# Coding Theory and Security, 2014, Part 2

 Coding Theory and Security, 2014 Part 2

Coding theory is one of the essential pieces of information theory. More important, coding theory is a core element in cryptography. The research work cited here looks at signal processing, crowdsourcing, matroid theory, WOM codes, and the N-P hard problem. These works were presented or published in 2014.

Okamoto, K.; Homma, N.; Aoki, T.; Morioka, S., "A Hierarchical Formal Approach to Verifying Side-Channel Resistant Cryptographic Processors," Hardware-Oriented Security and Trust (HOST), 2014 IEEE International Symposium on, vol., no., pp. 76, 79, 6-7 May 2014. doi:10.1109/HST.2014.6855572
Abstract: This paper presents a hierarchical formal verification method for cryptographic processors based on a combination of a word-level computer algebra procedure and a bit-level decision procedure using PPRM (Positive Polarity Reed-Muller) expansion. In the proposed method, the entire datapath structure of a cryptographic processor is described in the form of a hierarchical graph. The correctness of the entire circuit function is verified on this graph representation, by the algebraic method, and the function of each component is verified by the PPRM method, respectively. We have applied the proposed verification method to a complicated AES (Advanced Encryption Standard) circuit with a masking countermeasure against side-channel attack. The results show that the proposed method can verify such practical circuit automatically within 4 minutes while the conventional methods fail.
Keywords: Reed-Muller codes; cryptography; digital arithmetic; formal verification; graph theory; process algebra; AES circuit; PPRM; advanced encryption standard circuit; algebraic method; bit-level decision procedure; circuit function; datapath structure; graph representation; hierarchical formal approach; hierarchical formal verification method; hierarchical graph; positive polarity Reed-Muller expansion; side-channel attack; side-channel resistant cryptographic processors; word-level computer algebra procedure; Algebra; Computers; Cryptography; Polynomials; Program processors; Resistance; Galois fields; arithmetic circuits; cryptographic processors; design methodology for secure hardware; formal design (ID#: 15-4862)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6855572&isnumber=6855557

Zamani, S.; Javanmard, M.; Jafarzadeh, N.; Zamani, M., "A Novel Image Encryption Scheme Based on Hyper Chaotic Systems and Fuzzy Cellular Automata," Electrical Engineering (ICEE), 2014 22nd Iranian Conference on, vol., no., pp. 1136, 1141, 20-22 May 2014. doi:10.1109/IranianCEE.2014.6999706
Abstract: A new image encryption scheme based on hyper chaotic system and Fuzzy Cellular Automata is proposed in this paper. Hyper chaotic system has more complex dynamical characteristics than chaos systems. Hence it becomes a better choice for secure image encryption schemes. Four hyper chaotic systems are used to improve the security and speed of the algorithm in this approach. First, the image is divided into four sub images. Each of these sub images has its own hyper chaotic system. In shuffling phase, Pixels in the two adjacent sub images are selected for changing their positions based upon the generated numbers of their hyper chaotic systems. Five 1D non-uniform Fuzzy Cellular Automata used in encryption phase. Used rule to encrypt a cell is selected based upon cell's right neighbor. By utilization of two different encryption methods for odd and even cells, problem of being limited to recursive rules in rule selecting process in these FCAs is solved. The results of implementing this scheme on some images from USC-SIPI database, shows that our method has high security and advantages such as confusion, diffusion, and is sensitive to small changes in key.
Keywords: cellular automata; cryptography; fuzzy set theory; image coding; 1D nonuniform fuzzy cellular automata; FCA; dynamical characteristic; hyperchaotic system; image encryption; rule selecting process; shuffling phase; Automata; Chaos; Correlation; Encryption; Entropy; FCA; Hyper Chaotic System; Image encryption; Lorenz System; Non-uniform Cellular Automata (ID#: 15-4863)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6999706&isnumber=6999486

Baheti, A.; Singh, L.; Khan, A.U., "Proposed Method for Multimedia Data Security Using Cyclic Elliptic Curve, Chaotic System, and Authentication Using Neural Network," Communication Systems and Network Technologies (CSNT), 2014 Fourth International Conference on, vol., no., pp. 664, 668, 7-9 April 2014. doi:10.1109/CSNT.2014.139
Abstract: As multimedia applications are used increasingly, security becomes an important issue of security of images. The combination of chaotic theory and cryptography forms an important field of information security. In the past decade, chaos based image encryption is given much attention in the research of information security and a lot of image encryption algorithms based on chaotic maps have been proposed. But, most of them delay the system performance, security, and suffer from the small key space problem. This paper introduces an efficient symmetric encryption scheme based on a cyclic elliptic curve and chaotic system that can overcome these disadvantages. The cipher encrypts 256-bit of plain image to 256-bit of cipher image within eight 32-bit registers. The scheme generates pseudorandom bit sequences for round keys based on a piecewise nonlinear chaotic map. Then, the generated sequences are mixed with the key sequences derived from the cyclic elliptic curve points. The proposed algorithm has good encryption effect, large key space, high sensitivity to small change in secret keys and fast compared to other competitive algorithms.
Keywords: image coding; multimedia computing; neural nets; public key cryptography; authentication; chaos based image encryption; chaotic maps; chaotic system;  chaotic theory; competitive algorithms; cryptography; cyclic elliptic curve points; encryption effect; image encryption algorithms; information security; multimedia applications; multimedia data security; neural network; piecewise nonlinear chaotic map; pseudorandom bit sequences; small key space problem; system performance; Authentication; Chaotic communication; Elliptic curves; Encryption; Media; Multimedia communication; authentication; chaos; decryption; encryption; neural network (ID#: 15-4864)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6821481&isnumber=6821334

Lashgari, S.; Avestimehr, A.S., "Blind Wiretap Channel with Delayed CSIT," Information Theory (ISIT), 2014 IEEE International Symposium on, vol., no., pp. 36, 40, June 29 2014 – July 4 2014. doi:10.1109/ISIT.2014.6874790
Abstract: We consider the Gaussian wiretap channel with a transmitter, a legitimate receiver, and k eavesdroppers (k ∈ ℕ), where the secure communication is aided via a jammer. We focus on the setting where the transmitter and the jammer are blind with respect to the state of channels to eavesdroppers, and only have access to delayed channel state information (CSI) of the legitimate receiver, which is referred to as “blind cooperative wiretap channel with delayed CSIT.” We show that a strictly positive secure Degrees of Freedom (DoF) of 1 over 3 is achievable irrespective of the number of eavesdroppers (k) in the network, and further, 1 over 3 is optimal assuming linear coding strategies at the transmitters. The converse proof is based on two key lemmas. The first lemma, named Rank Ratio Inequality, shows that if two distributed transmitters employ linear strategies, the ratio of the dimensions of received linear sub-spaces at the two receivers cannot exceed 3/2, due to delayed CSI. The second lemma implies that once the transmitters in a network have no CSI with respect to a receiver, the least amount of alignment will occur at that receiver, meaning that transmit signals will occupy the maximal signal dimensions at that receiver. Finally, we show that once the transmitter and the jammer form a single transmitter with two antennas, which we refer to as MISO wiretap channel, 1 over 2 is the optimal secure DoF when using linear schemes.
Keywords: Gaussian channels; jamming; linear codes; radio transceivers; telecommunication security; transmitting antennas; CSI; DoF; Gaussian wiretap channel; MISO wiretap channel; antennas; blind cooperative wiretap channel; communication security; degrees of freedom; delayed CSIT; delayed channel state information; distributed transmitter; eavesdroppers; jammer; key lemmas; legitimate receiver; linear coding strategy; linear subspaces; rank ratio inequality; signal dimensions; transmit signals; Encoding; Jamming; Noise; Receivers; Transmitters; Vectors (ID#: 15-4865)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6874790&isnumber=6874773

Kochman, Y.; Ligong Wang; Wornell, G.W., "Toward Photon-Efficient Key Distribution over Optical Channels," Information Theory, IEEE Transactions on, vol. 60, no. 8, pp. 4958, 4972, Aug. 2014. doi:10.1109/TIT.2014.2331060
Abstract: This paper considers the distribution of a secret key over an optical (bosonic) channel in the regime of high photon efficiency, i.e., when the number of secret key bits generated per detected photon is high. While, in principle, the photon efficiency is unbounded, there is an inherent tradeoff between this efficiency and the key generation rate (with respect to the channel bandwidth). We derive asymptotic expressions for the optimal generation rates in the photon-efficient limit, and propose schemes that approach these limits up to certain approximations. The schemes are practical, in the sense that they use coherent or temporally entangled optical states and direct photodetection, all of which are reasonably easy to realize in practice, in conjunction with off-the-shelf classical codes.
Keywords: approximation theory; private key cryptography; quantum cryptography; quantum entanglement; approximations; asymptotic expressions; bosonic channel; channel bandwidth; coherent entangled optical states; direct photodetection; key generation rate; off-the-shelf classical codes; optical channels; optimal generation rates; photon-efficient key distribution; secret key distribution; temporally entangled optical states; Hilbert space; Optical receivers; Optical sensors; Photonics; Protocols; Quantum entanglement; Information-theoretic security; key distribution; optical communication; wiretap channel (ID#: 15-4866)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6835214&isnumber=6851961

Fuchun Lin; Cong Ling; Belfiore, J.-C., "Secrecy Gain, Flatness Factor, and Secrecy-Goodness of Even Unimodular Lattices," Information Theory (ISIT), 2014 IEEE International Symposium on, vol., no., pp. 971, 975, June 29 2014 – July 4 2014. doi:10.1109/ISIT.2014.6874977
Abstract: Nested lattices Ae ⊂ Ab have previously been studied for coding in the Gaussian wiretap channel and two design criteria, namely, the secrecy gain and flatness factor, have been proposed to study how the coarse lattice Ae should be chosen so as to maximally conceal the message against the eavesdropper. In this paper, we study the connection between these two criteria and show the secrecy-goodness of even unimodular lattices, which means exponentially vanishing flatness factor as the dimension grows.
Keywords: Gaussian channels; encoding; Gaussian wiretap channel; coding; flatness factor; secrecy gain; secrecy-goodness; unimodular lattices; Educational institutions; Encoding; Lattices; Security; Vectors; Zinc (ID#: 15-4867)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6874977&isnumber=6874773

Renna, F.; Laurenti, N.; Tomasin, S., "Achievable Secrecy Rates over MIMOME Gaussian Channels with GMM Signals in Low-Noise Regime," Wireless Communications, Vehicular Technology, Information Theory and Aerospace & Electronic Systems (VITAE), 2014 4th International Conference on, vol., no., pp. 1, 5, 11-14 May 2014. doi:10.1109/VITAE.2014.6934464
Abstract: We consider a wiretap multiple-input multiple-output multiple-eavesdropper (MIMOME) channel, where agent Alice aims at transmitting a secret message to agent Bob, while leaking no information on it to an eavesdropper agent Eve. We assume that Alice has more antennas than both Bob and Eve, and that she has only statistical knowledge of the channel towards Eve. We focus on the low-noise regime, and assess the secrecy rates that are achievable when the secret message determines the distribution of a multivariate Gaussian mixture model (GMM) from which a realization is generated and transmitted over the channel. In particular, we show that if Eve has fewer antennas than Bob, secret transmission is always possible at low-noise. Moreover, we show that in the low-noise limit the secrecy capacity of our scheme coincides with its unconstrained capacity, by providing a class of covariance matrices that allow to attain such limit without the need of wiretap coding.
Keywords: Gaussian channels; Gaussian processes; MIMO communication; covariance matrices; GMM signals; MIMOME Gaussian channels; achievable secrecy rates; covariance matrices; low-noise regime; multivariate Gaussian mixture model; secrecy capacity; secret transmission; statistical knowledge; wiretap multiple-input multiple-output multiple-eavesdropper channel; Antennas; Covariance matrices; Encoding; Entropy; Gaussian distribution; Signal to noise ratio; Vectors; Physical Layer Security; Secrecy Capacity; multiple-input multiple-output multiple-eavesdropper (MIMOME) Channels (ID#: 15-4868)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6934464&isnumber=6934393

James, S.P.; George, S.N.; Deepthi, P.P., "An Audio Encryption Technique Based on LFSR Based Alternating Step Generator," Electronics, Computing and Communication Technologies (IEEE CONECCT), 2014 IEEE International Conference on, vol., no., pp. 1, 6, 6-7 Jan. 2014. doi:10.1109/CONECCT.2014.6740185
Abstract: In this paper, a novel method of encrypting the encoded audio data based on LFSR based key stream generators is presented. The alternating step generator (ASG) is selected as keystream generator used for this application. Since the ASG is vulnerable to improved linear consistency attack, it is proposed to incorporate some nonlinearity with the stop/go LFSRs of the ASG so that the modified ASG can withstand the same. In the proposed approach, the selected bits of each frame of the encoded audio data is encrypted with the keystream generated by the modified ASG. In order to overcome known plaintext attack, it is proposed to use different keystreams for different frames of the audio data. The long keystream generated from the modified ASG is divided into smaller keystreams so that it can be used as the different keystreams for different frames of audio data. The proposed encryption approach can be applied to any audio coding system, which maintains the standard compatibility. The number of encrypted bits control the degree of degradation of the audio quality. The performance of proposed encryption method is verified with MP3 coded audio data and is proved that it can provide better security than the existing ones with very less system complexity.
Keywords: audio coding; cryptography; ASG; LFSR-based alternating step generator; LFSR-based key stream generators; MP3 coded audio data; alternating step generator; audio coding system; audio data frames; audio quality; encoded audio data encryption technique; improved linear consistency attack; known plaintext attack; modified ASG; standard compatibility; stop-go LFSR; system complexity; Clocks; Complexity theory; Cryptography; Filtering; Linearity; Zinc (ID#: 15-4869)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6740185&isnumber=6740167

Pujari, V.G.; Khot, S.R.; Mane, K.T., "Enhanced Visual Cryptography Scheme for Secret Image Retrieval Using Average Filter," Wireless Computing and Networking (GCWCN), 2014 IEEE Global Conference on, vol., no., pp. 88, 91, 22-24 Dec. 2014. doi:10.1109/GCWCN.2014.7030854
Abstract: Visual cryptography is one of the emerging technology which has been used for sending secret images in highly secure manner without performing the complex operations while encoding. This technology can be used in the many fields like transferring military data, financial scan documents, sensitive image data and so on. In the literature different methods are used for black and white image which produce good result but for color images the quality of the decoded secret image is not good. In this paper, the system has been proposed which increase the quality of color decoded image. In this system sender takes one secret image which is encoded into n share images using Jarvis halftoning and encoding table. For decoding, the share images are used with decoding table to get original secret image. The average filter has been applied to decrease the noise introduced between encoding operation so that decoded secret image quality has been increased. The result analysis has been made by considering various image quality analysis parameters such as MSE, PSNR, SC, NAE and so on. The results are better than previous systems which are mentioned in the literature.
Keywords: cryptography; filtering theory; image coding; image colour analysis; image denoising; image retrieval; Jarvis halftoning; average filter; black image; color decoded image quality; decoded secret image quality; encoding table; enhanced visual cryptography scheme; image quality analysis parameters; secret image retrieval; white image; Cryptography; Decoding; Image coding; Image color analysis; Image quality; Noise; Visualization; Average filter; Color halftoning; Decoding; Encoding; Jarvis error diffusion; Security; Visual cryptography (ID#: 15-4870)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7030854&isnumber=7030833

Wentao Huang; Ho, T.; Langberg, M.; Kliewer, J., "Reverse Edge Cut-Set Bounds for Secure Network Coding," Information Theory (ISIT), 2014 IEEE International Symposium on, vol., no., pp. 106, 110, June 29 2014 – July 4 2014. doi:10.1109/ISIT.2014.6874804
Abstract: We consider the problem of secure communication over a network in the presence of wiretappers. We give a new cut-set bound on secrecy capacity which takes into account the contribution of both forward and backward edges crossing the cut, and the connectivity between their endpoints in the rest of the network. We show the bound is tight on a class of networks, which demonstrates that it is not possible to find a tighter bound by considering only cut-set edges and their connectivity.
Keywords: network coding; telecommunication security; cut-set edges; reverse edge cut-set bounds; secrecy capacity; secure communication; secure network coding; wiretappers; Delays; Entropy; Mutual information; Network coding; Unicast; Upper bound (ID#: 15-4871)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6874804&isnumber=6874773

Kosut, O.; Lang Tong; Tse, D.N.C., "Polytope Codes Against Adversaries in Networks," Information Theory, IEEE Transactions on, vol. 60, no. 6, pp. 3308, 3344, June 2014. doi:10.1109/TIT.2014.2314642
Abstract: This paper investigates a network coding problem wherein an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than that of an adversary controlling a given number of edges in the network, in that linear codes are insufficient. To solve the node problem, the class of polytope codes is introduced. Polytope codes are constant composition codes operating over bounded polytopes in integer vector fields. The polytope structure creates additional complexity, but it induces properties on marginal distributions of code vectors so that validities of codewords can be checked by internal nodes of the network. It is shown that polytope codes achieve a cut-set bound for a class of planar networks. It is also shown that this cut-set bound is not always tight, and a tighter bound is given for an example network.
Keywords: linear codes; network coding; adversary controlling; adversary controls; code vectors; codewords; constant composition codes; integer vector fields; internal nodes; linear codes; network adversaries; network coding problem; polytope codes; Educational institutions; Linear codes; Network coding; Upper bound; Vectors; Xenon; Active adversaries; Byzantine attack; network coding; network error correction; nonlinear codes; polytope codes; security (ID#: 15-4872)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6781646&isnumber=6816018

Xiang He; Yener, A., "Providing Secrecy with Structured Codes: Two-User Gaussian Channels," Information Theory, IEEE Transactions on, vol. 60, no. 4, pp. 2121, 2138, April 2014. doi:10.1109/TIT.2014.2298132
Abstract: Recent results have shown that structured codes can be used to construct good channel codes, source codes, and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on Gaussian random codes. In this paper, we advocate that structure in random code generation is useful for providing secrecy as well. In particular, a Gaussian wiretap channel in the presence of a cooperative jammer is studied. Previously, the achievable secrecy rate for this channel was derived using Gaussian signaling, which saturated at high signal-to-noise ratio (SNR), owing to the fact that the cooperative jammer simultaneously helps by interfering with the eavesdropper, and hurts by interfering with the intended receiver. In this paper, a new achievable rate is derived through imposing a lattice structure on the signals transmitted by both the source and the cooperative jammer, which are aligned at the eavesdropper but remain separable at the intended receiver. We prove that the achieved secrecy rate does not saturate at high SNR for all values of channel gains except when the channel is degraded.
Keywords: Gaussian channels; cooperative communication; jamming; random codes; telecommunication security; Gaussian channels; Gaussian random codes; Gaussian signaling; Gaussian wiretap channel; channel codes; cooperative jammer; eavesdropper; lattice structure; physical layer network codes; random code generation; secrecy constraints; source codes; structured codes; Channel models; Encoding; Jamming; Lattices; Receivers; Transmitters; Vectors; Gaussian wiretap channels; Information theoretic secrecy; cooperative jamming; lattice codes (ID#: 15-4873)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6702446&isnumber=6766686

Boche, H.; Schaefer, R.F.; Poor, H.V., "On Arbitrarily Varying Wiretap Channels for Different Classes of Secrecy Measures," Information Theory (ISIT), 2014 IEEE International Symposium on, vol., no., pp. 2376, 2380, June 29 2014 – July 4 2014. doi:10.1109/ISIT.2014.6875259
Abstract: The wiretap channel models secure communication in the presence of an eavesdropper who must be kept ignorant of transmitted messages. In this paper, the arbitrarily varying wiretap channel (AVWC), in which the channel may vary in an unknown and arbitrary manner from channel use to channel use, is considered. For arbitrarily varying channels (AVCs) the capacity might differ depending on whether deterministic or common randomness (CR) assisted codes are used. The AVWC has been studied for both coding strategies and the relation between the corresponding secrecy capacities has been established. However, a characterization of the CR-assisted secrecy capacity itself or even a general CR-assisted achievable secrecy rate remain open in general for weak and strong secrecy. Here, the secrecy measure of high decoding error at the eavesdropper is considered, where the eavesdropper is further assumed to know channel states and to adapt its decoding strategy accordingly. For this secrecy measure a general CR-assisted achievable secrecy rate is established. The relation between secrecy capacities for different secrecy measures is discussed: The weak and strong secrecy capacities are smaller than or equal to the one for high decoding error. It is conjectured that this relation can be strict for certain channels.
Keywords: channel coding; decoding; telecommunication security; AVWC; CR-assisted achievable secrecy rate; CR-assisted secrecy capacity; arbitrarily varying wiretap channels; common randomness assisted codes; decoding error; secrecy measures; secure communication; Compounds; Decoding; Measurement uncertainty; Robustness; Security; Tin (ID#: 15-4874)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6875259&isnumber=6874773

Fan Cheng; Yeung, R.W., "Performance Bounds on a Wiretap Network with Arbitrary Wiretap Sets," Information Theory, IEEE Transactions on, vol. 60, no.6, pp. 3345, 3358, June 2014. doi:10.1109/TIT.2014.2315821
Abstract: Consider a communication network represented by a directed graph G = (V, ε), where V is the set of nodes and 8 is the set of point-to-point channels in the network. On the network, a secure message M is transmitted, and there may exist wiretappers who want to obtain information about the message. In secure network coding, we aim to find a network code, which can protect the message against the wiretapper whose power is constrained. Cai and Yeung studied the model in which the wiretapper can access any one but not more than one set of channels, called a wiretap set, out of a collection A of all possible wiretap sets. In order to protect the message, the message needs to be mixed with a random key K. They proved tight fundamental performance bounds when A consists of all subsets of ε of a fixed size r. However, beyond this special case, obtaining such bounds is much more difficult. In this paper, we investigate the problem when A consists of arbitrary subsets of ε and obtain the following results: 1) an upper bound on H(M) and 2) a lower bound on H(K) in terms of H(M). The upper bound on H(M) is explicit, while the lower bound on H(K) can be computed in polynomial time when |A| is fixed. The tightness of the lower bound for the point-to-point communication system is also proved.
Keywords: network coding; polynomials; radio networks; telecommunication security; Cai; Yeung; arbitrary wiretap sets; communication network; network code; performance bounds; point-to-point channels; polynomial time; random key; secure message; secure network coding; wiretap network; wiretapper; Cryptography; Encoding; Entropy; Network coding; Receivers; Upper bound; Information inequality; perfect secrecy; performance bounds; secure network coding (ID#: 15-4875)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6783737&isnumber=6816018

Bin Duo; Peng Wang; Yonghui Li; Vucetic, B., "Secure Transmission for Relay-Eavesdropper Channels Using Polar Coding," Communications (ICC), 2014 IEEE International Conference on, vol., no., pp. 2197, 2202, 10-14 June 2014. doi:10.1109/ICC.2014.6883649
Abstract: In this paper, we propose a practical transmission scheme using polar coding for the half-duplex degraded relay-eavesdropper channel. We prove that the proposed scheme can achieve the maximum perfect secrecy rate under the decode-and-forward (DF) strategy. Our proposed scheme provides an approach for ensuring both reliable and secure transmission over the relay-eavesdropper channel while enjoying practically feasible encoding/decoding complexity.
Keywords: channel coding; decode and forward communication; decoding; reliability; telecommunication security; wireless channels; DF strategy; decode and forward strategy; decoding complexity; half-duplex degraded relay eavesdropper channel; polar coding; reliable transmission; secure transmission; Complexity theory; Decoding; Encoding; Relays ;Reliability; Variable speed drives; Vectors (ID#: 15-4876)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6883649&isnumber=6883277

Loyka, S.; Charalambous, C.D., "Rank-Deficient Solutions for Optimal Signaling over Secure MIMO Channels," Information Theory (ISIT), 2014 IEEE International Symposium on, vol., no., pp.  201, 205, June 29 2014 – July 4 2014. doi:10.1109/ISIT.2014.6874823
Abstract: Capacity-achieving signaling strategies for the Gaussian wiretap MIMO channel are investigated without the degradedness assumption. In addition to known solutions, a number of new rank-deficient solutions for the optimal transmit covariance matrix are obtained. The case of weak eavesdropper is considered in details and the optimal covariance is established in an explicit, closed-form with no extra assumptions. The conditions for optimality of zero-forcing signaling are established, and the standard water-filling is shown to be optimal under those conditions. No wiretap codes are needed in this case. The case of identical right singular vectors for the required and eavesdropper channels is studied and the optimal covariance is established in an explicit closed form. As a by-product of this analysis, we establish a generalization of celebrated Hadamard determinantal inequality using information-theoretic tools.
Keywords: Gaussian channels; MIMO communication; covariance matrices; telecommunication security; telecommunication signalling; Gaussian wiretap MIMO channel; capacity-achieving signaling strategies; celebrated Hadamard determinantal inequality; eavesdropper channels; identical right singular vectors; information-theoretic tools; optimal covariance; optimal signaling; optimal transmit covariance matrix; rank-deficient solutions; secure MIMO channels; standard water-filling; weak eavesdropper; wiretap codes; zero-forcing signaling; Approximation methods; Covariance matrices; Information theory; MIMO; Signal to noise ratio; Standards; Vectors (ID#: 15-4877)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6874823&isnumber=6874773

Cong Ling; Luzzi, L.; Belfiore, J.-C.; Stehle, D., "Semantically Secure Lattice Codes for the Gaussian Wiretap Channel," Information Theory, IEEE Transactions on, vol. 60, no.10, pp. 6399, 6416, Oct. 2014. doi:10.1109/TIT.2014.2343226
Abstract: We propose a new scheme of wiretap lattice coding that achieves semantic security and strong secrecy over the Gaussian wiretap channel. The key tool in our security proof is the flatness factor, which characterizes the convergence of the conditional output distributions corresponding to different messages and leads to an upper bound on the information leakage. We not only introduce the notion of secrecy-good lattices, but also propose the flatness factor as a design criterion of such lattices. Both the modulo-lattice Gaussian channel and genuine Gaussian channel are considered. In the latter case, we propose a novel secrecy coding scheme based on the discrete Gaussian distribution over a lattice, which achieves the secrecy capacity to within a half nat under mild conditions. No a priori distribution of the message is assumed, and no dither is used in our proposed schemes.
Keywords: Gaussian channels; codes; telecommunication security; Gaussian wiretap channel; conditional output distribution; discrete Gaussian distribution; flatness factor; genuine Gaussian channel; information leakage; modulo lattice Gaussian channel; secrecy coding; secrecy good lattice; semantically secure lattice codes; wiretap lattice coding; Encoding; Gaussian distribution; Lattices; Mutual information; Security; Semantics; Zinc; Lattice coding; information theoretic security; semantic security; strong secrecy; wiretap channel (ID#: 15-4878)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6866169&isnumber=6895347

Mirghasemi, H.; Belfiore, J.-C., "The Semantic Secrecy Rate of the Lattice Gaussian Coding for the Gaussian Wiretap Channel," Information Theory Workshop (ITW), 2014 IEEE, vol., no., pp.112,116, 2-5 Nov. 2014. doi:10.1109/ITW.2014.6970803
Abstract: In this paper, we investigate the achievable semantic secrecy rate of existing lattice coding schemes, proposed in [6], for both the mod-Λ Gaussian wiretap and the Gaussian wiretap channels. For both channels, we propose new upper bounds on the amount of leaked information which provide milder sufficient conditions to achieve semantic secrecy. These upper bounds show that the lattice coding schemes in [6] can achieve the secrecy capacity to within ½ln e/2 nat for the mod-Λ Gaussian and to within ½(1 - ln (1 + SNRe / SNRe+1)) nat for the Gaussian wiretap channels where SNRe is the signal-to-noise ratio of Eve.
Keywords: Gaussian channels; channel capacity; data privacy; wireless channels; Gaussian wiretap channels; SNRe; lattice coding schemes; mod-Λ Gaussian wiretap; secrecy capacity; semantic secrecy rate; signal-to-noise ratio of Eve; Encoding; Gaussian distribution; Lattices; Security; Semantics; Upper bound; Zinc (ID#: 15-4879)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6970803&isnumber=6970773

Mirghasemi, H.; Belfiore, J.-C., "The Un-Polarized Bit-Channels in the Wiretap Polar Coding Scheme," Wireless Communications, Vehicular Technology, Information Theory and Aerospace & Electronic Systems (VITAE), 2014 4th International Conference on, vol., no., pp.1 ,5, 11-14 May 2014. doi:10.1109/VITAE.2014.6934465
Abstract: Polar coding theorems state that as the number of channel use, n, tends to infinity, the fraction of un-polarized bit-channels (the bit-channels whose Z parameters are in the interval (δ(n), 1- δ (n)), tends to zero. Consider two BEC channels W(z1) and W(z2). Motivated by polar coding scheme proposed for the wiretap channel, we investigate the number of bit-channels which are simultaneously un-polarized for both of W(z1) and W(z2). We show that for finite values of n, there is a considerable regime of (z1, Z2) where the set of (joint)un-polarized bit-channels is empty. We also show that for γ ≤ 1/2 and δ (n) = 2-nγ, the number of un-polarized bit-channels is lower bounded by 2γ log (n).
Keywords: encoding; security of data; Z-parameter; channel use number; unpolarized bit channel; wiretap channel; wiretap polar coding scheme; Decoding; Encoding; Mutual information; Noise measurement; Reliability; Security; Vectors (ID#: 15-4880)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6934465&isnumber=6934393

Tomamichel, M.; Martinez-Mateo, J.; Pacher, C.; Elkouss, D., "Fundamental Finite Key Limits for Information Reconciliation in Quantum Key Distribution," Information Theory (ISIT), 2014 IEEE International Symposium on, vol., no., pp. 1469, 1473, June 29 2014 – July 4 2014. doi:10.1109/ISIT.2014.6875077
Abstract: The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during one-way information reconciliation is flawed and we propose an improved estimate.
Keywords: cryptographic protocols; information theory; private key cryptography; quantum cryptography; quantum theory; QKD protocols; classical cryptography; fundamental finite key limits; information reconciliation; nonasymptotic classical information theory; quantum key distribution protocols; quantum mechanics security; secret key; Approximation methods; Error analysis; Parity check codes; Protocols; Quantum mechanics; Security (ID#: 15-4881)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6875077&isnumber=6874773

Merhav, N., "Exact Correct-Decoding Exponent of the Wiretap Channel Decoder," Information Theory, IEEE Transactions on, vol. 60, no. 12, pp. 7606, 7615, Dec. 2014. doi:10.1109/TIT.2014.2361765
Abstract: The performance of the achievability scheme for Wyner's wiretap channel model is examined from the perspective of the probability of correct decoding, Pc, at the wiretap channel decoder. In particular, for finite-alphabet memoryless channels, the exact random coding exponent of Pc is derived as a function of the total coding rate R1 and the rate of each subcode R2. Two different representations are given for this function and its basic properties are provided. We also characterize the region of pairs of rates (R1, R2) of full security in the sense of the random coding exponent of Pc, in other words, the region where the exponent of this achievability scheme is the same as that of blind guessing at the eavesdropper side. Finally, an analogous derivation of the correct-decoding exponent is outlined for the case of the Gaussian channel.
Keywords: Gaussian channels; channel coding; decoding; probability; random codes; Gaussian channel; Wyner wiretap channel model; blind guessing; correct decoding probability; finite-alphabet memoryless channels; random coding exponent; Decoding; Encoding; Random variables; Receivers; Reliability; Security; Vectors; Wiretap channel; information–theoretic security ;information theoretic security; random coding exponent; secrecy (ID#: 15-4882)
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6918525&isnumber=6960944

Yingbin Liang; Lifeng Lai; Poor, H.V.; Shamai, S., "A Broadcast Approach for Fading Wiretap Channels," Information Theory, IEEE Transactions on, vol. 60, no.2, pp. 842, 858, Feb. 2014. doi:10.1109/TIT.2013.2293756