Secrecy in an adversarial environment is an essential criterion in modern communication systems. Wireless communications is vulnerable to eavesdropping due to its broadcasting nature. If secrecy requirements are combined with active attacks on communication systems, the Arbitrarily Varying Wiretap Channel is the correct channel model.
We investigate the effects of constraints on the channel input and channel states with respect to secrecy capacities, [1]. Furthermore, we consider cases where the jammer possesses additional information about the channel input, [2]. We are able to describe situations in which a communication system is hacked and eavesdropped and provide information theoretical answers to the question, how much information can be transmitted reliably and securely.
For Gaussian wiretap channels, [3], if the channel gains of the legitimate's and eavesdropper's channels are perfectly known to the transmitter, the secrecy capacity has been proven. We have investigated the case when only the statistics of the channels are known at the transmitter, which is an open problem in general. By applying the tools from coupling and copulas, we have derived the sufficient condition on the fading distributions that leads to an explicit ergodic secrecy capacity expression, [4]. The underlying spirit is, we obtain an equivalent channel by changing the joint distribution in such a way that it now satisfies a certain information theoretic order while ensuring that the marginal distributions of the channels to the different users are not changed. The construction of this equivalent channel allows us to directly make use of existing capacity results.
In order to make a warden Willie unaware of the existence of meaningful communications between two communication partners, Alice and Bob, there have been different schemes proposed including covert and stealth communications. When Alice and Bob have no channel advantage over Willie, they may need additional secret keys to confuse him. However, secret key generation (SKG) may raise Willie's attention. To prevent Willie's attention, we consider the source model for SKG, which has further to fulfill a stealth constraint, [5]. If the stochastic dependence between Alice and Bob fulfill the more capable criterion with respect to the stochastic dependence between Alice and Willie, then the stealthy secret key rate is identical to the one without the stealth constraint. If the stochastic dependence forms a Markov chain, then the key capacity of the source model SKG is equal to the key capacity without stealth constraint. For fast fading models, a sufficient condition for the existence of an equivalent model which is degraded, is provided, based on stochastic orders.
[1] C. R. Janda, M. Wiese, J. Nötzel, H. Boche and E. A. Jorswieck, "Wiretap-channels under constrained active and passive attacks," 2015 IEEE Conference on Communications and Network Security (CNS), 2015, pp. 16-21.
[2] C. R. Janda, E. A. Jorswieck, M. Wiese and H. Boche, "Arbitrarily Varying Wiretap Channels with Non-Causal Side Information at the Jammer," 2020 IEEE International Symposium on Information Theory (ISIT), 2020, pp. 938-943.
[3] P.-H. Lin and E. A. Jorswieck, On the Fast Fading Gaussian Wiretap Channel with Statistical Channel State Information at Transmitter, IEEE Transactions on Information Forensics and Security, Vol. 11, No. 1, pp 46-58, Jan. 2016
[4] P.-H. Lin, E. A. Jorswieck, R. F. Schaefer, M. Mittelbach and C. R. Janda, New Capacity Results for Fading Gaussian Multiuser Channels with Statistical CSIT, IEEE Trans. on Communications, Vol. 68, No. 11, pp 6761-6774, Nov. 2020.
[5] P.-H. Lin, C. R. Janda, R. F. Schaefer, and E. A. Jorswieck, Stealthy secret key generation, the Entropy Journal, special issue on Wireless Networks: Information Theoretic Perspectives, Vol. 22, No. 6, June, 2020
