# Information Bytes

Matthieu Bloch
School of Electrical and Computer Engineering
Georgia Institute of Technology

# Recent works

1. M. Tahmasbi and M. R. Bloch, “A framework for covert and secret key expansion over quantum channels.” accepted to Physical Review A, Apr. 2019.

Covert and secret quantum key distribution aims at generating information-theoretically secret bits between distant legitimate parties in a manner that remains provably undetectable by an adversary. We propose a framework in which to precisely define and analyze such an operation, and we show that covert and secret key expansion is possible. For fixed and known classical-quantum channels, we develop and analyze protocols based on forward and reverse reconciliation. When the adversary applies the same quantum channel independently on each transmitted quantum state, akin to a collective attack in the quantum key distribution literature, we propose a protocol that achieves covert and secret key expansion under mild restrictions. The crux of our approach is the use of information reconciliation and privacy amplification techniques that are able to process the sparse signals required for covert operation and whose Shannon entropy scales as the square root of their length. In particular, our results show that the coordination required between legitimate parties to achieve covert communication can be achieved with a negligible number of secret key bits.

@misc{Tahmasbi2018b,
author = {Tahmasbi, Merhdad and Bloch, Matthieu R},
title = {A framework for covert and secret key expansion over quantum channels},
howpublished = {accepted to \emph{Physical Review A}},
month = apr,
year = {2019},
eprint = {1811.05626},
groups = {Quantum key distribution}
}


2. M. Tahmasbi and M. R. Bloch, “First and Second Order Asymptotics in Covert Communication,” IEEE Transactions on Information Theory, vol. 65, no. 4, pp. 2190–2212, Apr. 2019.

We study the first- and second-order asymptotics of covert communication over binary-input DMC for three different covertness metrics and under maximum probability of error constraint. When covertness is measured in terms of the relative entropy between the channel output distributions induced with and without communication, we characterize the exact first- and second-order asymptotics of the number of bits that can be reliably transmitted with a maximum probability of error less than εand a relative entropy less than δ. When covertness is measured in terms of the variational distance between the channel output distributions or in terms of the probability of missed detection for fixed probability of false alarm, we establish the exact first-order asymptotics and bound the second-order asymptotics. PPM achieves the optimal first-order asymptotics for all three metrics, as well as the optimal second-order asymptotics for relative entropy. The main conceptual contribution of this paper is to clarify how the choice of a covertness metric impacts the information-theoretic limits of covert communications. The main technical contribution underlying our results is a detailed expurgation argument to show the existence of a code satisfying the reliability and covertness criteria.

@article{Tahmasbi2017,
author = {Tahmasbi, Mehrdad and Bloch, Matthieu R},
title = {First and Second Order Asymptotics in Covert Communication},
journal = {IEEE Transactions on Information Theory},
year = {2019},
volume = {65},
number = {4},
pages = {2190 --2212},
month = apr,
doi = {10.1109/TIT.2018.2878526},
eprint = {1703.01362},
groups = {Steganography and covert communications}
}


3. I. A. Kadampot, M. Tahmasbi, and M. R. Bloch, “Codes for Covert Communication over Additive White Gaussian Noise Channels.” accepted to IEEE International Symposium on Information Theory, Mar. 2019.

@misc{Kadampot2019,
author = {Kadampot, Ishaque Ashar and Tahmasbi, Mehrdad and Bloch, Matthieu R},
title = {Codes for Covert Communication over Additive White Gaussian Noise Channels},
howpublished = {accepted to \emph{IEEE International Symposium on Information Theory}},
month = mar,
year = {2019}
}


4. K. S. K. Arumugam and M. R. Bloch, “Embedding Covert Information in Broadcast Communications.” accepted to IEEE Transactions on Information Forensics and Security, Mar. 2019.

We analyze a two-receiver binary-input discrete memoryless broadcast channel, in which the transmitter communicates a common message simultaneously to both receivers and a covert message to only one of them. The unintended recipient of the covert message is treated as an adversary who attempts to detect the covert transmission. This model captures the problem of embedding covert messages in an innocent codebook and generalizes previous covert communication models in which the innocent behavior corresponds to the absence of communication between legitimate users. We identify the exact asymptotic behavior of the number of covert bits that can be transmitted when the rate of the innocent codebook is close to the capacity of the channel to the adversary. Our results also identify the dependence of the number of covert bits on the channel parameters and the characteristics of the innocent codebook.

@misc{Arumugam2018b,
author = {Arumugam, Keerthi Suria Kumar and Bloch, Matthieu R.},
title = {Embedding Covert Information in Broadcast Communications},
howpublished = {accepted to \emph{IEEE Transactions on Information Forensics and Security}},
month = mar,
year = {2019},
doi = {10.1109/TIFS.2019.2907190},
eprint = {1808.09556},
groups = {Steganography and covert communications}
}