Common Source Of Randomness Research Articles

Privacy Amplification Strategies in Sequential Secret Key Distillation Protocols Based on Machine Learning

It is well known that Renyi’s entropy of order 2 determines the maximum possible length of the distilled secret keys in sequential secret key distillation protocols so that no information is leaked to the eavesdropper. There have been no attempts to estimate this key quantity based on information available to the legitimate parties to this protocol in the literature. We propose a new machine learning system, which estimates the lower bound of conditional Renyi entropy with high accuracy, based on 13 characteristics locally measured on the side of legitimate participants. The system is based on a prediction intervals deep neural network, trained for a given source of common randomness. We experimentally evaluated this result for two different sources, namely 14 and 6-dimensional EEG signals, of 50 participants, with varying advantage distillation and information reconciliation strategies with and without additional lossless compression block. Across all proposed systems and analyzed sources on average, the best machine learning strategy, called the hybrid strategy, increases the quantity of generated keys 2.77 times compared to the classical strategy. By introducing the Huffman lossless coder before the PA block, the loss of potential source randomness was reduced from 68.48% to a negligible 0.75%, while the leakage rate per one bit remains in the order of magnitude 10−4.

Hardware-Impaired PHY Secret Key Generation With Man-in-the-Middle Adversaries

In this letter, we examine the PHY layer secret key generation (PHY-SKG) scheme in the presence of man-in-the-middle (MiM) adversary, while legitimate parties suffer from <i>hardware impairments</i> (HIs). Different from previous works on PHY-SKG that consider adversaries who simply try to make an interference in the communication link, the MiM aims to deceive legitimate entities about the source of common randomness. To conquer the MiM attack, legitimate parties utilize randomized pilots (RPs) in our proposed scheme. We analyze the effect of HIs on the performance of system by deriving the achievable secret key rate (SKR). Our results highlight a fundamental limit, as a ceiling phenomena, on the SKR when having practical imperfections. Top-level guidelines for selecting impairment levels along the transceiver chains is also provided to maximize the performance of the PHY-SKG protocol. Our numerical results verify the analytic expressions derived, while providing insights on system design. We show that by properly considering the HIs, about 25&#x0025; improvement in the SKR is achievable.

Protokoli za ustanovljavanje tajnih simetričnih ključeva - savremen pristup

Introduction/purpose: The problem of efficient distribution of cryptographic keys in communication systems has existed since its first days and is especially emphasized by the emergence of mass communication systems. Defining and implementing efficient protocols for symmetric cryptographic keys establishment in such circumstances is of great importance in raising information security in cyberspace. Methods: Using the methods of Information Theory and Secure Multiparty Computation, protocols for direct establishment of cryptographic keys between communication parties have been defined. Results: The paper defines two new approaches to the problem of establishing cryptographic keys. The novelty in the protocol defined in the security model based on information theory is based on the source of common randomness, which in this case is the EEG signal of each subject participating in the communication system. Experimental results show that the amount of information leaking to the attacker is close to zero. A novelty in the second case, which provides security with keys at the level of computer security by applying Secure Multiparty Computation, is in the new application field, namely generation and distribution of symmetric cryptographic keys. It is characteristic of both approaches that within the framework of formal theories, it is possible to draw conclusions about their security characteristics in a formal way. Conclusions: The paper describes two new approaches for establishing cryptographic keys in symmetric cryptographic systems with experimental results. The significance of the proposed solutions lies in the fact that they enable the establishment of secure communication between communication parties from end to end, avoiding the influence of a trusted third party. In that way, the achieved communication level security significantly increases in relation to classical cryptographic systems.

Shared Secret Key Generation by Exploiting Inaudible Acoustic Channels

To build a secure wireless networking system, it is essential that the cryptographic key is known only to the two (or more) communicating parties. Existing key extraction schemes put the devices into physical proximity and utilize the common inherent randomness between the devices to agree on a secret key, but they often rely on specialized hardware (e.g., the specific wireless NIC model) and have low bit rates. In this article, we seek a key extraction approach that only leverages off-the-shelf mobile devices, while achieving significantly higher key generation efficiency. The core idea of our approach is to exploit the fast varying inaudible acoustic channel as the common random source for key generation and wireless parallel communication for exchanging reconciliation information to improve the key generation rate. We have carefully studied and validated the feasibility of our approach through both theoretical analysis and a variety of measurements. We implement our approach on different mobile devices and conduct extensive experiments in different real scenarios. The experiment results show that our approach achieves high efficiency and satisfactory robustness. Compared with state-of-the-art methods, our approach improves the key generation rate by 38.46% and reduces the bit mismatch ratio by 42.34%.

Atmospheric Turbulence-Controlled Cryptosystems

To overcome the limitations of QKD, post-quantum cryptography, and computational security-based cryptography protocols in this paper, an atmospheric turbulence-controlled cryptosystem is proposed. The proposed encryption scheme employs the traditional scheme to utilize the atmospheric turbulence as the common source of randomness only in the initialization stage to determine the common parameters to be used in the proposed encryption scheme. To overcome low secret-key rates of traditional scheme, dictated by the long coherence time Tc of turbulence channel, the proposed encryption scheme updates the parameters of gamma-gamma distribution, used to generate irradiance samples for cumulative distribution function-based determination of the key, every Tc seconds and as such the final key is shaped by the atmospheric turbulence channel. We also describe a scheme that randomly selects one of several available paths in which the simultaneously measured irradiance samples, after interleaving, are used to generate the raw key. The secret-key rates of the proposed schemes are orders of magnitude higher compared to corresponding traditional QKD and source type physical-layer security schemes and are comparable with the state-of-the-art optical communication data rates.

Group Secret-Key Generation Using Algebraic Rings in Wireless Networks

It is well known that physical-layer Group Secret-Key (GSK) generation techniques allow multiple nodes of a wireless network to synthesize a common secret-key, which can be subsequently used to keep their group messages confidential. As one of its salient features, the wireless nodes involved in physical-layer GSK generation extract randomness from a subset of their wireless channels, referred as the common source of randomness (CSR). Unlike two-user key generation, in GSK generation, some nodes must act as facilitators by broadcasting quantized versions of the linear combinations of the channel realizations, so as to assist all the nodes to observe a CSR. However, we note that broadcasting linear combination of channel realizations incurs non-zero leakage of the CSR to an eavesdropper, and moreover, quantizing the linear combination also reduces the overall key-rate. Identifying these issues, we propose a practical GSK generation protocol, referred to as Algebraic Symmetrically Quantized GSK (A-SQGSK) protocol, in a network of three nodes, wherein due to quantization of symbols at the facilitator, the other two nodes also quantize their channel realizations, and use them appropriately over algebraic rings to generate the keys. First, we prove that the A-SQGSK protocol incurs zero leakage to an eavesdropper. Subsequently, on the CSR provided by the A-SQGSK protocol, we propose a consensus algorithm among the three nodes, called the Entropy-Maximization Error-Minimization (EM-EM) algorithm, which maximizes the entropy of the secret-key subject to an upper-bound on the mismatch-rate. We use extensive analysis and simulation results to lay out guidelines to jointly choose the parameters of the A-SQGSK protocol and the EM-EM algorithm.

The Causal Effect of Service Satisfaction on Customer Loyalty

We propose an instrumental-variable (IV) approach to estimate the causal effect of service satisfaction on customer loyalty by exploiting a common source of randomness in the assignment of service employees to customers in service queues. Our approach can be applied at no incremental cost by using routine repeated cross-sectional customer survey data collected by firms. The IV approach addresses multiple sources of biases that pose challenges in estimating the causal effect using cross-sectional data: (1) the upward bias from common-methods variance resulting from the joint measurement of service satisfaction and loyalty intent in surveys, (2) the attenuation bias caused by measurement errors in service satisfaction, and (3) the omitted variable bias that may be in either direction. In contrast to the common concern about the upward common-methods bias in estimates using cross-sectional survey data, we find that ordinary-least-squares substantially underestimates the causal effect, suggesting that the downward bias resulting from measurement errors and/or omitted variables is dominant. The underestimation is even more significant with a behavioral measure of loyalty, where there is no common-methods bias. This downward bias leads to significant underestimation of the positive profit impact from improving service satisfaction and can lead to underinvestment by firms in service satisfaction. Finally, we find that the causal effect of service satisfaction on loyalty is greater for more difficult types of services. This paper was accepted by Juanjuan Zhang, marketing.

Jamming-Resilient Frequency Hopping-Aided Secure Communication for Internet-of-Things in the Presence of an Untrusted Relay

In this paper, we propose a light-weight jamming-resistant scheme for the Internet-of-Things (IoT) in 5G networks to ensure high-quality communication in a two-hop cooperative network. In the considered system model, a source communicates with a destination in the presence of an untrusted relay and a powerful multi-antenna adversary jammer. The untrusted relay is an authorized necessary helper who may wiretap the confidential information. Meanwhile, the jammer is an external attacker who tries to damage both the training and transmission phases. Different from traditional frequency hopping spread spectrum (FHSS) techniques that require a pre-determined pattern between communicating nodes, in our scheme, the source and destination enjoy the local observations of the two-hop channels. Then they exploit the measured channel as the source of common randomness to generate shared secret keys. By collecting multiple time slots into a frame, the sequence of channels observed in each frame is utilized to specify the adopted FHSS sequence in the next frame. Based on the derived FHSS sequence from the key generation phase, the source starts to transmit its message supporting by the the destination-assisted cooperative jamming (DACJ) technique which prevents the untrusted relay from discovering the secret message. For the mentioned system model, we present new closed-form expressions for characterizing the achievable secret key rate (SKR) and ergodic secrecy rate (ESR) to highlight the efficiency of our proposed scheme compared to the state-of-the-art. We next determine the optimal power allocation (OPA) between the pilot and data transmission phases that maximizes the ESR performance while escaping from jamming attack. Finally, several numerical examples and discussions are presented to gain engineering insights behind the studied communication scenario.

Stealthy Secret Key Generation.

In order to make a warden, Willie, unaware of the existence of meaningful communications, there have been different schemes proposed including covert and stealth communications. When legitimate users have no channel advantage over Willie, the legitimate users may need additional secret keys to confuse Willie, if the stealth or covert communication is still possible. However, secret key generation (SKG) may raise Willie’s attention since it has a public discussion, which is observable by Willie. To prevent Willie’s attention, we consider the source model for SKG under a strong secrecy constraint, which has further to fulfill a stealth constraint. Our first contribution is that, if the stochastic dependence between the observations at Alice and Bob fulfills the strict more capable criterion with respect to the stochastic dependence between the observations at Alice and Willie or between Bob and Willie, then a positive stealthy secret key rate is identical to the one without the stealth constraint. Our second contribution is that, if the random variables observed at Alice, Bob, and Willie induced by the common random source form a Markov chain, then the key capacity of the source model SKG with the strong secrecy constraint and the stealth constraint is equal to the key capacity with the strong secrecy constraint, but without the stealth constraint. For the case of fast fading models, a sufficient condition for the existence of an equivalent model, which is degraded, is provided, based on stochastic orders. Furthermore, we present an example to illustrate our results.

The Causal Effect of Service Satisfaction on Customer Loyalty

We propose an instrumental-variable (IV) approach to estimate the causal effect of service satisfaction on customer loyalty, by exploiting a common source of randomness in the assignment of service employees to customers in service queues. Our approach can be applied at no incremental cost by using routine repeated cross-sectional customer survey data collected by firms. The IV approach addresses multiple sources of biases that pose challenges in estimating the causal effect using cross-sectional data: (i) the upward bias from common-method variance due to the joint measurement of service satisfaction and loyalty intent in surveys; (ii) the attenuation bias caused by measurement errors in service satisfaction; and (iii) the omitted-variable bias that may be in either direction. In contrast to the common concern about the upward common-method bias in the estimates using cross-sectional survey data, we find that ordinary-least-squares (OLS) substantially underestimates the casual effect, suggesting that the downward bias due to measurement errors and/or omitted variables is dominant. The underestimation is even more significant with a behavioral measure of loyalty--where there is no common methods bias. This downward bias leads to significant underestimation of the positive profit impact from improving service satisfaction and can lead to under-investment by firms in service satisfaction. Finally, we find that the causal effect of service satisfaction on loyalty is greater for more difficult types of services.

Secret Key Generation With Cross Multiplication of Two-Way Random Signals

The secret key generation rate (SKGR) of current physical layer security methods is not high enough for practical requirements. A novel SKG method based on the cross multiplication (XM) of two-way random signals is proposed for TDD-MIMO system. The principle concealed beneath the XM method is found that the XM operation not only derives the common random source for both legitimate partners, but also employs new generated cross-terms due to bilinear operation to provide more measurements of the random source and more secret keys accordingly, which is essentially superior to the existing paired multiplication (PM) method. Then, the theoretical SKGR of two-way random signals is analyzed and it is validated that SKGR is determined by the randomness of the reciprocal channel and the two-way secure transmission rates collectively. Furthermore, SKGR of XM and PM methods are derived in closed-form respectively under infinite antenna condition and the former shows a linear increase with the channel coherence interval, which are also approximately valid for finite antenna. The innovative conclusion means the slow-changing property of some channel environments can be further exploited and the proposed XM method can be applied to solve the low SKGR problem in static or quasi-static channel environment such as IoT. Finally, the simulations verify the theoretical results and show that the XM method achieves several orders of magnitude higher SKGR than the PM method.

A Novel Physical Layer Secure Key Generation and Refreshment Scheme for Wireless Sensor Networks

Physical layer secure key generation (PL-SKG) schemes have received a lot of attention from the wireless security community in recent years because of the potential benefits that they could bring to the security landscape. These schemes aim to strengthen current security protocols by reducing the amount of key material that devices need for deployment. They do this by harnessing the common source of randomness provided by the wireless channel that the physical layer is communicating over. This is of particular importance in wireless sensor networks (WSNs) where resources are particularly scarce and where issues, such as key revocation and recovery make the design of efficient key management schemes extremely difficult. This paper discusses the issues and challenges encountered in the design and implementation of PL-SKG schemes on off-the-shelf WSNs. It then proposes a novel key generation scheme that takes advantage of both the power and simplicity of classic error correcting codes and also the diversity of frequency channels available on 802.15.4 compliant nodes to generate keys from received signal strength readings. This paper shows that our key generation and refreshment scheme can achieve a near 100% key reconciliation rate whilst also providing perfect forward and backward security.

Spatial Signature Modulation: A Novel Secure Modulation Approach for MIMO Wiretap Channel

Security in physical and application layers have been always thought of as a complementary paradigm. In this paper, we argue that potential cooperation between physical and application layers provides several advantages and unique features that are not available in each paradigm by itself. The problem of exchanging confidential messages between nodes, A and B, in the presenceof an active adversary, E, over an insecure MIMO channel is considered. We introduce a double layer spatial signature modulation (SSM) in which the transmitted information is conveyed into the spatial signature of the transmitting antenna array observed by the intended receiver. Meanwhile, any other eavesdropper does not share the same bearing angle of the legitimate receiver obtains infinitesimally small amount of information. Further, to establish a secure link, A and B are required to share a secret common information prior to communication while keeping E ignorant about it. To that end, we introduce a novel physical layer assisted secret key agreement (SKA) protocol that leverages the cooperation between physical and application layer security. Angle of Arrival (AoA) and Angle of Departure (AoD) are physical layer parameters that can be exploited not only for their well performance at low SNR, but also for their contextual meaning that provides security advantages. In the proposed SKA protocol, AoA is explored as a physical mean for message source authentication, meanwhile, AoD is used as a common source of randomness in a smart signal processing approach to generate secret key bits without any extra communication overhead. We show that E can be kept ignorant about the generated key bit stream conditioned on its physical location. This work introduces the notion of physical hardness to an adversary pursuing either active or passive strategy. After establishing a secret common information, we show that the continuous use of AoA as a mean for message source authenticity provides a considerable advantage against active adversary during the message exchange phase. Extending the proposed scheme to a mobile communication environment is also provided. Finally, quantitative analysis for the security gain due to the potential cooperation between physical and application layer security is developed..

Joint Design of Massive MIMO Precoder and Security Scheme for Multiuser Scenarios under Reciprocal Channel Conditions

The exploration of the physical layer characteristics of the wireless channel is currently the object of intensive research in order to develop advanced secrecy schemes that can protect information against eavesdropping attacks. Following this line of work, in this manuscript we consider a massive MIMO system and jointly design the channel precoder and security scheme. By doing that we ensure that the precoding operation does not reduce the degree of secrecy provided by the security scheme. The fundamental working principle of the proposed technique is to apply selective random rotations in the transmitted signal at the antenna level in order to achieve a compromise between legitimate and eavesdropper channel capacities. These rotations use the phase of the reciprocal wireless channel as a common random source between the transmitter and the intended receiver. To assess the security performance, the proposed joint scheme is compared with a recently proposed approach for massive MIMO systems. The results show that, with the proposed joint design, the number of antenna elements does not influence the eavesdropper channel capacity, which is proved to be equal to zero, in contrast to previous approaches.

Robust secret key extraction from channel secondary random process

AbstractThe vast majority of existing secret key generation protocols exploit the inherent randomness of the wireless channel as a common source of randomness. However, independent noise added at the receivers of the legitimate nodes affects the reciprocity of the channel. In this paper, we propose a new simple technique to generate the secret key that mitigates the effect of noise. Specifically, we exploit the estimated channel to generate a secondary random process (SRP) that is common between the two legitimate nodes. We compare the estimated channel gain and phase to a preset threshold. The moving differences between the locations at which the estimated channel gain and phase exceed the threshold are the realization of our SRP. We study the properties of our generated SRP and derive a closed form expression for the probability mass function of the realizations of our SRP. We simulate an orthogonal frequency division multiplexing system and show that our proposed technique provides a drastic improvement in the key bit mismatch rate between the legitimate nodes when compared with the techniques that exploit the estimated channel gain or phase directly. In addition to that, the secret key generated through our technique is longer than that generated by conventional techniques. Moreover, we compute the conditional probabilities used to estimate the secret key capacity. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Unleashing the secure potential of the wireless physical layer: Secret key generation methods

Within the paradigm of physical layer security, a physical layer characteristic is used as a common source of randomness to generate the secret key. This key is then used to encrypt the data to hide information from eavesdroppers. In this paper, we survey the most recent common sources of randomness used to generate the secret key. We present the steps used to extract the secret key from the estimated common source of randomness. We describe the metrics used to evaluate the strength of the generated key. We follow that with a qualitative comparison between different common sources of randomness along with a proposed new direction which capitalizes on hybridization of sources of randomness. We conclude by a discussion about current open research problems in secret key generation.

Secret Information of Wireless Multi-Dimensional Gaussian Channels

Wireless channel reciprocity can be exploited by two users willing to achieve confidential communications over a public channel as a common source of randomness for the generation of a secret key. This paper presents an analytical framework for investigating the amount of secret information that characterizes wireless multi-dimensional Gaussian channels used as source of randomness. The intrinsic secrecy content of wide-sense stationary wireless channels in frequency, time and spatial domains is derived through asymptotic analysis. Some significant case studies are presented, where single and multiple antenna eavesdroppers are considered. In the numerical results, the role of signal-to-noise ratio, spatial correlation, frequency and time selectivity, sampling frequency and imperfect channel reciprocity is investigated.

Analysis of Secret Key Randomness Exploiting the Radio Channel Variability

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.

Secret key generation exploiting Ultra-wideband indoor wireless channel characteristics

Existing algorithms of secret key generation from Ultra-wideband UWB channels mostly exploited received signal strength to extract secret bits, however, this method is limited in key match probability. To investigate the issue, an efficient secret key generation mechanism using multipath relative delay is developed. Furthermore, a statistical characterization of UWB channels for a Chinese residential scenario is studied to simulate the proposed scheme. Simulation results demonstrate that our mechanism can achieve better performance in terms of common secret bit generation compared with the conventional method using received signal strength as a common random source, and the number of multipath proportionally affects key generation rate and key-mismatch probability. Additionally, for the first time, we verify key generation mechanism in both line-of-sight LOS and non-line-of-sight NLOS UWB channels. The results indicate that communicating transceivers have a slightly lower key-mismatch probability in NLOS condition than in LOS condition, as NLOS channels can provide a larger number of multipath. Copyright © 2014 John Wiley & Sons, Ltd.

Secret Key Generation from Common Randomness over Ultra-wideband Wireless Channels

We develop a secret key generation scheme using phase estimation in ultra-wideband (UWB) wireless fading channels. Based on the reciprocity theorem, two terminals extract the phase of the channel as a common random source to generate secret bits. Moreover, we study the secret key rate by a pair of nodes observing correlated sources and communicating to achieve secret key agreement over public communication channels. As our main results, we establish a more practical upper bound from Cramer-Rao bound (CRB) and compare it with a universally theoretical upper bound on the shared maximum key rate from mutual information of correlated random sources. Derivation and numerical examples are presented to demonstrate the bound. Simulation studies are also provided to validate feasibility and efficiency of the proposed scheme.