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

Analysis of Symmetric Key Establishment Based on Reciprocal Channel Quantization

David M. Wagner

Published Jan 1, 2010• 1 citation
OpenAlex

Abstract

Methods of symmetric key establishment using reciprocal quantization of channel parameters in wireless Rayleigh and Rician fading channels are considered. Two important aspects are addressed through generic analysis: impact of a proximity attack by a passive eavesdropper and achievable key establishing rates. The analysis makes use of the National Institute of Standards and Technology statistical test suite applied to the channel quantization bits as the outputs of a random number generator. For proximity attacks, a passive mobile eavesdropper with an ability to approach one of the communicating parties and a possible signal-to-noise ratio advantage is assumed. The minimal required distance from the eavesdropper in order to maintain perfect secrecy during key establishment is evaluated as a function of the Rician factor and quantization depth. For key establishing rates, the maximal rates are evaluated while ensuring that the generated secret key bits pass the entire statistical test suite. The generic analysis is applied to channel-phase quantization and performance in practical systems is considered as well.

Related papers

Threshold Constraints on Symmetric Key Extraction from Rician Fading Estimates

Gill R. Tsouri, David M. Wagner

Symmetric key establishment using reciprocal quantization of channel estimates in wireless Rician fading environments is considered. The quantization bits from channel-phase and channel-amplitude are treated as the output of a random number generator. We determine threshold constraints on the required minimal distance of the legitimate communicating parties from a passive eavesdropper, and determine threshold constraints on maximal key establishing rates. The analysis makes use of widely accepted statistical test suites applied to the generated bit streams along with a lemma we define and prove. For distance analysis, the minimal required distance from the eavesdropper to maintain perfect secrecy during key establishment is derived. For key establishing rates, the maximal rates are derived while ensuring the generated bits streams pass the statistical test suites. The work results in generic and clear threshold requirements on distance and rates as function of the Rician factor and quantization bit for any transmission frequency. Clear thresholds are useful for systems operating in a-priori known or estimated propagation environments. In addition, we address the effect of imperfect channel reciprocity on key agreement. Results show practical systems can operate under reciprocal and secure conditions, and that channel-phase estimates perform better than channel-amplitude estimates.

IEEE Transactions on Mobile Computing•Oct 24, 2012•18 citations

Analysis of Secret Key Randomness Exploiting the Radio Channel Variability

Taghrid Mazloum, Alain Sibille

A few years ago, physical layer based techniques have started to be considered as a way to improve security in wireless communications. A well known problem is the management of ciphering keys, both regarding the generation and distribution of these keys. A way to alleviate such difficulties is to use a common source of randomness for the legitimate terminals, not accessible to an eavesdropper. This is the case of the fading propagation channel, when exact or approximate reciprocity applies. Although this principle has been known for long, not so many works have evaluated the effect of radio channel properties in practical environments on the degree of randomness of the generated keys. To this end, we here investigate indoor radio channel measurements in different environments and settings at either 2.4625 GHz or 5.4 GHz band, of particular interest for WIFI related standards. Key bits are extracted by quantizing the complex channel coefficients and their randomness is evaluated using the NIST test suite. We then look at the impact of the carrier frequency, the channel variability in the space, time, and frequency degrees of freedom used to construct a long secret key, in relation to the nature of the radio environment such as the LOS/NLOS character.

International Journal of Antennas and Propagation•Jan 1, 2015•3 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

A practical wireless reciprocity-aware key establishment protocol

Satya Prakash Ponnaluri, Babak Azimi-Sadjadi, Yik‐Kiong Hue +3 more

Practical generation of secret bits using wireless channel measurements between two terminals is presented in this paper. The model used for this implementation assumes imperfect reciprocity between the channel measurements made by the two terminals in the presence of a passive eavesdropper. The channel measurements (e.g., received signal strength values) are used to estimate the secret key rate in order to establish the number of secret bits that can be generated between any two terminals. The main contributions of this paper are: 1) algorithm to generate uncorrelated channel measurements even when channel measurement statistics between the two terminals are time-varying; 2) development of a reconciliation algorithm based on BCH codes, where the statistics of error between bits generated by the two terminals is not known a priori; and 3) implementation of secret bit generation using channel reciprocity in a Linux environment. The channel measurement data that was collected for this paper is available at http://downloads.i-a-i.com/RAPOR.

IEEE Military Communications Conference (MILCOM)•Nov 1, 2016•3 citations

Physical layer key generation methods for arbitrary fading channels

R. K. Sharma, Jon W. Wallace

Two methods are developed that can be applied to generate secret keys automatically from fading propagation channels that are reciprocal but have arbitrary (i.e. non Gaussian) statistics. Such methods may be necessary for physical-layer key generation in cases where the line-of-sight (LOS) component produces Rician channel statistics, not only because channel quantization based on Gaussian statistics will not provide equally probable symbols, but also because the symbol error rate (SER) and efficiency analysis based on Gaussian channels does not reflect true performance. An improved channel quantization method compared to [1], [2] is developed, where the empirical cumulative distribution function (cdf) of the channel is used directly to ensure equal probability of the key symbols. The results show that LOS channels can have slightly better SER performance than strictly Gaussian channels, especially at low SNR. Second, the idea of positional coding is developed, where a secret key can be transmitted by dividing empirical channel observations into multiple codewords and conveying a secret message from Alice to Bob in the sequence of channels fed forward from Alice to Bob. Analysis of the method illustrates that key mismatch rate can be made arbitrarily low by properly selecting the codeword length.

•Jul 1, 2011•5 citations

Secret key establishment using wireless channels as common randomness in time-variant MIMO systems

Chan Chen

Encryption of confidential data with a secret key has become a widespread technique for securing wireless transmissions. However, existing key distribution methods that either deliver the secret key with a key distribution center or exchange the secret key using public-key cryptosystems are unable to establish perfect secret keys necessary for symmetric encryption techniques. This research considers secret key establishment, under the broad research area of information theoretic security, using the reciprocal wireless channel as common randomness for the extraction of perfect secret keys in multiple-input multiple-output (MIMO)communication systems. The presentation discusses the fundamental characteristics of the time-variant MIMO wireless channel and establishes a realistic channel simulation model useful for assessing key establishment algorithms. Computational examples show the accuracy and applicability of the model. The discussion then turns to an investigation of the influence of the spatial and temporal correlation of the channel coefficients on the bound of the key size generated from the common channel, and it is found that a sampling approach exists that can generate a key using the minimum sampling time. A practical key generation protocol is then developed based on an enhancement of a published channel coefficient quantization method that incorporates flexible quantization levels, public transmission of the correlation eigenvector matrix and low-density parity-check (LDPC) coding to improve key agreement. This investigation leads to the development of improved channel quantization techniques that dynamically shift the quantization boundaries at one node based on the information provided by the other node. Analysis based on a closed-form bound for the key error rate (KER) and simulations based on the channel model and measurement data show that the enhanced algorithms are able to dramatically reduce key mismatch and asymptotically approach the KER bound. Finally, other secret key generation algorithms based on channel-encryption rather than quantization are discussed, leading to a new concept for secret key generation using the common wireless channel.

•Jan 1, 2010•3 citations
Methods of symmetric key establishment using reciprocal quantization of channel parameters in wireless Rayleigh and Rician fading channels are considered. Two important aspects are addressed through generic analysis: impact of a proximity attack by a passive eavesdropper and achievable key establishing rates. The analysis makes use of the National Institute of Standards and Technology statistical test suite applied to the channel quantization bits as the outputs of a random number generator. For proximity attacks, a passive mobile eavesdropper with an ability to approach one of the communicating parties and a possible signal-to-noise ratio advantage is assumed. The minimal required distance from the eavesdropper in order to maintain perfect secrecy during key establishment is evaluated as a function of the Rician factor and quantization depth. For key establishing rates, the maximal rates are evaluated while ensuring that the generated secret key bits pass the entire statistical test suite. The generic analysis is applied to channel-phase quantization and performance in practical systems is considered as well.
Symmetric key establishment using reciprocal quantization of channel estimates in wireless Rician fading environments is considered. The quantization bits from channel-phase and channel-amplitude are treated as the output of a random number generator. We determine threshold constraints on the required minimal distance of the legitimate communicating parties from a passive eavesdropper, and determine threshold constraints on maximal key establishing rates. The analysis makes use of widely accepted statistical test suites applied to the generated bit streams along with a lemma we define and prove. For distance analysis, the minimal required distance from the eavesdropper to maintain perfect secrecy during key establishment is derived. For key establishing rates, the maximal rates are derived while ensuring the generated bits streams pass the statistical test suites. The work results in generic and clear threshold requirements on distance and rates as function of the Rician factor and quantization bit for any transmission frequency. Clear thresholds are useful for systems operating in a-priori known or estimated propagation environments. In addition, we address the effect of imperfect channel reciprocity on key agreement. Results show practical systems can operate under reciprocal and secure conditions, and that channel-phase estimates perform better than channel-amplitude estimates.
A few years ago, physical layer based techniques have started to be considered as a way to improve security in wireless communications. A well known problem is the management of ciphering keys, both regarding the generation and distribution of these keys. A way to alleviate such difficulties is to use a common source of randomness for the legitimate terminals, not accessible to an eavesdropper. This is the case of the fading propagation channel, when exact or approximate reciprocity applies. Although this principle has been known for long, not so many works have evaluated the effect of radio channel properties in practical environments on the degree of randomness of the generated keys. To this end, we here investigate indoor radio channel measurements in different environments and settings at either 2.4625 GHz or 5.4 GHz band, of particular interest for WIFI related standards. Key bits are extracted by quantizing the complex channel coefficients and their randomness is evaluated using the NIST test suite. We then look at the impact of the carrier frequency, the channel variability in the space, time, and frequency degrees of freedom used to construct a long secret key, in relation to the nature of the radio environment such as the LOS/NLOS character.
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.
Practical generation of secret bits using wireless channel measurements between two terminals is presented in this paper. The model used for this implementation assumes imperfect reciprocity between the channel measurements made by the two terminals in the presence of a passive eavesdropper. The channel measurements (e.g., received signal strength values) are used to estimate the secret key rate in order to establish the number of secret bits that can be generated between any two terminals. The main contributions of this paper are: 1) algorithm to generate uncorrelated channel measurements even when channel measurement statistics between the two terminals are time-varying; 2) development of a reconciliation algorithm based on BCH codes, where the statistics of error between bits generated by the two terminals is not known a priori; and 3) implementation of secret bit generation using channel reciprocity in a Linux environment. The channel measurement data that was collected for this paper is available at http://downloads.i-a-i.com/RAPOR.
Two methods are developed that can be applied to generate secret keys automatically from fading propagation channels that are reciprocal but have arbitrary (i.e. non Gaussian) statistics. Such methods may be necessary for physical-layer key generation in cases where the line-of-sight (LOS) component produces Rician channel statistics, not only because channel quantization based on Gaussian statistics will not provide equally probable symbols, but also because the symbol error rate (SER) and efficiency analysis based on Gaussian channels does not reflect true performance. An improved channel quantization method compared to [1], [2] is developed, where the empirical cumulative distribution function (cdf) of the channel is used directly to ensure equal probability of the key symbols. The results show that LOS channels can have slightly better SER performance than strictly Gaussian channels, especially at low SNR. Second, the idea of positional coding is developed, where a secret key can be transmitted by dividing empirical channel observations into multiple codewords and conveying a secret message from Alice to Bob in the sequence of channels fed forward from Alice to Bob. Analysis of the method illustrates that key mismatch rate can be made arbitrarily low by properly selecting the codeword length.
Encryption of confidential data with a secret key has become a widespread technique for securing wireless transmissions. However, existing key distribution methods that either deliver the secret key with a key distribution center or exchange the secret key using public-key cryptosystems are unable to establish perfect secret keys necessary for symmetric encryption techniques. This research considers secret key establishment, under the broad research area of information theoretic security, using the reciprocal wireless channel as common randomness for the extraction of perfect secret keys in multiple-input multiple-output (MIMO)communication systems. The presentation discusses the fundamental characteristics of the time-variant MIMO wireless channel and establishes a realistic channel simulation model useful for assessing key establishment algorithms. Computational examples show the accuracy and applicability of the model. The discussion then turns to an investigation of the influence of the spatial and temporal correlation of the channel coefficients on the bound of the key size generated from the common channel, and it is found that a sampling approach exists that can generate a key using the minimum sampling time. A practical key generation protocol is then developed based on an enhancement of a published channel coefficient quantization method that incorporates flexible quantization levels, public transmission of the correlation eigenvector matrix and low-density parity-check (LDPC) coding to improve key agreement. This investigation leads to the development of improved channel quantization techniques that dynamically shift the quantization boundaries at one node based on the information provided by the other node. Analysis based on a closed-form bound for the key error rate (KER) and simulations based on the channel model and measurement data show that the enhanced algorithms are able to dramatically reduce key mismatch and asymptotically approach the KER bound. Finally, other secret key generation algorithms based on channel-encryption rather than quantization are discussed, leading to a new concept for secret key generation using the common wireless channel.