Confidentialité persistante | EPFL Graph Search

La confidentialité persistante (forward secrecy en anglais), est une propriété en cryptographie qui garantit que la découverte par un adversaire de la clé privée d'un correspondant (secret à long terme) ne compromet pas la confidentialité des communications passées. Elle peut être fournie, par exemple, par la génération des clefs de session au moyen du protocole d'échange de clés Diffie-Hellman. Ces clés de session (temporaires) ne pourront pas être retrouvées à partir des clés des participants, et inversement. Lors d'une connexion TLS, le choix des algorithmes d'échange de clé permet ou ne permet pas de profiter d'une confidentialité persistante. Les méthodes « DH » (pour Diffie-Hellman) ou « Ephemeral DH », lorsqu'elles sont utilisées, fournissent une telle caractéristique. Cela signifie que, même si vous avez obtenu la clé privée du serveur en soudoyant un administrateur, en la volant, ou même grâce à une décision de justice, vous ne serez pas en mesure de déchiffrer les échange

Coding for Communications and Secrecy

Mani Bastaniparizi

Shannon, in his landmark 1948 paper, developed a framework for characterizing the fundamental limits of information transmission. Among other results, he showed that reliable communication over a channel is possible at any rate below its capacity. In 2008, Arikan discovered polar codes; the only class of explicitly constructed low-complexity codes that achieve the capacity of any binary-input memoryless symmetric-output channel. Arikan's polar transform turns independent copies of a noisy channel into a collection of synthetic almost-noiseless and almost-useless channels. Polar codes are realized by sending data bits over the almost-noiseless channels and recovering them by using a low-complexity successive-cancellation (SC) decoder, at the receiver. In the first part of this thesis, we study polar codes for communications. When the underlying channel is an erasure channel, we show that almost all correlation coefficients between the erasure events of the synthetic channels decay rapidly. Hence, the sum of the erasure probabilities of the information-carrying channels is a tight estimate of the block-error probability of polar codes when used for communication over the erasure channel. We study SC list (SCL) decoding, a method for boosting the performance of short polar codes. We prove that the method has a numerically stable formulation in log-likelihood ratios. In hardware, this formulation increases the decoding throughput by 53% and reduces the decoder's size about 33%. We present empirical results on the trade-off between the length of the CRC and the performance gains in a CRC-aided version of the list decoder. We also make numerical comparisons of the performance of long polar codes under SC decoding with that of short polar codes under SCL decoding. Shannon's framework also quantifies the secrecy of communications. Wyner, in 1975, proposed a model for communications in the presence of an eavesdropper. It was shown that, at rates below the secrecy capacity, there exist reliable communication schemes in which the amount of information leaked to the eavesdropper decays exponentially in the block-length of the code. In the second part of this thesis, we study the rate of this decay. We derive the exact exponential decay rate of the ensemble-average of the information leaked to the eavesdropper in Wyner's model when a randomly constructed code is used for secure communications. For codes sampled from the ensemble of i.i.d. random codes, we show that the previously known lower bound to the exponent is exact. Our ensemble-optimal exponent for random constant-composition codes improves the lower bound extant in the literature. Finally, we show that random linear codes have the same secrecy power as i.i.d. random codes. The key to securing messages against an eavesdropper is to exploit the randomness of her communication channel so that the statistics of her observation resembles that of a pure noise process for any sent message. We study the effect of feedback on this approximation and show that it does not reduce the minimum entropy rate required to approximate a given process. However, we give examples where variable-length schemes achieve much larger exponents in this approximation in the presence of feedback than the exponents in systems without feedback. Upper-bounding the best exponent that block codes attain, we conclude that variable-length coding is necessary for achieving the improved exponents.

EPFL2017

Symmetry in design and decoding of polar-like codes

Kirill Ivanov

The beginning of 21st century provided us with many answers about how to reach the channel capacity. Polarization and spatial coupling are two techniques for achieving the capacity of binary memoryless symmetric channels under low-complexity decoding algorithms. Recent results prove that another way to achieve capacity is via symmetry, which is the case of the Reed-Muller and extended Bose-Chaudhuri-Hocquenghem (BCH) codes. However, this proof holds only for erasure channel and maximum a posteriori decoding, which is computationally intractable for the general channels.In the first part of this thesis, we talk about the performance improvements that an automorphism group of the code brings on board. We propose two decoding algorithms for the Reed-Muller codes, which are invariant under a large group of permutations and are expected to benefit the most. The former is based on plugging the codeword permutations in successive cancellation decoding, and the latter utilizes the code representation as the evaluations of Boolean monomials. However, despite the performance improvements, it is clear that the decoding complexity grows quickly and becomes impractical for moderate-length codes. In the second part of this thesis, we provide an explanation for this observation. We use the Boolean polynomial representation of the code in order to show that polar-like decoding of sufficiently symmetric codes asymptotically needs an exponential complexity. The automorphism groups of the Reed-Muller and eBCH codes limit the efficiency of their polar-like decoding for long codes, hence we either should focus on short lengths or find another way. We demonstrate that asymptotically same restrictions (although with a slower convergence) hold for more relaxed condition that we call partial symmetry. The developed framework also enables us to prove that the automorphism group of polar codes cannot include a large affine subgroup.In the last part of this thesis, we address a completely different problem. A device-independent quantum key distribution (DIQKD) aims to provide private communication between parties and has the security guarantees that come mostly from quantum physics, without making potentially unrealistic assumptions about the nature of the communication devices. After the quantum part of the DIQKD protocol, the parties share a secret key that is not perfectly correlated. In order to synchronize, some information needs to be revealed publicly, which makes this formulation equivalent to the asymmetric Slepian-Wolf problem that can be solved using binary linear error-correction codes. As any amount of the revealed information reduces the key secrecy, the utilized code should operate close to the finite-length limits. The channel in consideration is non-standard and, due to its experimental nature, it can actually slightly differ from the considered models. In order to solve this problem, we designed a simple scheme using universal SC-LDPC codes and used in the first successful experimental demonstration of DIQKD protocol.

EPFL2022

CFMA (Compute-Forward Multiple Access) and its Applications in Network Information Theory

Jingge Zhu

While both fundamental limits and system implementations are well understood for the point-to-point communication system, much less is developed for general communication networks. This thesis contributes towards the design and analysis of advanced coding schemes for multi-user communication networks with structured codes. The first part of the thesis investigates the usefulness of lattice codes in Gaussian networks with a generalized compute-and-forward scheme. As an application, we introduce a novel multiple access technique --- Compute-Forward Multiple Access (CFMA), and show that it achieves the capacity region of the Gaussian multiple access channel (MAC) with low receiver complexities. Similar coding schemes are also devised for other multi-user networks, including the Gaussian MAC with states, the two-way relay channel, the many-to-one interference channel, etc., demonstrating improvements of system performance because of the good interference mitigation property of lattice codes. As a common theme in the thesis, computing the sum of codewords over a Gaussian MAC is of particular theoretical importance. We study this problem with nested linear codes, and improve upon the currently best known results obtained by nested lattice codes. Inspired by the advantages of linear and lattice codes in Gaussian networks, we make a further step towards understanding intrinsic properties of the sum of linear codes. The final part of the thesis introduces the notion of typical sumset and presents asymptotic results on the typical sumset size of linear codes. The results offer new insight to coding schemes with structured codes.

EPFL2016