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This book provides a first course on lattices – mathematical objects pertaining to the realm of discrete geometry, which are of interest to mathematicians for their structure and, at the same time, are used by electrical and computer engineers working on coding theory and cryptography. The book presents both fundamental concepts and a wealth of applications, including coding and transmission over Gaussian channels, techniques for obtaining lattices from finite prime fields and quadratic fields, constructions of spherical codes, and hard lattice problems used in cryptography. The topics selected are covered in a level of detail not usually found in reference books. As the range of applications of lattices continues to grow, this work will appeal to mathematicians, electrical and computer engineers, and graduate or advanced undergraduate in these fields.
Book Synopsis Lattices Applied to Coding for Reliable and Secure Communications by : Sueli I.R. Costa
Download or read book Lattices Applied to Coding for Reliable and Secure Communications written by Sueli I.R. Costa and published by Springer. This book was released on 2018-04-02 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a first course on lattices – mathematical objects pertaining to the realm of discrete geometry, which are of interest to mathematicians for their structure and, at the same time, are used by electrical and computer engineers working on coding theory and cryptography. The book presents both fundamental concepts and a wealth of applications, including coding and transmission over Gaussian channels, techniques for obtaining lattices from finite prime fields and quadratic fields, constructions of spherical codes, and hard lattice problems used in cryptography. The topics selected are covered in a level of detail not usually found in reference books. As the range of applications of lattices continues to grow, this work will appeal to mathematicians, electrical and computer engineers, and graduate or advanced undergraduate in these fields.
The two-volume proceedings set LNCS 13940 and 13941 constitutes the refereed proceedings of the 26th IACR International Conference on Practice and Theory of Public Key Cryptography, PKC 2023, which took place in March 2023 in Atlanta, GA, USA. The 49 papers included in these proceedings were carefully reviewed and selected from 183 submissions. They focus on all aspects of public-key cryptography, covering Post-Quantum Cryptography, Key Exchange and Messaging, Encryption, Homomorphic Cryptography and other topics.
Book Synopsis Public-Key Cryptography – PKC 2023 by : Alexandra Boldyreva
Download or read book Public-Key Cryptography – PKC 2023 written by Alexandra Boldyreva and published by Springer Nature. This book was released on 2023-05-01 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume proceedings set LNCS 13940 and 13941 constitutes the refereed proceedings of the 26th IACR International Conference on Practice and Theory of Public Key Cryptography, PKC 2023, which took place in March 2023 in Atlanta, GA, USA. The 49 papers included in these proceedings were carefully reviewed and selected from 183 submissions. They focus on all aspects of public-key cryptography, covering Post-Quantum Cryptography, Key Exchange and Messaging, Encryption, Homomorphic Cryptography and other topics.
Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research
Book Synopsis Concise Encyclopedia of Coding Theory by : W. Cary Huffman
Download or read book Concise Encyclopedia of Coding Theory written by W. Cary Huffman and published by CRC Press. This book was released on 2021-03-26 with total page 998 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research
This book celebrates the 50th anniversary of the Institute of Mathematics, Statistics and Scientific Computing (IMECC) of the University of Campinas, Brazil, by offering reviews of selected research developed at one of the most prestigious mathematics institutes in Latin America. Written by senior professors at the IMECC, it covers topics in pure and applied mathematics and statistics ranging from differential geometry, dynamical systems, Lie groups, and partial differential equations to computational optimization, mathematical physics, stochastic process, time series, and more. A report on the challenges and opportunities of research in applied mathematics - a highly active field of research in the country - and highlights of the Institute since its foundation in 1968 completes this historical volume, which is unveiled in the same year that the International Mathematical Union (IMU) names Brazil as a member of the Group V of countries with the most relevant contributions in mathematics.
Book Synopsis Advances in Mathematics and Applications by : Carlile Lavor
Download or read book Advances in Mathematics and Applications written by Carlile Lavor and published by Springer. This book was released on 2018-09-07 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book celebrates the 50th anniversary of the Institute of Mathematics, Statistics and Scientific Computing (IMECC) of the University of Campinas, Brazil, by offering reviews of selected research developed at one of the most prestigious mathematics institutes in Latin America. Written by senior professors at the IMECC, it covers topics in pure and applied mathematics and statistics ranging from differential geometry, dynamical systems, Lie groups, and partial differential equations to computational optimization, mathematical physics, stochastic process, time series, and more. A report on the challenges and opportunities of research in applied mathematics - a highly active field of research in the country - and highlights of the Institute since its foundation in 1968 completes this historical volume, which is unveiled in the same year that the International Mathematical Union (IMU) names Brazil as a member of the Group V of countries with the most relevant contributions in mathematics.
This volume explores the rich interplay between number theory and wireless communications, reviewing the surprisingly deep connections between these fields and presenting new research directions to inspire future research. The contributions of this volume stem from the Workshop on Interactions between Number Theory and Wireless Communication held at the University of York in 2016. The chapters, written by leading experts in their respective fields, provide direct overviews of highly exciting current research developments. The topics discussed include metric Diophantine approximation, geometry of numbers, homogeneous dynamics, algebraic lattices and codes, network and channel coding, and interference alignment. The book is edited by experts working in number theory and communication theory. It thus provides unique insight into key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research. Great effort has been made to present the material in a manner that is accessible to new researchers, including PhD students. The book will also be essential reading for established researchers working in number theory or wireless communications looking to broaden their outlook and contribute to this emerging interdisciplinary area.
Book Synopsis Number Theory Meets Wireless Communications by : Victor Beresnevich
Download or read book Number Theory Meets Wireless Communications written by Victor Beresnevich and published by Springer Nature. This book was released on 2021-01-08 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores the rich interplay between number theory and wireless communications, reviewing the surprisingly deep connections between these fields and presenting new research directions to inspire future research. The contributions of this volume stem from the Workshop on Interactions between Number Theory and Wireless Communication held at the University of York in 2016. The chapters, written by leading experts in their respective fields, provide direct overviews of highly exciting current research developments. The topics discussed include metric Diophantine approximation, geometry of numbers, homogeneous dynamics, algebraic lattices and codes, network and channel coding, and interference alignment. The book is edited by experts working in number theory and communication theory. It thus provides unique insight into key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research. Great effort has been made to present the material in a manner that is accessible to new researchers, including PhD students. The book will also be essential reading for established researchers working in number theory or wireless communications looking to broaden their outlook and contribute to this emerging interdisciplinary area.
Wireless communication networks are widely deployed today and the networks are used in many applications which require that the data transmitted be secure. Due to the open nature of wireless systems, it is important to have a fundamental understanding of coding schemes that allow for simultaneously secure and reliable transmission. The information theoretic approach is able to give us this fundamental insight into the nature of the coding schemes required for security. The security issue is approached by focusing on the confidentiality of message transmission and reception at the physical layer. The goal is to design coding and signal processing schemes that provide security, in the information theoretic sense. In so doing, we are able to prove the simultaneously secure and reliable transmission rates for different network building blocks. The multi-receiver broadcast channel is an important network building block, where the rate region for the channel without security constraints is still unknown. In the thesis this channel is investigated with security constraints, and the secure and reliable rates are derived for the proposed coding scheme using a random coding argument. Cooperative relaying is next applied to the wiretap channel, the fundamental physical layer model for the communication security problem, and signal processing techniques are used to show that the secure rate can be improved in situations where the secure rate was small due to the eavesdropper enjoying a more favorable channel condition compared to the legitimate receiver. Finally, structured lattice codes are used in the wiretap channel instead of unstructured random codes, used in the vast majority of the work so far. We show that lattice coding and decoding can achieve the secrecy rate of the Gaussian wiretap channel; this is an important step towards realizing practical, explicit codes for the wiretap channel.
Book Synopsis Coding and Signal Processing for Secure Wireless Communication by : L. C. Choo
Download or read book Coding and Signal Processing for Secure Wireless Communication written by L. C. Choo and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Wireless communication networks are widely deployed today and the networks are used in many applications which require that the data transmitted be secure. Due to the open nature of wireless systems, it is important to have a fundamental understanding of coding schemes that allow for simultaneously secure and reliable transmission. The information theoretic approach is able to give us this fundamental insight into the nature of the coding schemes required for security. The security issue is approached by focusing on the confidentiality of message transmission and reception at the physical layer. The goal is to design coding and signal processing schemes that provide security, in the information theoretic sense. In so doing, we are able to prove the simultaneously secure and reliable transmission rates for different network building blocks. The multi-receiver broadcast channel is an important network building block, where the rate region for the channel without security constraints is still unknown. In the thesis this channel is investigated with security constraints, and the secure and reliable rates are derived for the proposed coding scheme using a random coding argument. Cooperative relaying is next applied to the wiretap channel, the fundamental physical layer model for the communication security problem, and signal processing techniques are used to show that the secure rate can be improved in situations where the secure rate was small due to the eavesdropper enjoying a more favorable channel condition compared to the legitimate receiver. Finally, structured lattice codes are used in the wiretap channel instead of unstructured random codes, used in the vast majority of the work so far. We show that lattice coding and decoding can achieve the secrecy rate of the Gaussian wiretap channel; this is an important step towards realizing practical, explicit codes for the wiretap channel.
This volume contains the proceedings of the CIMPA Research School and Conference on Algebra for Secure and Reliable Communication Modeling, held from October 1-13, 2012, in Morelia, State of Michoacán, Mexico. The papers cover several aspects of the theory of coding theory and are gathered into three categories: general theory of linear codes, algebraic geometry and coding theory, and constacyclic codes over rings. The aim of this volume is to fill the gap between the theoretical part of algebraic geometry and the applications to problem solving and computational modeling in engineering, signal processing and information theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).
Book Synopsis Algebra for Secure and Reliable Communication Modeling by : Mustapha Lahyane
Download or read book Algebra for Secure and Reliable Communication Modeling written by Mustapha Lahyane and published by American Mathematical Soc.. This book was released on 2015-06-23 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the CIMPA Research School and Conference on Algebra for Secure and Reliable Communication Modeling, held from October 1-13, 2012, in Morelia, State of Michoacán, Mexico. The papers cover several aspects of the theory of coding theory and are gathered into three categories: general theory of linear codes, algebraic geometry and coding theory, and constacyclic codes over rings. The aim of this volume is to fill the gap between the theoretical part of algebraic geometry and the applications to problem solving and computational modeling in engineering, signal processing and information theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).
Since its introduction in the year 2000 by Ahlswede et al., the network coding paradigm has revolutionized the way we understand information flows in networks. Traditionally, information transmitted in a communication network was treated as a commodity in a transportation network, much like cars on highways or fluids in pipes. This approach, however, fails to capture the very nature of information, which in contrast to material goods, can be coded and decoded. The network coding techniques take full advantage of the inherent properties of information, and allow the nodes in a network, not only to store and forward, but also to "mix", i.e., encode, their received data. This approach was shown to result in a substantial throughput gain over the traditional routing and tree packing techniques. In this dissertation, we study applications of network coding for guarantying reliable and secure information transmission in networks with compromised edges. First, we investigate the construction of robust network codes for achieving network resilience against link failures. We focus on the practical important case of unicast networks with non-uniform edge capacities where a single link can fail at a time. We demonstrate that these networks exhibit unique structural properties when they are minimal, i.e., when they do not contain redundant edges. Based on this structure, we prove that robust linear network codes exist for these networks over GF(2), and devise an efficient algorithm to construct them. Second, we consider the problem of securing a multicast network against an eavesdropper that can intercept the packets on a limited number of network links. We recast this problem as a network generalization of the classical wiretap channel of Type II introduced by Ozarow and Wyner in 1984. In particular, we demonstrate that perfect secrecy can be achieved by using the Ozarow-Wyner scheme of coset coding at the source, on top of the implemented network code. Consequently, we transparently recover important results available in the literature on secure network coding. We also derive new bounds on the required secure code alphabet size and an algorithm for code construction. In the last part of this dissertation, we study the connection between index coding, network coding, and matroid linear representation. We devise a reduction from the index coding problem to the network coding problem, implying that in the linear case these two problems are equivalent. We also present a second reduction from the matroid linear representability problem to index coding, and therefore, to network coding. The latter reduction establishes a strong connection between matroid theory and network coding theory. These two reductions are then used to construct special instances of the index coding problem where vector linear codes outperform scalar linear ones, and where non-linear encoding is needed to achieve the optimal number of transmission. Thereby, we provide a counterexample to a related conjecture in the literature and demonstrate the benefits of vector linear codes.
Book Synopsis Network and Index Coding with Application to Robust and Secure Communications by : Salim Y. El Rouayheb
Download or read book Network and Index Coding with Application to Robust and Secure Communications written by Salim Y. El Rouayheb and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its introduction in the year 2000 by Ahlswede et al., the network coding paradigm has revolutionized the way we understand information flows in networks. Traditionally, information transmitted in a communication network was treated as a commodity in a transportation network, much like cars on highways or fluids in pipes. This approach, however, fails to capture the very nature of information, which in contrast to material goods, can be coded and decoded. The network coding techniques take full advantage of the inherent properties of information, and allow the nodes in a network, not only to store and forward, but also to "mix", i.e., encode, their received data. This approach was shown to result in a substantial throughput gain over the traditional routing and tree packing techniques. In this dissertation, we study applications of network coding for guarantying reliable and secure information transmission in networks with compromised edges. First, we investigate the construction of robust network codes for achieving network resilience against link failures. We focus on the practical important case of unicast networks with non-uniform edge capacities where a single link can fail at a time. We demonstrate that these networks exhibit unique structural properties when they are minimal, i.e., when they do not contain redundant edges. Based on this structure, we prove that robust linear network codes exist for these networks over GF(2), and devise an efficient algorithm to construct them. Second, we consider the problem of securing a multicast network against an eavesdropper that can intercept the packets on a limited number of network links. We recast this problem as a network generalization of the classical wiretap channel of Type II introduced by Ozarow and Wyner in 1984. In particular, we demonstrate that perfect secrecy can be achieved by using the Ozarow-Wyner scheme of coset coding at the source, on top of the implemented network code. Consequently, we transparently recover important results available in the literature on secure network coding. We also derive new bounds on the required secure code alphabet size and an algorithm for code construction. In the last part of this dissertation, we study the connection between index coding, network coding, and matroid linear representation. We devise a reduction from the index coding problem to the network coding problem, implying that in the linear case these two problems are equivalent. We also present a second reduction from the matroid linear representability problem to index coding, and therefore, to network coding. The latter reduction establishes a strong connection between matroid theory and network coding theory. These two reductions are then used to construct special instances of the index coding problem where vector linear codes outperform scalar linear ones, and where non-linear encoding is needed to achieve the optimal number of transmission. Thereby, we provide a counterexample to a related conjecture in the literature and demonstrate the benefits of vector linear codes.
This book provides a practical introduction to the theory and practice of coding and information theory for application in the field of electronic communications. It is written at an introductory level and assumes no prior background in coding or information theory. While the mathematical level is detailed, it is still introductory. Through a discussion that balances theory and practical applications and abandons the traditional "theorem-proof" format, this valuable book presents an overview of digital communication systems and the concept of information. It is written in a easy-to-follow conversational style that integrates practical engineering issues through formal and conceptual discussions of mathematical issues. It also makes extensive use of explicit examples that illustrate methods and theory throughout the book. For the professional, it provides an essential hands-on head start for real-world projects and situations. An essential reference for professional engineers in the field of electronic communications.
Book Synopsis Applied Coding and Information Theory for Engineers by : Richard B. Wells
Download or read book Applied Coding and Information Theory for Engineers written by Richard B. Wells and published by Pearson. This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a practical introduction to the theory and practice of coding and information theory for application in the field of electronic communications. It is written at an introductory level and assumes no prior background in coding or information theory. While the mathematical level is detailed, it is still introductory. Through a discussion that balances theory and practical applications and abandons the traditional "theorem-proof" format, this valuable book presents an overview of digital communication systems and the concept of information. It is written in a easy-to-follow conversational style that integrates practical engineering issues through formal and conceptual discussions of mathematical issues. It also makes extensive use of explicit examples that illustrate methods and theory throughout the book. For the professional, it provides an essential hands-on head start for real-world projects and situations. An essential reference for professional engineers in the field of electronic communications.
The mathematical theory and practice of cryptography and coding underpins the provision of effective security and reliability for data communication, processing, and storage. Theoretical and implementational advances in the fields of cryptography and coding are therefore a key factor in facilitating the growth of data communications and data networks of various types. Thus, this Eight International Conference in an established and successful IMA series on the theme of “Cryptography and Coding” was both timely and relevant. The theme of this conference was the future of coding and cryptography, which was touched upon in presentations by a number of invited speakers and researchers. The papers that appear in this book include recent research and development in error control coding and cryptography. These start with mathematical bounds, statistical decoding schemes for error correcting codes, and undetected error probabilities and continue with the theoretical aspects of error correction coding such as graph and trellis decoding, multifunctional and multiple access communication systems, low density parity check codes, and iterative decoding. These are followed by some papers on key recovery attack, authentication, stream cipher design, and analysis of ECIES algorithms, and lattice attacks on IP based protocols.
Book Synopsis Cryptography and Coding by : Bahram Honary
Download or read book Cryptography and Coding written by Bahram Honary and published by Springer. This book was released on 2001-12-10 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical theory and practice of cryptography and coding underpins the provision of effective security and reliability for data communication, processing, and storage. Theoretical and implementational advances in the fields of cryptography and coding are therefore a key factor in facilitating the growth of data communications and data networks of various types. Thus, this Eight International Conference in an established and successful IMA series on the theme of “Cryptography and Coding” was both timely and relevant. The theme of this conference was the future of coding and cryptography, which was touched upon in presentations by a number of invited speakers and researchers. The papers that appear in this book include recent research and development in error control coding and cryptography. These start with mathematical bounds, statistical decoding schemes for error correcting codes, and undetected error probabilities and continue with the theoretical aspects of error correction coding such as graph and trellis decoding, multifunctional and multiple access communication systems, low density parity check codes, and iterative decoding. These are followed by some papers on key recovery attack, authentication, stream cipher design, and analysis of ECIES algorithms, and lattice attacks on IP based protocols.
