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A construction of public-key cryptosystem using algebraic coding on the basis of superimposition and randomness

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2006年第1期E89A卷 47-54页

作者： Kasahara, M Osaka Gakuin Univ Fac Informat Suita Osaka 5648511 Japan

In this paper, we present a new class of public-key cryptosystem (PKC) using algebraic coding on the basis of superimposition and randomness. The proposed PKC is featured by a generator matrix, in a characteristic form, where the generator matrix of an algebraic code is repeatedly used along with the generator matrix of a random code, as submatrices. This generator matrix, in the characteristic form, will be referred to as K-matrix. We show that the K-matrix yields the following advantages compared with the conventional schemes: (i) It realizes an abundant supply of PKCs, yielding more secure PKCs, (ii) It realizes a short public key.

关键词： algebraic coding random coding public-key cryptosystem

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Deterministic Network Model Revisited: An algebraic Network coding Approach

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IEEE TRANSACTIONS ON INFORMATION THEORY 2014年第8期60卷 4867-4879页

作者： Erez, Elona Kim, MinJi Xu, Yun Yeh, Edmund M. Medard, Muriel Yale Univ Dept Elect Engn New Haven CT 06511 USA MIT Dept Elect Engn & Comp Sci Cambridge MA 02139 USA

The capacity of multiuser networks has been a long-standing problem in information theory. Recently, Avestimehr et al. have proposed a deterministic network model to approximate multiuser wireless networks. This model, known as the ADT network model, takes into account the broadcast nature as well as the multiuser interference inherent in the wireless medium. For the types of connections we consider, we show that the results of Avestimehr et al. under the ADT model can be reinterpreted within the algebraic network coding framework introduced by Koetter and Medard. Using this framework, we propose an efficient distributed linear code construction for the deterministic wireless multicast relay network model. Unlike several previous coding schemes, we do not attempt to find flows in the network. Instead, for a layered network, we maintain an invariant where it is required that at each stage of the code construction, certain sets of codewords are linearly independent.

关键词： Network coding deterministic network algebraic coding multicast non-multicast code construction

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An algebraic approach to network coding

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IEEE-ACM TRANSACTIONS ON NETWORKING 2003年第5期11卷 782-795页

作者： Koetter, R Médard, M Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA MIT Informat & Decis Syst Lab Cambridge MA 02139 USA

We take a new look at the issue of network capacity. It is shown that network coding is an essential ingredient in achieving the capacity of a network. Building on recent work by Li et al., who examined the network capacity of multicast networks, we extend the network coding framework to arbitrary networks and robust networking. For networks which are restricted to using linear network codes, we find necessary and sufficient conditions for the feasibility of any given set of connections over a given network. We also consider the problem of network recovery for nonergodic link failures. For the multicast setup we prove that there exist coding strategies that provide maximally robust networks and that do not require adaptation of the network interior to the failure pattern in question. The results are derived for both delay-free networks and networks with delays.

关键词： algebraic coding network information theory network robustness

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Low-Complexity Secure Network coding Against Wiretapping Using Intra/Inter-generation coding

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China Communications 2015年第6期12卷 116-125页

作者： LIU Guangjun LIU Binyue LIU Ximeng LI Fang GUO Wangmei School of Information Engineering Xi'an University State Key Laboratory of Integrated Service Networks Xidian University

Existing solutions against wiretapping attacks for network coding either bring significant bandwidth overhead or incur a high computational *** order to reduce the security overhead of the existing solutions for securing network coding,a novel securing network coding paradigm is presented relying on two coding models:intra-generation coding and inter-generation *** basic idea to secure network coding using intra-generation coding is to limit the encryption operations for each generation,and then subject the scrambled and the remaining original source vectors to a linear *** method is then generalized seamlessly using inter-generation coding by further exploiting the algebraic structure of network *** show that the proposed schemes have properties of low-complexity security,little bandwidth consumption,and high efficiency in integrating with the existing security techniques effectively.

关键词： network coding security wiretap-ping attacks algebraic coding encryption

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Secure Network coding on a Wiretap Network

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第1期57卷 424-435页

作者： Cai, Ning Yeung, Raymond W. Chinese Univ Hong Kong Dept Informat Engn Hong Kong Hong Kong Peoples R China Chinese Univ Hong Kong Inst Network Coding Shatin Hong Kong Peoples R China

In the paradigm of network coding, the nodes in a network are allowed to encode the information received from the input links. With network coding, the full capacity of the network can be utilized. In this paper, we propose a model, call the wiretap network, that incorporates information security with network coding. In this model, a collection of subsets of the channels in the network is given, and a wiretapper is allowed to access any one (but not more than one) of these subsets without being able to obtain any information about the message transmitted. Our model includes secret sharing in classical cryptography as a special case. We present a construction of secure linear network codes that can be used provided a certain graph-theoretic condition is satisfied. We also prove the necessity of this condition for the special case that the wiretapper may choose to access any subset of channels of a fixed size. The optimality of our code construction is established for this special case. Finally, we extend our results to the scenario when the wiretapper is allowed to obtain a controlled amount of information about the message.

关键词： algebraic coding cryptography multicast network coding secret sharing wiretap channel

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Network Generalized Hamming Weight

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第2期57卷 1136-1143页

作者： Ngai, Chi-Kin Yeung, Raymond W. Zhang, Zhixue Chinese Univ Hong Kong Dept Informat Engn Hong Kong Hong Kong Peoples R China Chinese Univ Hong Kong Inst Network Coding Hong Kong Hong Kong Peoples R China Beijing Univ Posts & Telecommun Beijing 100088 Peoples R China

In this work, we extend the notion of generalized Hamming weight for classical linear block codes to linear network codes by introducing the network generalized Hamming weight (NGHW) for a given network with respect to a fixed linear network code. The basic properties of NGHW are studied. We further show that NGHW can be used as a tool to characterize the security performance of a linear network code on a wiretap network. We also introduce the notion of network maximum distance separable code (NMDS code) by extending the notion of Maximum Distance Separable code in classical algebraic coding theory. We prove that NMDS codes play an important role in minimizing the information that an eavesdropper can obtain from the network.

关键词： algebraic coding cryptography generalized Hamming weight MDS code multicast network coding secret sharing wiretap channel

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A distributed space-time coding in asynchronous wireless relay networks

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2008年第5期7卷 1812-1816页

作者： Guo, Xiaoyong Xia, Xiang-Gen Univ Delaware Dept Elect & Comp Engn Newark DE 19716 USA

Jing and Hassibi recently presented a detailed analysis on the problem of distributed space-time coding for a synchronized wireless relay network, where only linear transforms are implemented at relay nodes, and proposed a linear dispersion coding scheme. In this letter, we extend it to asynchronous wireless networks by employing OFDM to combat timing errors from relay nodes. Based on a layered structure, we present a distributed space-time code design achieving full spatial diversity for an asynchronous wireless relay network.

关键词： algebraic coding asynchronous cooperative networks distributive linear dispersion space-time coding

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Dual of codes over finite quotients of polynomial rings

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FINITE FIELDS AND THEIR APPLICATIONS 2017年 45卷 323-340页

作者： Nikseresht, Ashkan Inst Adv Studies Basic Sci Dept Math POB 45195-1159 Zanjan Iran

Let A = F[x]/, where f (x) is a monic polynomial over a finite field F. In this paper, we study the relation between A-codes and their duals. In particular, we state a counterexample and a correction to a theorem of B... 详细信息

Let A = F[x]/< f(x)>, where f (x) is a monic polynomial over a finite field F. In this paper, we study the relation between A-codes and their duals. In particular, we state a counterexample and a correction to a theorem of Berger and El Amrani (2014) [3] and present an efficient algorithm to find a system of generators for the dual of a given A-code. Also we characterize self-dual A-codes of length 2 and investigate when the F-dual of A-codes are A-codes. (C) 2017 Elsevier Inc. All rights reserved.

关键词： algebraic coding Dual of a code Basis of divisors Polynomial ring

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Unconventional construction of DNA codes: Group Homomorphism

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JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY 2014年第3期17卷 227-237页

作者： Selvakumar, R. VIT Univ Sch Adv Sci Appl Algebra Div Vellore Tamil Nadu India

One of the key problems in DNA computation is the design of large and reliable codes. Due to the biological and chemical restrictions, DNA codes need to satisfy certain constraints. Here, we provide an algebraic procedure to construct DNA codes by using homomorphism of groups. The construction procedure is used to determine mutation.

关键词： DNA computation DNA coding algebraic coding Group codes

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Design of diagonal algebraic space time codes with 8-star-PSK signals

Design of diagonal algebraic space time codes with 8-star-PS...

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14th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications

作者： Fan, PY Tsing Hua Univ Dept Elect Engn State Key Lab Microwave & Digital Commun Beijing 100084 Peoples R China

ISBN: (纸本)7505350668

Diagonal algebraic space time (DAST) block codes was proved to outperform the codes from orthogonal design with the equivalent spectral efficiency when the number of transmit antennas employed is larger than 2. However, due to the limitation on the signal constellation with complex integer points, no good 3bits/symbol DAST block code was not given previously. In this paper, we propose a general form of 8-star-PSK constellations with integer points and present some theoretical results on the performance of the equivalent 8-star-PSK modulations. By using our proposed 8-star-PSKs, we present a searching algorithm to construct optimal DAST codes with 3 bits per symbol under some criteria and investigate their performances. over flat Rayleigh fading channels.

关键词： space time coding algebraic coding Rayleigh fading channel multiple antennas

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