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Quantization Aspects in LDPC Key Reconciliation for Physical Layer Security

Oana Graur, Nazia Islam, Alexandra Filip, Werner Henkel

Published Feb 1, 2015• 10 citations
OpenAlex

Abstract

For physical-layer security, key reconciliation procedures are needed to correct key differences that can arise as a consequence of independent noise at the two ends of a reciprocal link. We assume either a random link in a mobile environment or use reconfigurable antenna elements to randomize the channel, such that it allows for frequent key generation. We apply LDPC codes to reconcile the keys on both sides. In here, we derive the LLRs taking into account the underlying quantization.

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Common randomness of channels offers the possibility to create cryptographic keys without the need for a key exchange procedure. Channel reciprocity for TDD (time-division duplexing) systems has been used for this purpose many times. FDD (frequency-division duplexing) systems, however, were long considered to not provide any usable symmetry. However, since the scattering transmission parameters S12and S21would ideally be the same due to reciprocity, when using neighboring frequency ranges for both directions, they would just follow a continuous curve when putting them next to each other. To not rely on absolute phase, we use phase differences between antennas and apply a polynomial curve fitting, thereafter, quantize the midpoint between the two frequency ranges with the two measurement directions. This is shown to work even with some spacing between the two bands. For key reconciliation, we force the measurement point from one direction to be in the midpoint of the quantization interval by a grid shift (or likewise measurement data shift). Since the histogram over the quantization intervals does not follow a uniform distribution, some source coding / hashing will be necessary. The key disagreement rate toward an eavesdropper was found to be close to 0.5. Additionally, when using an antenna array, a random permutation of antenna measurements can even further improve the protection against eavesdropping.

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Physical layer key generation is based on reciprocal channels providing common randomness, which was so far known from TDD wireless channels. This paper opens the door to wireline physical-layer security, especially focusing on power-line connections. Additionally to the known reciprocity, we now also provide randomization by terminating idle branching connections (e.g., empty sockets) with random (reactive) loads. Alternatively, unused pairs at the power-line modem's end may be terminated by random (reactive) loads. Simulation and measurement results are shown. We also indicate, how the actual key generation can be realized by quantizing a frequency range and using the position of notches of the transfer function or of transmission coefficients selecting a quantization interval and with it a binary label as a key segment. Key reconciliation can simply be realized by a publicly announced shift of the quantization grid. Applications are seen for in-home and industrial devices required to exchange data over the power-line network securely.

International Conference on Communications•Jun 1, 2020•16 citations
For physical-layer security, key reconciliation procedures are needed to correct key differences that can arise as a consequence of independent noise at the two ends of a reciprocal link. We assume either a random link in a mobile environment or use reconfigurable antenna elements to randomize the channel, such that it allows for frequent key generation. We apply LDPC codes to reconcile the keys on both sides. In here, we derive the LLRs taking into account the underlying quantization.
The problem of key reconciliation based on Low-Density Parity-Check (LDPC) codes and Slepian-Wolf coding for physical layer key generation is investigated.When using the channel-state-information (CSI) of a reciprocal wireless channel for key generation between two legitimate users, independent noise components, quantization, and synchronization errors at the end nodes give rise to key differences that need to be corrected by sending side information.We provide a comparison of three different quantization schemes in terms of key disagreement rate and output probability distributions and present the loglikelihood formulations required by a soft decision LDPC decoder to perform key reconciliation, for the investigated quantization methods.
Physical layer approaches for generating secret encryption keys for wireless systems using channel information have attracted increased interest from researchers in recent years. This paper presents a new approach for calculating log-likelihood ratios (LLRs) for secret key generation that is based on one-bit quantization of channel measurements and the difference between channel estimates at legitimate reciprocal nodes. The studied secret key agreement approach, which implements advantage distillation along with information reconciliation using Slepian-Wolf low-density parity-check (LDPC) codes, is discussed and illustrated with numerical results obtained from simulations. These results show the probability of bit disagreement for keys generated using the proposed LLR calculations compared with alternative LLR calculation methods for key generation based on channel state information. The proposed LLR calculations are shown to be an improvement to the studied approach of physical layer secret key agreement.
Key reconciliation procedures are needed to correct key differences that can arise as a consequence of independent noise at the two ends of a reciprocal link. We assume a line-of-sight channel and use reconfigurable antenna elements to randomize it, such that it allows for key generation. The Linde-Buzo-Gray algorithm is employed to quantize the complex channel transfer characteristic, and adaptive guard bands, symmetric to the quantization thresholds, are further constructed. To limit the number of key errors, we ensure that only the points that fall outside the guard band interval are accepted for key generation. The steps for constructing the guard bands are presented.
Physical layer approaches for generating secret encryption keys for wireless systems using channel information has attracted increased interest from researchers in recent years. This paper presents a new approach for secret key generation that is based on one-bit quantization of channel measurements along with log-likelihood ratios (LLRs) that are calculated based on the difference between channel estimates at legitimate reciprocal nodes. The proposed approach, which implements advantage distillation along with information reconciliation using Slepian-Wolf low-density parity check (LDPC) codes, is discussed and illustrated with numerical results obtained from simulations. These show the probability of bit disagreement for keys generated through the proposed approach and compare it with that of alternative methods for key generation based on channel state information.
Common randomness of channels offers the possibility to create cryptographic keys without the need for a key exchange procedure. Channel reciprocity for TDD (time-division duplexing) systems has been used for this purpose many times. FDD (frequency-division duplexing) systems, however, were long considered to not provide any usable symmetry. However, since the scattering transmission parameters S12and S21would ideally be the same due to reciprocity, when using neighboring frequency ranges for both directions, they would just follow a continuous curve when putting them next to each other. To not rely on absolute phase, we use phase differences between antennas and apply a polynomial curve fitting, thereafter, quantize the midpoint between the two frequency ranges with the two measurement directions. This is shown to work even with some spacing between the two bands. For key reconciliation, we force the measurement point from one direction to be in the midpoint of the quantization interval by a grid shift (or likewise measurement data shift). Since the histogram over the quantization intervals does not follow a uniform distribution, some source coding / hashing will be necessary. The key disagreement rate toward an eavesdropper was found to be close to 0.5. Additionally, when using an antenna array, a random permutation of antenna measurements can even further improve the protection against eavesdropping.
Physical layer key generation is based on reciprocal channels providing common randomness, which was so far known from TDD wireless channels. This paper opens the door to wireline physical-layer security, especially focusing on power-line connections. Additionally to the known reciprocity, we now also provide randomization by terminating idle branching connections (e.g., empty sockets) with random (reactive) loads. Alternatively, unused pairs at the power-line modem's end may be terminated by random (reactive) loads. Simulation and measurement results are shown. We also indicate, how the actual key generation can be realized by quantizing a frequency range and using the position of notches of the transfer function or of transmission coefficients selecting a quantization interval and with it a binary label as a key segment. Key reconciliation can simply be realized by a publicly announced shift of the quantization grid. Applications are seen for in-home and industrial devices required to exchange data over the power-line network securely.