Traditional approaches to secret key establishment based on common randomness have been based on certain restrictive assumptions, such as considering the available common randomness to consist of independent and identically distributed (i.i.d) repetitions of correlated random variables. Unfortunately, the i.i.d assumption does not generally reflect the conditions of real-life scenarios. For this reason, the current paper investigates the key-establishment potential of a more pragmatic model, in which all parties have access to imperfect information about a common source modeled as a Markov chain. Each party's information thus comes in the form of a hidden Markov model and, since the different parties share the same underlying Markov chain, we call the overall model a sibling hidden Markov model (SHMM). This paper studies upper and lower bounds on the secret key capacity for various types of SHMM. The difficulty of the problem emerges from its prohibitive computational cost. To address this obstacle, we represent the joint probability of the observations as the L1norm of a Markov random matrix, and use its convergence to a Lyapunov exponent.
Traditional approaches to secret key establishment based on common randomness have been based on certain restrictive assumptions, such as considering the available common randomness to consist of independent and identically distributed (i.i.d) repetitions of correlated random variables. Unfortunately, the i.i.d assumption does not generally reflect the conditions of real-life scenarios. For this reason, the current paper investigates the key-establishment potential of a more pragmatic model, in which all parties have access to imperfect information about a common source modeled as a Markov chain. Each party's information thus comes in the form of a hidden Markov model and, since the different parties share the same underlying Markov chain, we call the overall model a sibling hidden Markov model (SHMM). This paper studies upper and lower bounds on the secret key capacity for various types of SHMM. The difficulty of the problem emerges from its prohibitive computational cost. To address this obstacle, we represent the joint probability of the observations as the L1norm of a Markov random matrix, and use its convergence to a Lyapunov exponent.
Secret key establishment from common randomness has been traditionally investigated under cartain limiting assumptions, of which the most ubiquitous appears to be that the information available to all parties comes in the form of independent and identically distributed (i.i.d.) samples of some correlated random variables. Unfortunately, models employing the i.i.d assumption are often not accurate representations of real scenarios. A more capable model would represent the available information as correlated hidden Markov models (HMMs), based on the same underlying Markov chain. Such a model accurately reflects the scenario where all parties have access to imperfect observations of the same source random process, exhibiting a certain time dependency. In this paper, we derive a computationally-efficient asymptotic converse bound for the secret key capacity of the correlated-HMM scenario. The main obstacle, not only for our model, but also for other non-i.i.d cases, is the computational complexity. We address this by converting the initial bound to a product of Markov random matrices, and using recent results regarding its convergence to a Lyapunov exponent. The methods developed in the paper are easily extensible to derive a secret-key capacity lower bound.
Establishing secret common randomness between two or multiple devices in a network resides at the root of communication security. In its most frequent form of key establishment, the problem is traditionally decomposed into a randomness generation stage (randomness purity is subject to employing often costly true random number generators) and an information-exchange agreement stage, which relies either on public-key infrastructure or on symmetric encryption (key wrapping).\nThis dissertation has been divided into two main parts. In the first part, an algorithm called KERMAN is proposed to establish secret-common-randomness for ad-hoc networks, which works by harvesting randomness directly from the network routing metadata, thus achieving both pure randomness generation and (implicitly) secret-key agreement. This algorithm relies on the route discovery phase of an ad-hoc network employing the Dynamic Source Routing protocol, is lightweight, and requires relatively little communication overhead. The algorithm is evaluated for various network parameters, and different levels of complexity, in OPNET network simulator. The results show that, in just ten minutes, thousands of secret random bits can be generated network-wide, between different pairs in a network of fifty users.\nThe proposed algorithm described in this first part of this research study has inspired study of the problem of generating a secret key\nbased on a more practical model to be explored in the second part of this dissertation. Indeed, secret key establishment from common randomness has been traditionally investigated under certain limiting assumptions, of which the most ubiquitous appears to be that the information available to all parties comes in the form of independent and identically distributed (i.i.d.) samples of some correlated andom variables. Unfortunately, models employing the i.i.d assumption are often not accurate representations of real scenarios. A more capable model would represent the available information as correlated hidden Markov models (HMMs), based on the same underlying Markov chain. Such a model accurately reflects the scenario where all parties have access to imperfect observations of the same source random process, exhibiting a certain time dependency. In the second part of the dissertation , a computationally-efficient asymptotic bounds for the secret key capacity of the correlated-HMM scenario has been derived. The main obstacle, not only for this model, but also for other non-i.i.d cases, is the computational complexity. This problem has been addressed by converting the initial bound to a product of Markov random matrices, and using recent results regarding its convergence to a Lyapunov exponent.
Abstract. We consider secret key agreement by multiple parties observ-ing correlated data and communicating interactively over an insecure communication channel. Our main contribution is a single-shot upper bound on the length of the secret keys that can be generated, with-out making any assumptions on the distribution of the underlying data. Heuristically, we bound the secret key length in terms of “how far ” is the joint distribution of the initial observations of the parties and the eaves-dropper from a distribution that renders the observations of the parties conditionally independent across some partition, when conditioned on the eavesdropper’s side information. The closeness of the two distribu-tions is measured in terms of the exponent of the probability of error of type II for a binary hypothesis testing problem, thus bringing out a structural connection between secret key agreement and binary hypoth-esis testing. When the underlying data consists of an independent and identically distributed sequence, an application of our bound recovers
We study the problem of information-theoretically secure secret key agreement under the well-known source model and channel model. In both of these models, multiple terminals wish to create a shared secret key that is secure from a passive eavesdropper. The terminals have access to a noiseless public communication channel and an additional resource that depends on the model. In the source model, the resource is an external source that repeatedly beams correlated randomness to the terminals; whereas in the channel model, the resource is a secure but noisy discrete memoryless broadcast channel. We derive new lower and upper bounds on the secret key capacity under both the source model and the channel model. The technique used for deriving our bound for the source model is to find certain properties of functions of joint probability distributions which, applied to the joint distribution of the source, will imply that they dominate the secret key capacity, and then prove the bound by a verification argument. A similar technique is used for the channel model. Finally, we also define a problem of communication for omniscience by a neutral observer and establish the equivalence between this new problem and the problem of secret key agreement. This generalizes an earlier result of Csiszár and Narayan.
Abstract—We study the secret-key capacity in a joint source-channel coding setup—the terminals are connected over a discrete memoryless channel and have access to side information, modelled as a pair of discrete memoryless source sequences. As our main result, we establish the upper and lower bounds on the secret-key capacity. In the lower bound expression, the equivocation terms of the source and channel components are functionally additive even though the coding scheme generates a single secret-key by jointly taking into account the source and channel equivocations. Our bounds coincide, thus establishing the capacity, when the underlying wiretap channel can be decomposed into a set of independent, parallel, and reversely degraded channels. For the case of parallel Gaussian channels and jointly Gaussian sources we show that Gaussian codebooks achieve the secret-key capacity. In addition, when the eavesdropper also observes a correlated side information sequence, we establish the secret-key capacity when both the source and channel of the eavesdropper are a degraded version of the legitimate receiver. We finally also treat the case when a public discussion channel is available, propose a separation based coding scheme, and establish its optimality when the channel output symbols of the legitimate receiver and eavesdropper are conditionally independent given the input. Index Terms—Information theoretic security, joint sourcechannel coding, public discussion, secret-key agreement, wiretap channel. I.
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.