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Rate Secrecy of Networks with Game Theory Approach

Sadegh Bamohabbat Chafjiri, Mohammad Ali Tebbi, Yasser Karimian

Published Jan 1, 2011• 0 citations
Publisher

Abstract

In this paper, we introduce a three-way discrete memoryless Broadcast channel (T-DMBC) between a transmitter (Alice), a receiver (Bob), and an intruder (Eve). We represent a protocol for secret key establishment (SKE) between Alice and Bob so that Eve can also participate in the second round of the secret key establishment. We assume that the intruder cannot act as an initiator (under the conditions that the FCC acts as a dictator of the game). Thus, any transmission by an intruder as his activity in the first round must not make the protocol vulnerable to the DOS attack. We use the Nash Equilibrium (NE) of the game between the receiver and the intruder to prove that there is no guarantee for achievable secure rate stabilization toward the main receiver by using passive intruder protocols for DMC or 2DMBC. In order to achieve secure rate stabilization, we modify the passive model for the secrecy of 2DMBC with a noise-forwarding strategy and post-computations in a game model.

DOI
10.1115/1.859896.paper172

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In this paper, we introduce a three-way discrete memoryless Broadcast channel (T-DMBC) between a transmitter (Alice), a receiver (Bob), and an intruder (Eve). We represent a protocol for secret key establishment (SKE) between Alice and Bob so that Eve can also participate in the second round of the secret key establishment. We assume that the intruder cannot act as an initiator (under the conditions that the FCC acts as a dictator of the game). Thus, any transmission by an intruder as his activity in the first round must not make the protocol vulnerable to the DOS attack. We use the Nash Equilibrium (NE) of the game between the receiver and the intruder to prove that there is no guarantee for achievable secure rate stabilization toward the main receiver by using passive intruder protocols for DMC or 2DMBC. In order to achieve secure rate stabilization, we modify the passive model for the secrecy of 2DMBC with a noise-forwarding strategy and post-computations in a game model.
Secret Key Establishment (SKE) over a pair of independent Discrete Memoryless Broadcast Channels (DMBCs) was studied in where lower and upper bounds on the secret-key capacity were provided. In this paper, we study the above setup for two cases: (1) the DMBCs have “secrecy potential”, and (2) the DMBCs are stochastically degraded with independent channels. For (1), we propose a simple SKE protocol using the novel Interactive Channel Coding (ICC) method and prove that it achieves the lower bound. For (2), we give a simplified expression for the lower bound and prove that, when one of the legitimate parties sends only i.i.d. variables, the lower bound is tight and the capacity is achieved by a two-round protocol.
A secret-key generation scheme based on a layered broadcasting strategy is introduced for slow-fading channels. In the model considered, Alice wants to share a key with Bob while keeping the key secret from Eve, who is a passive eavesdropper. Both Alice-Bob and Alice-Eve channels are assumed to undergo slow fading, and perfect channel state information (CSI) is assumed to be known only at the receivers during the transmission. In each fading slot, Alice broadcasts a continuum of coded layers and, hence, allows Bob to decode at the rate corresponding to the fading state (unknown to Alice). The index of a reliably decoded layer is sent back from Bob to Alice via a public and error-free channel and used to generate a common secret key. In this paper, the achievable secrecy key rate is first derived for a given power distribution over coded layers. The optimal power distribution is then characterized. It is shown that layered broadcast coding can increase the secrecy key rate significantly compared to single-level coding.
In this work we study the problem of key agreement over a public noiseless channel when Alice, Bob and Charlie observe discrete memoryless sources of an unknown distribution. Alice and Bob want to agree on a key KABthat is protected from Charlie. At the same time, Alice and Charlie want to agree on a key KACthat is protected from Bob. In order to construct codebooks for the key agreement, Alice has to know how the sources are distributed. Therefore, she requests Bob and Charlie to send her sufficient information about their observations. We also assume that Bob and Charlie, besides agreeing with Alice on the keys, want to learn as much as possible about the other user's key: we call this quantity the leakage. We model these reports by having Bob and Charlie select discrete memoryless channels and passing their true observations through them. We approach this problem from a game-theoretic point of view. For a class of Bob and Charlie's objective functions which are linear in the key rate and the leakage rate, we characterize a Nash equilibrium. Also, we propose a strategy that Alice can apply in order to ensure that Bob and Charlie's honest reporting is a Nash equilibrium.
Abstract. We study the problem of unconditionally secure Secret Key Establishment (SKE) when Alice and Bob are connected by two noisy channels in opposite directions, and the channels are eavesdropped by Eve. We consider the case that Alice and Bob do not have any sources of initial randomness at their disposal. We start by discussing special cases of interest where SKE is impossible, and then provide a simple SKE construction over a binary symmetric channel that achieves some rates of secret key. We next focus on the Secret Key (SK) capacity, i.e., the highest rate of secure and reliable key establishment (in bits per channel use) that the parties can achieve. Relying on the existence of capacity-achieving coding schemes, we propose a multi-round SKE protocol, called the main protocol, that proves a lower bound on the SK capacity. The main protocol consists of an initialization round, followed by repeated use of a two-round SKE protocol, called the basic protocol. We also provide an upper bound on the SK capacity and show that the two bounds coincide when channels do not leak information to the adversary. We apply the results to the case that communicants are connected by binary symmetric channels. 1
A secret-key sharing strategy based on layered broadcast coding is introduced for slow fading channels. In the model considered, Alice wants to share a key with Bob while keeping the key secret from a passive eavesdropper, Eve. Both Alice-Bob and Alice-Eve channels are assumed to undergo slow fading, and perfect channel state information (CSI) is assumed to be known only at the receivers during the transmission. Layered coding facilitates adapting the reliably decoded rate at Bob to the actual channel state without CSI available at Alice. The index of a reliably decoded layer is sent back to Alice via a public and error-free channel, which is exploited by Alice and Bob to generate the secret key. In this paper, the secrecy key rate is derived. In addition, the optimal power distribution over coded layers is characterized. It is shown that layered coding can increase the secrecy key rate significantly compared with single-level coding.