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Conference on Information Sciences and Systems

Empirical Bounds on the Rate of Secret Bits Extracted from Received Signal Strength

Sima Azizi, Arash Komaee

Published Mar 1, 2019• 0 citations
Publisher

Abstract

Symmetric cryptography relies on pairs of identical secret keys shared by the legitimate communicating parties. To implement a symmetric-key algorithm for cryptography, a major concern is to develop secure methods for distribution of the secret key. In securing the wireless fading channels by symmetric-key algorithms, the physical layer properties of the channel can be exploited for distribution of the secret keys. In this approach, the channel state provides a common randomness which is shared by the legitimate users but is mostly unknown to an eavesdropper. by means of signal processing techniques, this common randomness is extracted into random secret keys. This paper establishes an information theoretic upper bound on the rate at which the secret keys can be extracted. Instead of the conventional approach that relies on mathematical models for the wireless channel, this paper adopts an experimental approach to estimate this bound from empirical data. A set of signal processing techniques is developed here to numerically estimate this bound for a pair of received signal strength (RSS) recorded by indoor commercial radios.

DOI
10.1109/ciss.2019.8693028

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Symmetric cryptography relies on pairs of identical secret keys shared by the legitimate communicating parties. To implement a symmetric-key algorithm for cryptography, a major concern is to develop secure methods for distribution of the secret key. In securing the wireless fading channels by symmetric-key algorithms, the physical layer properties of the channel can be exploited for distribution of the secret keys. In this approach, the channel state provides a common randomness which is shared by the legitimate users but is mostly unknown to an eavesdropper. by means of signal processing techniques, this common randomness is extracted into random secret keys. This paper establishes an information theoretic upper bound on the rate at which the secret keys can be extracted. Instead of the conventional approach that relies on mathematical models for the wireless channel, this paper adopts an experimental approach to estimate this bound from empirical data. A set of signal processing techniques is developed here to numerically estimate this bound for a pair of received signal strength (RSS) recorded by indoor commercial radios.
Extraction of shared secret keys from random state of multipath fading channels is a growing trend in symmetric cryptography. In this context, an essential question is the rate at which the secret keys can be extracted (number of bits per unit of time). This question is addressed in this paper by establishing an empirical upper bound on the extraction rate of the secret bits. A coherent set of signal processing techniques is proposed to numerically estimate this bound from empirical data generated by commercial radios. It is emphasized to solely rely on empirical data rather than mathematical models of fading channels.
In symmetric cryptography systems have problems in the distribution of secret keys. The two users who will communicate require sharing keys through the public channel. The proposed solution to overcome these problems is to utilize information from the physical layer (e.g. RSS). Received Signal Strength (RSS) is an indicator for measuring the power received by wireless devices. The advantage of secret key extraction using physical layer information from a wireless channel is that it allows both devices within the transmission range to extract the secret key together. In this paper, we propose a secret key generation scheme adopted from an existing scheme with modifications to improve performance. Our proposed system is applied to static and dynamic conditions to test performance. The proposed algorithm is able to obtain a reduction in KDR (Key Disagreement Rate) up to 48.42% and an increase in the KGR (Key Generation Rate) up to 23.35% when compared to the existing scheme. Our proposed system also successfully passed the randomness using the NIST test with the approximate value of entropy generated 0.80 in static conditions and 0.81 in dynamic conditions.
The emergence of Internet of things (IoT) applications brings the challenge of finding lightweight schemes for secret key distribution. A promising solution coming from the physical layer is the so called secret key generation (SKG) from shared randomness. SKG allows two communicating parties to extract the shared randomness already present in wireless channels. This work investigates the achievable SKG rates using received signal strength (RSS) as a key generation parameter. A multi-path scenario is considered and the probability density function of the RSS in different channel conditions is evaluated. Next, through a numerical evaluation, the SKG rates are derived in the form of mutual information (MI) estimates, using a 3GPP standard channel model. The simulations are performed for different values of bandwidth and delay spread. We demonstrate that while both parameters have similar impact on how multi-path components are resolved, their effect on the MI is opposite.
Physical layer security (PLS) techniques hold promise for augmenting secure communications in the 5thgeneration of mobile wireless networks. Secret key generation (SKG) is a PLS technique which exploits the wireless propagation channel's randomness to generate symmetric key bits for information encryption and decryption. This work proposes symmetric key generation based on non-uniform quantization of the received signal strength (RSS) samples of a Nakagami-mmm fading channel. The proposed strategy for non-uniform quantization for SKG aims to set quantization thresholds for maximal key randomness and high values of key generation rate (KGR) and key agreement probability (KAP). Finally, a framework is proposed to use single node RSS measurements, readily available in the literature, to generate RSS samples at the other link end. This framework facilitates the testing of new SKG algorithms that require simultaneous RSS measurements by the legitimate nodes, which are not readily available in the open literature. The effectiveness of the proposed SKG scheme is validated through Monte Carlo methods and the National Institute of Standards and Technology (NIST) test suite for assessing the randomness of the generated key sequence.
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.
We evaluate the effectiveness of secret key extraction, for private communication between two wireless devices, from the received signal strength (RSS) variations on the wireless channel between the two devices. We use real world measurements of RSS in a variety of environments and settings. Our experimental results show that (i) in certain environments, due to lack of variations in the wireless channel, the extracted bits have very low entropy making these bits unsuitable for a secret key, (ii) an adversary can cause predictable key generation in these static environments, and (iii) in dynamic scenarios where the two devices are mobile, and/or where there is a significant movement in the environment, high entropy bits are obtained fairly quickly. Building on the strengths of existing secret key extraction approaches, we develop an environment adaptive secret key generation scheme that uses an adaptive lossy quantizer in conjunction with Cascade-based information reconciliation [7] and privacy amplification [14]. Our measurements show that our scheme, in comparison to the existing ones that we evaluate, performs the best in terms of generating high entropy bits at a high bit rate. The secret key bit streams generated by our scheme also pass the randomness tests of the NIST test suite [21] that we conduct.