Remi A. Chou

Polar Coding for Secret-Key Generation

Practical implementations of secret-key generation are often based on sequential strategies, which handle reliability and secrecy in two successive steps, called reconciliation and privacy amplification. In this paper, we propose an alternative approach based on polar codes that jointly deals with reliability and secrecy. Specifically, we propose secret-key capacity-achieving polar coding schemes for the following models: (i) the degraded binary memoryless source (DBMS) model with rate-unlimited public communication, (ii) the DBMS model with one-way rate-limited public communication, (iii) the 1-to-m broadcast model and (iv) the Markov tree model with uniform marginals. For models (i) and (ii) our coding schemes remain valid for non-degraded sources, although they may not achieve the secret-key capacity. For models (i), (ii) and (iii), our schemes rely on pre-shared secret seed of negligible rate; however, we provide special cases of these models for which no seed is required. Finally, we show an application of our results to secrecy and privacy for biometric systems. We thus provide the first examples of low-complexity secret-key capacity-achieving schemes that are able to handle vector quantization for model (ii), or multiterminal communication for models (iii) and (iv).

Separation of Reliability and Secrecy in Rate-Limited Secret-Key Generation

For a discrete or a continuous source model, we study the problem of secret-key generation with one round of rate-limited public communication between two legitimate users. Although we do not provide new bounds on the wiretap secret-key (WSK) capacity for the discrete source model, we use an alternative achievability scheme that may be useful for practical applications. As a side result, we conveniently extend known bounds to the case of a continuous source model. Specifically, we consider a sequential key-generation strategy, that implements a rate-limited reconciliation step to handle reliability, followed by a privacy amplification step performed with extractors to handle secrecy. We prove that such a sequential strategy achieves the best known bounds for the rate-limited WSK capacity (under the assumption of degraded sources in the case of two-way communication). However, we show that, unlike the case of rate-unlimited public communication, achieving the reconciliation capacity in a sequential strategy does not necessarily lead to achieving the best known bounds for the WSK capacity. Consequently, reliability and secrecy can be treated successively but not independently, thereby exhibiting a limitation of sequential strategies for rate-limited public communication. Nevertheless, we provide scenarios for which reliability and secrecy can be treated successively and independently, such as the two-way rate-limited SK capacity, the one-way rate-limited WSK capacity for degraded binary symmetric sources, and the one-way rate-limited WSK capacity for Gaussian degraded sources.

Experimental aspects of secret key generation in indoor wireless environments

This paper proposes a proof-of-principle design of a secret key generation system along with the desirable secrecy analysis to guarantee information-theoretic security. We conduct physical experiments on programmable radios in an indoor environment to analyze the statistical characteristics of the induced source that we employ to generate secret keys. We also provide a generic security analysis of the system, and we give an estimate of the achievable secret key rates for a target information leakage in the finite block-length regime.

Data compression with nearly uniform output

For any lossless fixed-length compression scheme operating at the optimal coding rate, it is known that the encoder output is not uniform in variational distance, which yet might be desirable in some security schemes. In the case of independent and identically distributed (i.i.d.) sources, uniformity in divergence might be achieved if a uniformly distributed sequence, called seed, of length dn negligible compared to the message length n, is shared between the encoder and the decoder. We show that the optimal scaling of dn that jointly ensures an optimal coding rate and a uniform encoder output in divergence, is roughly on the order of √n. We also develop a near optimal achievability scheme using invertible extractors.

Polar coding for empirical and strong coordination via distribution approximation

We design low-complexity polar codes for empirical and strong coordination in two-node network. Our constructions hinge on the observation that polar codes may be used to approximate distribution; which we leverage to prove that nested polar codes achieve the capacity region of empirical coordination and strong coordination.

Polar coding for the multiple access wiretap channel via rate-splitting and cooperative jamming

We consider strongly secure communication over a discrete memoryless multiple access wiretap channel with two transmitters - no degradation or symmetry assumptions are made on the channel. Our main result is that any rate pair known to be achievable with a random coding like proof, is also achievable with a low-complexity polar coding scheme. Moreover, if the rate pair is known to be achievable without time-sharing, then time-sharing is not needed in our polar coding scheme as well. Our proof technique relies on rate-splitting and different cooperative jamming strategies. Specifically, our coding scheme combines several point-to-point codes that either aim at secretly conveying a message to the legitimate receiver or at performing cooperative jamming. Each point-to-point code relies on a chaining construction to be able to deal with an arbitrary channel and strong secrecy. We assess reliability and strong secrecy through a detailed analysis of the dependencies between the random variables involved in the scheme.

Low-complexity channel resolvability codes for the symmetric multiple-access channel.

We investigate channel resolvability for the l-user multiple-access channel (MAC) with two different families of encoders. The first family consists of invertible extractors, while the second one consists of injective group homomorphisms, and was introduced by Hayashi for the point-to-point channel resolvability. The main benefit of these two families is to provide explicit low-complexity channel resolvability codes in the case of symmetric MACs. Specifically, we provide two examples of families of invertible extractors suitable for MAC resolvability with uniform input distributions, one based on finite-field multiplication, which can be implemented in O(n log n) for a limited range of values of the encoding blocklength n, and a second based on modified Toeplitz matrices, which can be implemented in O(n log n) for a wider range of values of n. We also provide an example of family of injective group homomorphisms based on finite-field multiplication suitable for MAC resolvability with uniform input distributions, which can be implemented in O(n log n) for some values of n.

Using deterministic decisions for low-entropy bits in the encoding and decoding of polar codes

We show how to replace some of the randomized decisions in the encoding and decoding of polar codes by deterministic decisions. Specifically, we prove that random decisions on low-entropy bits may be replaced by an argmax decision without any loss of performance. We illustrate the usefulness of this result in the case of polar coding for the Wyner-Ziv problem and for channel coding.

Uniform distributed source coding for the multiple access wiretap channel

We study the transmission of public and secret messages over the l-input multiple-access wiretap channel with deterministic encoders. Specifically, we assume that no additional source of randomness is available at the encoders and that public messages may be non-uniform and correlated. We develop a coding scheme that achieves information-theoretic security by combining existing constructions for wiretap codes with a distributed source code with nearly independent and nearly uniform encoder outputs.

A game theoretic treatment for pair-wise secret-key generation in many-to-one networks

We consider secret-key generation between several agents and a base station that observe independent and identically distributed (i.i.d.) realizations of correlated random variables. Each agent wishes to generate the longest possible individual key with the base station by means of public communication. All keys must be jointly kept secret from all external entities. We do not require them to be kept secret among the agents. In this many-to-one secret-key generation setting, it can be shown that the agents can take advantage of a collective protocol to increase the sum-rate of all the generated keys. However, when each agent is only interested in maximizing its own secret-key rate, agents may be unwilling to participate in a collective protocol. Furthermore, when such a collective protocol is employed, how to fairly allocate individual key rates arises as a valid issue. We study this tension between cooperation and self-interest with a game-theoretic treatment. We establish that cooperation is in the best interest of all agents and that there exists individual secret-key rate allocations that incentivize the agents to follow the protocol. Additionally, we propose an explicit and low-complexity coding scheme based on polar codes and hash functions that achieves such allocations.