Semantically Secure Lattice Codes for Compound MIMO Channels

We consider compound multi-input multi-output (MIMO) wiretap channels where minimal channel state information at the transmitter (CSIT) is assumed. Code construction is given for the special case of isotropic mutual information, which serves as a conservative strategy for general cases. Using the flatness factor for MIMO channels, we propose lattice codes universally achieving the secrecy capacity of compound MIMO wiretap channels up to a constant gap (measured in nats) that is equal to the number of transmit antennas. The proposed approach improves upon existing works on secrecy coding for MIMO wiretap channels from an error probability perspective, and establishes information theoretic security (in fact semantic security). We also give an algebraic construction to reduce the code design complexity, as well as the decoding complexity of the legitimate receiver. Thanks to the algebraic structures of number fields and division algebras, our code construction for compound MIMO wiretap channels can be reduced to that for Gaussian wiretap channels, up to some additional gap to secrecy capacity.Comment: IEEE Trans. Information Theory, to appea

Polynomial-Time, Semantically-Secure Encryption Achieving the Secrecy Capacity

In the wiretap channel setting, one aims to get information-theoretic privacy of communicated data based only on the assumption that the channel from sender to receiver is noisier than the one from sender to adversary. The secrecy capacity is the optimal (highest possible) rate of a secure scheme, and the existence of schemes achieving it has been shown. For thirty years the ultimate and unreached goal has been to achieve this optimal rate with a scheme that is polynomial-time. (This means both encryption and decryption are proven polynomial time algorithms.) This paper finally delivers such a scheme. In fact it does more. Our scheme not only meets the classical notion of security from the wiretap literature, called MIS-R (mutual information security for random messages) but achieves the strictly stronger notion of semantic security, thus delivering more in terms of security without loss of rate

Information-theoretic Physical Layer Security for Satellite Channels

Shannon introduced the classic model of a cryptosystem in 1949, where Eve has access to an identical copy of the cyphertext that Alice sends to Bob. Shannon defined perfect secrecy to be the case when the mutual information between the plaintext and the cyphertext is zero. Perfect secrecy is motivated by error-free transmission and requires that Bob and Alice share a secret key. Wyner in 1975 and later I.~Csisz\'ar and J.~K\"orner in 1978 modified the Shannon model assuming that the channels are noisy and proved that secrecy can be achieved without sharing a secret key. This model is called wiretap channel model and secrecy capacity is known when Eve's channel is noisier than Bob's channel. In this paper we review the concept of wiretap coding from the satellite channel viewpoint. We also review subsequently introduced stronger secrecy levels which can be numerically quantified and are keyless unconditionally secure under certain assumptions. We introduce the general construction of wiretap coding and analyse its applicability for a typical satellite channel. From our analysis we discuss the potential of keyless information theoretic physical layer security for satellite channels based on wiretap coding. We also identify system design implications for enabling simultaneous operation with additional information theoretic security protocols

Achieving Secrecy Capacity of the Gaussian Wiretap Channel with Polar Lattices

In this work, an explicit wiretap coding scheme based on polar lattices is proposed to achieve the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel. Firstly, polar lattices are used to construct secrecy-good lattices for the mod-$\Lambda_s$ Gaussian wiretap channel. Then we propose an explicit shaping scheme to remove this mod-$\Lambda_s$ front end and extend polar lattices to the genuine Gaussian wiretap channel. The shaping technique is based on the lattice Gaussian distribution, which leads to a binary asymmetric channel at each level for the multilevel lattice codes. By employing the asymmetric polar coding technique, we construct an AWGN-good lattice and a secrecy-good lattice with optimal shaping simultaneously. As a result, the encoding complexity for the sender and the decoding complexity for the legitimate receiver are both O(N logN log(logN)). The proposed scheme is proven to be semantically secure.Comment: Submitted to IEEE Trans. Information Theory, revised. This is the authors' own version of the pape

Almost universal codes for fading wiretap channels

We consider a fading wiretap channel model where the transmitter has only statistical channel state information, and the legitimate receiver and eavesdropper have perfect channel state information. We propose a sequence of non-random lattice codes which achieve strong secrecy and semantic security over ergodic fading channels. The construction is almost universal in the sense that it achieves the same constant gap to secrecy capacity over Gaussian and ergodic fading models.Comment: 5 pages, to be submitted to IEEE International Symposium on Information Theory (ISIT) 201

A Stronger Soft-Covering Lemma and Applications

Wyner's soft-covering lemma is a valuable tool for achievability proofs of information theoretic security, resolvability, channel synthesis, and source coding. The result herein sharpens the claim of soft-covering by moving away from an expected value analysis. Instead, a random codebook is shown to achieve the soft-covering phenomenon with high probability. The probability of failure is doubly-exponentially small in the block-length, enabling more powerful applications through the union bound.Comment: IEEE CNS 2015, 2nd Workshop on Physical-layer Methods for Wireless Security, 4 page