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arXiv:2111.15046

A Secure Key Sharing Algorithm Exploiting Phase Reciprocity in Wireless Channels

Shayan Mohajer Hamidi, Amir Keyvan Khandani, E. Bateni

Published Nov 30, 2021• 3 citations
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Abstract

This article presents a secure key exchange algorithm that exploits reciprocity in wireless channels to share a secret key between two nodes $A$ and $B$. Reciprocity implies that the channel phases in the links $A\rightarrow B$ and $B\rightarrow A$ are the same. A number of such reciprocal phase values are measured at nodes $A$ and $B$, called shared phase values hereafter. Each shared phase value is used to mask points of a Phase Shift Keying (PSK) constellation. Masking is achieved by rotating each PSK constellation with a shared phase value. Rotation of constellation is equivalent to adding phases modulo-$2π$, and as the channel phase is uniformly distributed in $[0,2π)$, the result of summation conveys zero information about summands. To enlarge the key size over a static or slow fading channel, the Radio Frequency (RF) propagation path is perturbed to create several independent realizations of multi-path fading, each used to share a new phase value. To eavesdrop a phase value shared in this manner, the Eavesdropper (Eve) will always face an under-determined system of linear equations which will not reveal any useful information about its actual solution value. This property is used to establish a secure key between two legitimate users.

DOI
10.48550/arxiv.2111.15046

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This article presents a secure key exchange algorithm that exploits reciprocity in wireless channels to share a secret key between two nodes AAA and BBB. Reciprocity implies that the channel phases in the links A→BA\rightarrow BA→B and B→AB\rightarrow AB→A are the same. A number of such reciprocal phase values are measured at nodes AAA and BBB, called shared phase values hereafter. Each shared phase value is used to mask points of a Phase Shift Keying (PSK) constellation. Masking is achieved by rotating each PSK constellation with a shared phase value. Rotation of constellation is equivalent to adding phases modulo-2π2π2π, and as the channel phase is uniformly distributed in [0,2π)[0,2π)[0,2π), the result of summation conveys zero information about summands. To enlarge the key size over a static or slow fading channel, the Radio Frequency (RF) propagation path is perturbed to create several independent realizations of multi-path fading, each used to share a new phase value. To eavesdrop a phase value shared in this manner, the Eavesdropper (Eve) will always face an under-determined system of linear equations which will not reveal any useful information about its actual solution value. This property is used to establish a secure key between two legitimate users.
This article presents a practical approach for secure key exchange exploiting reciprocity in wireless transmission. The method relies on the reciprocal channel phase to mask points of a Phase Shift Keying (PSK) constellation. Masking is achieved by adding (modulo 2π) the measured reciprocal channel phase to the PSK constellation points carrying some of the key bits. As the channel phase is uniformly distributed in [0, 2π], knowing the sum of the two phases does not disclose any information about any of its two components. To enlarge the key size over a static or slow fading channel, the Radio Frequency (RF) propagation path is perturbed to create independent realizations of multi-path fading. Prior techniques have relied on quantizing the reciprocal channel state measured at the two ends and thereby suffer from information leakage in the process of key consolidation (ensuring the two ends have access to the same key). The proposed method does not suffer from such shortcomings as raw key bits can be equipped with Forward Error Correction (FEC) without affecting the masking (zero information leakage) property. To eavesdrop a phase value shared in this manner, the Eavesdropper (Eve) would require to solve a system of linear equations defined over angles, each equation corresponding to a possible measurement by the Eve. Channel perturbation is performed such that each new channel state creates an independent channel realization for the legitimate nodes, as well as for each of Eves antennas. As a result, regardless of the Eves Signal-to-Noise Ratio (SNR) and number of antennas, Eve will always face an under-determined system of equations. On the other hand, trying to solve any such under-determined system of linear equations in terms of an unknown phase will not reveal any useful information about the actual answer, meaning that the distribution of the answer remains uniform in [0, 2π].
A less expensive and more flexible solution to the problem of sharing secret keys between wireless nodes is to use the inherent randomness in the wireless channel between them as the source for extracting bits of the secret key between these nodes. We propose a new secret key distribution approach that utilizes the uniformly distributed phase information of channel responses to extract shared cryptographic keys under narrowband multipath fading models. Compared to existing approaches which only support pair wise key distribution, our scheme is highly scalable and can support efficient group key distribution. Various key distribution schemes are appraised to determine the level of security and connectivity. Simulated results show that key distribution exploiting channel phase has improved resilience against node capture. them as the source for extracting bits of the secret key between these nodes. Shared secret key distribution from channel measurements is an application which benefits from the randomnessof the multipath channel. It would not, for example, work in a truly free-space environment (such as deep space radio links). Secret sharing benefits from: • Reciprocity of the wireless radio channel: The multipath properties of the radio channel (gains, phase shifts, and delays) at any point in time and on any given frequency channel are identical on both directions of the link. • Temporal variations in the radio channel: Over time, the multipath channel changes due to movement of either end of the link, and any motion of people and objects in the environment near the link. An application may specifically request a user to move or shake the wireless device in order to generate more temporal variation. • Spatial variations: The properties of the radio channel are unique to the locations of the two endpoints of the link. An eavesdropper at a third location more than a few wavelengths from either endpoint will measure a different, uncorrelated radio channel. The proposed scheme is more flexible and can be applied in both static and mobile environments. Our scheme introduces phase randomness to bit distribution and removes the reliance on node mobility to obtain high entropy bits. We evaluate the proposed schemes through both analytical and simulation studies. The parameters of the scheme can be selected such that a desired level of key distribution accuracy and reliability is achieved with high efficiency.
Now-a-days, secure communication is a significant characteristic that should be proficient to accommodate increasing demand of wireless communication. The fundamental principle of secure communication is the extraction of secret key and keeping this secret. In this paper, we propose innovative approach for secret key extraction and reconciliation. We exploit channel reciprocity through relative calibration and use this reciprocal channel as a secret key between two legitimate users. In this method, there is no physical sharing of key between users so that eavesdropper could not interfere the confidential communication. We also prove that this algorithm is more secure as compare to other algorithms. We use AES algorithm for reconciliation of secret key for secure communication.
Due to the broadcast nature of wireless channels, wireless communication is vulnerable to eavesdropping, message modification, and node impersonation. Securing the wireless communication requires the shared secret keys between the communicating entities. Traditional security schemes rely on public key infrastructures and cryptographic algorithms to manage secret keys. Recently, many physical-layer-based methods have been proposed as alternative solutions for key generation in wireless networks. These methods exploit the inherent randomness of the wireless fading channel to generate secret keys while providing information-theoretical security without intensive cryptographic computations. This article provides an overview of the existing PHY-based key generation schemes exploiting the randomness of the wireless channels. Specifically, we first introduce the fundamental and general framework of the PHY-based key generation schemes and then categorize them into two classes: received-signal-strength-based and channel- phase-based protocols. Finally, we present a performance comparison of them in terms of key disagreement probability, key generation rate, key bit randomness, scalability, and implementation issues.
New approaches that generate secret keys from radio channel characteristics have been recently proposed. The security of these schemes usually relies on the reciprocity principle which states that the channel fluctuations can be a source of common randomness for two communicating peers and these fluctuations can't be measured by any eavesdropper. A validation of these properties for indoor environments is presented in this work. The shared keys are created by measuring the reciprocal channel features and converting this information to binary vectors using a quantization algorithm. This paper addresses the problem of quantization. It identifies an important weakness of existing key generation algorithms and it shows that the secret bits extraction has a significant impact on the robustness and security of these algorithms. A new adaptive quantization algorithm for secret key generation is presented. This method has the advantages to create sufficient long secret keys with a high key agreement ratio between authorized users without revealing information to the attacker. The new scheme is experimentally validated using Ultra Wide Band technology.
Secure wireless communications is a challenging problem due to the shared nature of the wireless medium. Most existing security protocols apply cryptographic techniques for bit scrambling at the application layer by exploiting a shared secret key between pairs of communicating nodes. However, more recent research argues that multipath propagation - a salient feature of wireless channels - provides a physical resource for secure communications. In this context, we propose a protocol that exploits the inherent randomness in multipath wireless channels for generating secret keys through channel estimation and quantization. Our approach is particularly attractive in wideband channels which exhibit a large number of statistically independent degrees of freedom (DoF), thereby enabling the generation of large, more-secure, keys. We show that the resulting keys are distinct for distinct pairwise links with a probability that increases exponentially with the key-size/channel DoF. We also characterize the probability that the two users sharing a common link generate the same key. This characterization is used to analyze the energy consumption in successful acquisition of a secret key by the two users. For a given key size, our results show that there is an optimum transmit power, and an optimum quantization strategy, that minimizes the energy consumption. The proposed approach to secret key generation through channel quantization also obviates the problem of key pre-distribution inherent to many existing cryptographic approaches.