# Information Bytes

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

# Recent works

1. M. Tahmasbi and M. R. Bloch, “Covert and secret key expansion over quantum channels under collective attacks,” IEEE Transactions on Information Theory, vol. 66, no. 11, pp. 7113–7131, Nov. 2020.

We consider an enhanced measure of security for a quantum key distribution protocol, in which we require not only that the adversary obtains no information about the key but also remains unaware that a key generation protocol has been executed. When the adversary applies the same quantum channel independently to 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. A crucial component of the protocol is a covert estimation stage, which is then combined with universal channel coding for reliability and resolvability in the covert regime.

@article{Tahmasbi2019a,
author = {Tahmasbi, Mehrdad and Bloch, Matthieu R},
journal = {IEEE Transactions on Information Theory},
title = {Covert and secret key expansion over quantum channels under collective attacks},
year = {2020},
issn = {1557-9654},
month = nov,
number = {11},
pages = {7113-7131},
volume = {66},
doi = {10.1109/TIT.2020.3021595},
file = {:2020-Tahmasbi-IEEETransIT-b.pdf:PDF},
howpublished = {accepted to \emph{IEEE Transactions on Information Theory}}
}


2. M. Le Treust and M. R. Bloch, “State Leakage and Coordination of Actions: Core of the Receiver’s Knowledge.” accepted to IEEE Transactions on Information Theory, Oct. 2020.

We revisit the problems of state masking and state amplification through the lens of empirical coordination by considering a state-dependent channel in which the encoder has causal and strictly causal state knowledge. We show that the problem of empirical coordination provides a natural framework in which to jointly study the problems of reliable communication, state masking, and state amplification. We characterize the regions of rate-equivocation-coordination trade-offs for several channel models with causal and strictly causal state knowledge. We introduce the notion of “core of the receiver’s knowledge” to capture what the decoder can infer about all the signals involved in the model. We exploit this result to solve a channel state estimation zero-sum game in which the encoder prevents the decoder to estimate the channel state accurately.

@misc{LeTreust2018,
author = {{Le Treust}, Ma\"el and Bloch, Matthieu R},
howpublished = {accepted to \emph{IEEE Transactions on Information Theory}},
month = oct,
title = {State Leakage and Coordination of Actions: Core of the Receiver's Knowledge},
year = {2020},
doi = {10.1109/TIT.2020.3036987},
eprint = {1812.07026}
}


3. I. A. Kadampot, M. Tahmasbi, and M. R. Bloch, “Multilevel-Coded Pulse-Position Modulation for Covert Communications over Binary-Input Discrete Memoryless Channels,” IEEE Transactions on Information Theory, vol. 66, no. 10, pp. 6001–6023, Oct. 2020.

We consider the problem of coding to ensure covert communication, which involves ensuring reliable communication between two legitimate parties while simultaneously guaranteeing a low probability of detection by an eavesdropper. Specifically, we develop an optimal low-complexity coding scheme that achieves the information-theoretic limits of covert communications over binary-input discrete memoryless channels (BI-DMCs). To justify our design, we first consider a regime in which information theory proves the possibility of covert communication without shared secret key and show the impossibility of achieving information-theoretic limits using linear codes without secret key. We then circumvent this impossibility by introducing non-linearity into the coding scheme through the use of pulse position modulation (PPM) and multilevel coding (MLC). This MLC-PPM scheme exhibits several appealing properties; in particular, for an appropriate decoder, the channel at a given level is independent of the total number of levels and the codeword length. We exploit these properties to show how one can use families of channel capacity- and channel resolvability-achieving codes to concretely instantiate a covert communication scheme.

@article{Kadampot2018a,
author = {Kadampot, Ishaque Ashar and Tahmasbi, Mehrdad and Bloch, Matthieu R},
journal = {IEEE Transactions on Information Theory},
title = {Multilevel-Coded Pulse-Position Modulation for Covert Communications over Binary-Input Discrete Memoryless Channels},
year = {2020},
month = oct,
number = {10},
pages = {6001-6023},
volume = {66},
doi = {10.1109/TIT.2020.3019996},
eprint = {1811.09695},
}


4. N. Helal, M. Bloch, and A. Nosratinia, “Cooperative Resolvability and Secrecy in the Cribbing Multiple-Access Channel,” IEEE Transactions on Information Theory, vol. 66, no. 9, pp. 5429–5447, Sep. 2020.

We study channel resolvability for the discrete memoryless multiple-access channel with cribbing, i.e., the characterization of the amount of randomness required at the inputs to approximately produce a chosen i.i.d. output distribution according to Kullback-Leibler divergence. We analyze resolvability rates when one encoder cribs (i) the input of the other encoder; or the output of the other encoder, (ii) non-causally, (iii) causally, or (iv) strictly-causally. For scenarios (i)-(iii), we exactly characterize the channel resolvability region. For (iv), we provide inner and outer bounds for the channel resolvability region; the crux of our achievability result is to handle the strict causality constraint with a block-Markov coding scheme in which dependencies across blocks are suitably hidden. Finally, we leverage the channel resolvability results to derive achievable secrecy rate regions for each of the cribbing scenarios under strong secrecy constraints.We study channel resolvability for the discrete memoryless multiple-access channel with cribbing, i.e., the characterization of the amount of randomness required at the inputs to approximately produce a chosen i.i.d. output distribution according to Kullback-Leibler divergence. We analyze resolvability rates when one encoder cribs (i) the input of the other encoder; or the output of the other encoder, (ii) non-causally, (iii) causally, or (iv) strictly-causally. For scenarios (i)-(iii), we exactly characterize the channel resolvability region. For (iv), we provide inner and outer bounds for the channel resolvability region; the crux of our achievability result is to handle the strict causality constraint with a block-Markov coding scheme in which dependencies across blocks are suitably hidden. Finally, we leverage the channel resolvability results to derive achievable secrecy rate regions for each of the cribbing scenarios under strong secrecy constraints.

@article{Helhal2018a,
author = {Helal, Noha and Bloch, Matthieu and Nosratinia, Aria},
title = {Cooperative Resolvability and Secrecy in the Cribbing Multiple-Access Channel},
journal = {IEEE Transactions on Information Theory},
year = {2020},
volume = {66},
number = {9},
pages = {5429-5447},
month = sep,
doi = {10.1109/TIT.2020.2995565},
eprint = {1811.11649},
file = {:2020-Helal-IEEETransIT.pdf:PDF},
howpublished = {accepted for \emph{IEEE Transactions on Information Theory}}
}