Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Conference on Information Sciences and Systems

Secret Key Generation from MIMO Channel With or Without Reciprocity

Yingbo Hua, Ahmed Maksud

Published Mar 22, 2023• 2 citations
Publisher

Abstract

This paper presents a generalized channel probing (GCP) method and a generalized pre-processing (GPP) method as two consecutive frontend steps for secret key generation from a MIMO channel between two multi-antenna legitimate nodes against a multi-antenna eavesdropper (Eve). The degree of freedom (DoF) of the secret key capacity (SKC) of GCP/GPP are highlighted and discussed. If the number of antennas on Eve is larger than or equal to the larger number of the antennas on the two legitimate nodes, the SKC-DoF of GCP/GPP within each coherence period equals its minimum, which is either zero for non-reciprocal channel or the product of the numbers of antennas on the two legitimate nodes for reciprocal channel. Otherwise, the SKC-DoF of GCP/GPP increases with the number of random transmissions in GCP within each coherence period regardless of the channel reciprocity. A computational algorithm required for GPP is also discussed, and its performance illustrated via simulations.

DOI
10.1109/ciss56502.2023.10089738

Related papers

Generalized Channel Probing and Generalized Pre-Processing for Secret Key Generation

Yingbo Hua

The paper considers secret key generation (SKG) from a channel between Alice and Bob against Eve all with multiple antennas. A generalized channel probing (GCP) method and a generalized pre-processing (GPP) method are proposed as two major steps before quantization, information reconciliation and privacy amplification for SKG. The degree-of-freedom (DoF) of the secret key capacity (SKC), relative to power or signal-to-noise ratio, based on the data sets at Alice, Bob and Eve after the execution of GCP is shown. The SKC-DoF is also shown to be the same as that based the new data sets after the application of GPP except for modifications chosen for computational efficiency. In particular, if Eve has a less number of antennas than either Alice and/or Bob, the SKC-DoF grows with the number of random transmissions from either Alice and/or Bob within each channel coherence period. This SKC-DoF property for GCP and GPP does not require the reciprocity of the channel. A reciprocal channel simply adds a product of the numbers of antennas at Alice and Bob towards the total SKC-DoF. Also shown in this paper is GCP with embedded public pilots, which results in no loss of SKC-DoF. Two prior methods for channel probing are also reviewed, and it is shown that none of them has the above mentioned SKC-DoF property despite previous claims. The potential application areas of GCP and GPP include both wireless and wireline networks.

IEEE Transactions on Signal Processing•Jan 1, 2023•27 citations

Second-Order Analysis of Secret-Key Capacity From a MIMO Channel

Ahmed Maksud, Yingbo Hua

This paper presents an analysis of Maurer-Ahlswede-Csiszar (MAC) bounds on secret-key capacity (SKC) based on a MIMO channel probing scheme between two multi-antenna nodes against a multi-antenna eavesdropper (Eve). To reveal useful insights into SKC, we consider the regime of high signal powers or high signal-to-noise ratios (SNR) where SKC consists of a first-order term (FoT) which is proportional to the logarithm of signal power, and a second-order term (SoT) which is invariant to signal power. Applying random-matrix theory for large numbers of antennas on all nodes, this paper shows the FoT and SoT of a lower MAC bound on SKC. While the FoT is consistent with prior work, which vanishes if none of the two nodes has more antennas than Eve and the channel is not perfectly reciprocal, the SoT shows a positive secrecy that increases linearly with the length of random transmissions from one node to another during channel probing even if Eve has many more antennas than the legitimate nodes.

IEEE Military Communications Conference (MILCOM)•Oct 30, 2023•1 citation

Key generation exploiting MIMO channel evolution: Algorithms and theoretical limits

Jon W. Wallace, Chan Chen, Michael A. Jensen

An emerging area of research in wireless communications is the generation of secret encryption keys based on the shared (or common) randomness of the wireless channel between two legitimate nodes in a communication network. However, to date, little work has appeared on methods to use the increased randomness available when the network nodes have multiple antennas. This paper provides theoretical performance bounds associated with using multi-antenna communications and proposes two practical methods for generating secret keys exploiting the increased randomness. Performance simulations reveal the efficiency of the methods.

European Conference on Antennas and Propagation•Mar 23, 2009•79 citations

Secret-Key Capacity From MIMO Channel Probing

Yingbo Hua, Ahmed Maksud

Revealing expressions of secret-key capacity (SKC) based on data sets from Gaussian MIMO channel probing are presented. It is shown that Maurer’s upper and lower bounds on SKC coincide when the used data sets are produced from one-way channel probing. As channel coherence time increases, SKC in bits per probing channel use is always lower bounded by a positive value unless eavesdropper’s observations are noiseless, which is unlike SKC solely based on reciprocal channels.

arXiv:2403.02529•IEEE Wireless Communications Letters•Mar 5, 2024•9 citations

Secret key generation from reciprocal spatially correlated MIMO channels

Eduard Axel Jorswieck, Anne Wolf, Sabrina Engelmann

Secret key generation from reciprocal multi-antenna channels is an interesting alternative to cryptographic key management in wireless systems without infrastructure access. In this work, we study the secret key rate for the basic source model with a MIMO channel. First, we derive an expression for the secret key rate under spatial correlation modelled by the Kronecker model and with spatial precoding at both communication nodes. Next, we analyze the result for uncorrelated antennas to understand the optimal precoding for this special case, which is equal power allocation. Then, the impact of correlation is characterized using Majorization theory. Surprisingly for small SNR, spatial correlation increases the secret key rate. For high SNR, the maximum secret key rate is achieved for uncorrelated antennas. The results indicate that a solid system design for reciprocal MIMO key generation is required to establish the secret key rate gains.

IEEE Globecom Workshops (GC Wkshps)•Dec 1, 2013•38 citations

Experimental Investigation of MIMO Reciprocal Channel Key Generation

Jon W. Wallace, R. K. Sharma

There is growing interest in physical-layer key generation schemes that provide very strong or even perfect security in wireless communication systems. One such scheme is reciprocal channel key generation, where two nodes quantize reciprocal channel state information to generate keys. Although the use of multiple-input multiple-output (MIMO) techniques is interesting in this case since the number of random parameters available for rapid key generation is increased, MIMO techniques may also provide more information to an eavesdropper. This work presents a new MIMO measurement campaign performed in LOS and NLOS indoor environments that studies the correlation of the channel between legitimate users with the eavesdropper channel, revealing what key generation rates can be attained in practice and what fraction of generated key bits are safe from eavesdroppers. The effect of eavesdropper separation, number of antennas, eavesdropper advantage, and covariance separability are studied.

International Conference on Communications•May 1, 2010•10 citations
This paper presents a generalized channel probing (GCP) method and a generalized pre-processing (GPP) method as two consecutive frontend steps for secret key generation from a MIMO channel between two multi-antenna legitimate nodes against a multi-antenna eavesdropper (Eve). The degree of freedom (DoF) of the secret key capacity (SKC) of GCP/GPP are highlighted and discussed. If the number of antennas on Eve is larger than or equal to the larger number of the antennas on the two legitimate nodes, the SKC-DoF of GCP/GPP within each coherence period equals its minimum, which is either zero for non-reciprocal channel or the product of the numbers of antennas on the two legitimate nodes for reciprocal channel. Otherwise, the SKC-DoF of GCP/GPP increases with the number of random transmissions in GCP within each coherence period regardless of the channel reciprocity. A computational algorithm required for GPP is also discussed, and its performance illustrated via simulations.
The paper considers secret key generation (SKG) from a channel between Alice and Bob against Eve all with multiple antennas. A generalized channel probing (GCP) method and a generalized pre-processing (GPP) method are proposed as two major steps before quantization, information reconciliation and privacy amplification for SKG. The degree-of-freedom (DoF) of the secret key capacity (SKC), relative to power or signal-to-noise ratio, based on the data sets at Alice, Bob and Eve after the execution of GCP is shown. The SKC-DoF is also shown to be the same as that based the new data sets after the application of GPP except for modifications chosen for computational efficiency. In particular, if Eve has a less number of antennas than either Alice and/or Bob, the SKC-DoF grows with the number of random transmissions from either Alice and/or Bob within each channel coherence period. This SKC-DoF property for GCP and GPP does not require the reciprocity of the channel. A reciprocal channel simply adds a product of the numbers of antennas at Alice and Bob towards the total SKC-DoF. Also shown in this paper is GCP with embedded public pilots, which results in no loss of SKC-DoF. Two prior methods for channel probing are also reviewed, and it is shown that none of them has the above mentioned SKC-DoF property despite previous claims. The potential application areas of GCP and GPP include both wireless and wireline networks.
This paper presents an analysis of Maurer-Ahlswede-Csiszar (MAC) bounds on secret-key capacity (SKC) based on a MIMO channel probing scheme between two multi-antenna nodes against a multi-antenna eavesdropper (Eve). To reveal useful insights into SKC, we consider the regime of high signal powers or high signal-to-noise ratios (SNR) where SKC consists of a first-order term (FoT) which is proportional to the logarithm of signal power, and a second-order term (SoT) which is invariant to signal power. Applying random-matrix theory for large numbers of antennas on all nodes, this paper shows the FoT and SoT of a lower MAC bound on SKC. While the FoT is consistent with prior work, which vanishes if none of the two nodes has more antennas than Eve and the channel is not perfectly reciprocal, the SoT shows a positive secrecy that increases linearly with the length of random transmissions from one node to another during channel probing even if Eve has many more antennas than the legitimate nodes.
An emerging area of research in wireless communications is the generation of secret encryption keys based on the shared (or common) randomness of the wireless channel between two legitimate nodes in a communication network. However, to date, little work has appeared on methods to use the increased randomness available when the network nodes have multiple antennas. This paper provides theoretical performance bounds associated with using multi-antenna communications and proposes two practical methods for generating secret keys exploiting the increased randomness. Performance simulations reveal the efficiency of the methods.
Secret key generation from reciprocal multi-antenna channels is an interesting alternative to cryptographic key management in wireless systems without infrastructure access. In this work, we study the secret key rate for the basic source model with a MIMO channel. First, we derive an expression for the secret key rate under spatial correlation modelled by the Kronecker model and with spatial precoding at both communication nodes. Next, we analyze the result for uncorrelated antennas to understand the optimal precoding for this special case, which is equal power allocation. Then, the impact of correlation is characterized using Majorization theory. Surprisingly for small SNR, spatial correlation increases the secret key rate. For high SNR, the maximum secret key rate is achieved for uncorrelated antennas. The results indicate that a solid system design for reciprocal MIMO key generation is required to establish the secret key rate gains.
There is growing interest in physical-layer key generation schemes that provide very strong or even perfect security in wireless communication systems. One such scheme is reciprocal channel key generation, where two nodes quantize reciprocal channel state information to generate keys. Although the use of multiple-input multiple-output (MIMO) techniques is interesting in this case since the number of random parameters available for rapid key generation is increased, MIMO techniques may also provide more information to an eavesdropper. This work presents a new MIMO measurement campaign performed in LOS and NLOS indoor environments that studies the correlation of the channel between legitimate users with the eavesdropper channel, revealing what key generation rates can be attained in practice and what fraction of generated key bits are safe from eavesdroppers. The effect of eavesdropper separation, number of antennas, eavesdropper advantage, and covariance separability are studied.