# Information Bytes

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

# Recent works

1. M. Tahmasbi and M. R. Bloch, “Framework for covert and secret key expansion over classical-quantum channels,” Physical Review A, vol. 99, no. 5, p. 052329, May 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 wiretap channels, we develop and analyze protocols based on forward and reverse reconciliation. 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 the Shannon entropy of which 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.

@article{Tahmasbi2018b,
author = {Tahmasbi, Mehrdad and Bloch, Matthieu R.},
title = {Framework for covert and secret key expansion over classical-quantum channels},
journal = {Physical Review A},
year = {2019},
volume = {99},
pages = {052329},
month = may,
doi = {10.1103/PhysRevA.99.052329},
eprint = {1811.05626},
file = {:2019-Tahmasbi-PRA.pdf:PDF},
groups = {Quantum key distribution},
issue = {5},
numpages = {11},
publisher = {American Physical Society}
}


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. W. Harrison and M. R. Bloch, “Attributes of Generator Matrices for Best Finite Blocklength Wiretap Codes.” accepted to IEEE International Symposium on Information Theory, Mar. 2019.

@misc{Harrison2019,
author = {Harrison, Willie and Bloch, Matthieu R},
title = {Attributes of Generator Matrices for Best Finite Blocklength Wiretap Codes},
howpublished = {accepted to \emph{IEEE International Symposium on Information Theory}},
month = mar,
year = {2019}
}