation methods used in QKD.
In Part I of this two-part paper on confidential communication over wireless channels, we studied the fundamental security limits of quasi-static fading channels from the point of view of outage secrecy capacity with perfect and imperfect channel state information. In Part II, we develop a practical secret key agreement protocol for Gaussian and quasi-static fading wiretap channels. The protocol uses a four-step procedure to secure communications: establish common randomness via an opportunistic transmission, perform message reconciliation, establish a common key via privacy amplification, and use of the key. We introduce a new reconciliation procedure that uses multilevel coding and optimized low density parity check codes which in some cases comes close to achieving the secrecy capacity limits established in Part I. Finally, we develop new metrics for assessing average secure key generation rates and show that our protocol is effective in secure key renewal.
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.
With the advent of quantum key distribution (QKD) systems, perfect (i.e. information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical errorcorrecting codes for both error correction (for the honest p arties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model for such a setting is the wire tap channel introduced by Wyner in 1975. In this paper, we study fundamental limits and coding methods for wire tap channels. We provide a novel proof for the secrecy capacity theorem for wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide complete security at rates below secrecy capacity in some specific cases.