Mathematical Modelling For Next Generation Cryptography

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Mathematical Modelling for Next-Generation Cryptography

Author : Tsuyoshi Takagi
Publisher : Springer
ISBN 13 : 9811050651
Total Pages : 363 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Mathematical Modelling for Next-Generation Cryptography by : Tsuyoshi Takagi

Download or read book Mathematical Modelling for Next-Generation Cryptography written by Tsuyoshi Takagi and published by Springer. This book was released on 2017-07-25 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics, among others. Recent advances in cryptanalysis, brought about in particular by quantum computation and physical attacks on cryptographic devices, such as side-channel analysis or power analysis, have revealed the growing security risks for state-of-the-art cryptographic schemes. To address these risks, high-performance, next-generation cryptosystems must be studied, which requires the further development of the mathematical background of modern cryptography. More specifically, in order to avoid the security risks posed by adversaries with advanced attack capabilities, cryptosystems must be upgraded, which in turn relies on a wide range of mathematical theories. This book is suitable for use in an advanced graduate course in mathematical cryptography, while also offering a valuable reference guide for experts.

International Symposium on Mathematics, Quantum Theory, and Cryptography

Author : Tsuyoshi Takagi
Publisher : Springer Nature
ISBN 13 : 981155191X
Total Pages : 275 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis International Symposium on Mathematics, Quantum Theory, and Cryptography by : Tsuyoshi Takagi

Download or read book International Symposium on Mathematics, Quantum Theory, and Cryptography written by Tsuyoshi Takagi and published by Springer Nature. This book was released on 2020-10-22 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography.

Smart and Innovative Trends in Next Generation Computing Technologies

Author : Pushpak Bhattacharyya
Publisher : Springer
ISBN 13 : 9811086605
Total Pages : 1010 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Smart and Innovative Trends in Next Generation Computing Technologies by : Pushpak Bhattacharyya

Download or read book Smart and Innovative Trends in Next Generation Computing Technologies written by Pushpak Bhattacharyya and published by Springer. This book was released on 2018-06-08 with total page 1010 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set CCIS 827 and 828 constitutes the thoroughly refereed proceedings of the Third International Conference on Next Generation Computing Technologies, NGCT 2017, held in Dehradun, India, in October 2017. The 135 full papers presented were carefully reviewed and selected from 948 submissions. There were organized in topical sections named: Smart and Innovative Trends in Communication Protocols and Standards; Smart and Innovative Trends in Computational Intelligence and Data Science; Smart and Innovative Trends in Image Processing and Machine Vision; Smart Innovative Trends in Natural Language Processing for Indian Languages; Smart Innovative Trends in Security and Privacy.

Automated Secure Computing for Next-Generation Systems

Author : Amit Kumar Tyagi
Publisher : John Wiley & Sons
ISBN 13 : 139421359X
Total Pages : 484 pages
Book Rating : 4.3/5 (942 download)

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Book Synopsis Automated Secure Computing for Next-Generation Systems by : Amit Kumar Tyagi

Download or read book Automated Secure Computing for Next-Generation Systems written by Amit Kumar Tyagi and published by John Wiley & Sons. This book was released on 2024-01-04 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: AUTOMATED SECURE COMPUTING FOR NEXT-GENERATION SYSTEMS This book provides cutting-edge chapters on machine-empowered solutions for next-generation systems for today’s society. Security is always a primary concern for each application and sector. In the last decade, many techniques and frameworks have been suggested to improve security (data, information, and network). Due to rapid improvements in industry automation, however, systems need to be secured more quickly and efficiently. It is important to explore the best ways to incorporate the suggested solutions to improve their accuracy while reducing their learning cost. During implementation, the most difficult challenge is determining how to exploit AI and ML algorithms for improved safe service computation while maintaining the user’s privacy. The robustness of AI and deep learning, as well as the reliability and privacy of data, is an important part of modern computing. It is essential to determine the security issues of using AI to protect systems or ML-based automated intelligent systems. To enforce them in reality, privacy would have to be maintained throughout the implementation process. This book presents groundbreaking applications related to artificial intelligence and machine learning for more stable and privacy-focused computing. By reflecting on the role of machine learning in information, cyber, and data security, Automated Secure Computing for Next-Generation Systems outlines recent developments in the security domain with artificial intelligence, machine learning, and privacy-preserving methods and strategies. To make computation more secure and confidential, the book provides ways to experiment, conceptualize, and theorize about issues that include AI and machine learning for improved security and preserve privacy in next-generation-based automated and intelligent systems. Hence, this book provides a detailed description of the role of AI, ML, etc., in automated and intelligent systems used for solving critical issues in various sectors of modern society. Audience Researchers in information technology, robotics, security, privacy preservation, and data mining. The book is also suitable for postgraduate and upper-level undergraduate students.

Next Generation SSH2 Implementation

Author : Dale Liu
Publisher : Syngress
ISBN 13 : 0080570003
Total Pages : 336 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Next Generation SSH2 Implementation by : Dale Liu

Download or read book Next Generation SSH2 Implementation written by Dale Liu and published by Syngress. This book was released on 2011-04-18 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: New security risks, continuously evolving regulation and increasing security standards have created new and growing needs for secure internal information transfers, which SSH provides. This book addresses these new trends in depth, offering the most up-to-date information on the integration of SSH into a security environment. It covers the newest features and applications of SSH-2 (which received Proposed Standard status from the IETF in 2006). SSH2 is more secure than previous versions and has many expanded uses on a wider variety of computing platforms. Another particular note driving new SSH2 adoption are the requirements of recent legislation (PCI/HIPAA/SOX/FISMA). SSH 2 has become an even more valuable tool, as it provides communications security compliance with the latest standards.This book offers the most up-to-date information on SSH2 in a practical, hands-on, tutorial-style reference that goes well beyond UNIX implementation. It concentrates on the latest version of SSH 2 with all new information. - Discover why SSH2 offers more robust security than SSH1 and how to incorporate it into your network administration software toolbox

Enabling Technologies for Next Generation Wireless Communications

Author : Mohammed Usman
Publisher : CRC Press
ISBN 13 : 1000328945
Total Pages : 296 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Enabling Technologies for Next Generation Wireless Communications by : Mohammed Usman

Download or read book Enabling Technologies for Next Generation Wireless Communications written by Mohammed Usman and published by CRC Press. This book was released on 2020-12-28 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Enabling Technologies for Next Generation Wireless Communications provides up-to-date information on emerging trends in wireless systems, their enabling technologies and their evolving application paradigms. This book includes the latest trends and developments toward next generation wireless communications. It highlights the requirements of next generation wireless systems, limitations of existing technologies in delivering those requirements and the need to develop radical new technologies. It focuses on bringing together information on various technological developments that are enablers vital to fulfilling the requirements of future wireless communication systems and their applications. Topics discussed include spectrum issues, network planning, signal processing, transmitter, receiver, antenna technologies, channel coding, security and application of machine learning and deep learning for wireless communication systems. The book also provides information on enabling business models for future wireless systems. This book is useful as a resource for researchers and practitioners worldwide, including industry practitioners, technologists, policy decision-makers, academicians, and graduate students.

Quantum and Blockchain for Modern Computing Systems: Vision and Advancements

Author : Adarsh Kumar
Publisher : Springer Nature
ISBN 13 : 3031046137
Total Pages : 371 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Quantum and Blockchain for Modern Computing Systems: Vision and Advancements by : Adarsh Kumar

Download or read book Quantum and Blockchain for Modern Computing Systems: Vision and Advancements written by Adarsh Kumar and published by Springer Nature. This book was released on 2022-07-21 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book states that blockchain technology provides a secure distributed, peer-to-peer, and decentralized network with advanced cryptography primitives and protocols. The important question that arises in the quantum computing world is to test the existing blockchain networks against quantum attacks and design quantum computing enabled secure blockchain solutions. This book encourages professionals from different fields to provide blockchain and quantum technology-integrated solutions that incorporate low-cost, effective QoS, fast, secure, and futuristic demands. This book has surveyed and proposed approaches that improve quantum computing and cryptography protocols. Quantum computing and quantum science are not just helpful in software but the hardware world as well. To design networks with quantum science, quantum-enabled devices like quantum memories and quantum repeaters can be useful to demonstrate for organizations. For example, designing a single quantum repeater for long-distance quantum communication is useful in reducing the network cost, and ensuring better security levels. This book has introduced the quantum computing and blockchain technology aspects, their integration approaches and future directions.

Computer Information Systems and Industrial Management

Author : Khalid Saeed
Publisher : Springer
ISBN 13 : 3642409253
Total Pages : 541 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Computer Information Systems and Industrial Management by : Khalid Saeed

Download or read book Computer Information Systems and Industrial Management written by Khalid Saeed and published by Springer. This book was released on 2013-09-20 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 12th IFIP TC 8 International Conference, CISIM 2013, held in Cracow, Poland, in September 2013. The 44 papers presented in this volume were carefully reviewed and selected from over 60 submissions. They are organized in topical sections on biometric and biomedical applications; pattern recognition and image processing; various aspects of computer security, networking, algorithms, and industrial applications. The book also contains full papers of a keynote speech and the invited talk.

Security and Privacy for Next-Generation Wireless Networks

Author : Sheng Zhong
Publisher : Springer
ISBN 13 : 303001150X
Total Pages : 194 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Security and Privacy for Next-Generation Wireless Networks by : Sheng Zhong

Download or read book Security and Privacy for Next-Generation Wireless Networks written by Sheng Zhong and published by Springer. This book was released on 2018-11-22 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This timely book provides broad coverage of security and privacy issues in the macro and micro perspective. In macroperspective, the system and algorithm fundamentals of next-generation wireless networks are discussed. In micro-perspective, this book focuses on the key secure and privacy techniques in different emerging networks from the interconnection view of human and cyber-physical world. This book includes 7 chapters from prominent international researchers working in this subject area. This book serves as a useful reference for researchers, graduate students, and practitioners seeking solutions to wireless security and privacy related issues Recent advances in wireless communication technologies have enabled the large-scale deployment of next-generation wireless networks, and many other wireless applications are emerging. The next generation of mobile networks continues to transform the way people communicate and access information. As a matter of fact, next-generation emerging networks are exploiting their numerous applications in both military and civil fields. For most applications, it is important to guarantee high security of the deployed network in order to defend against attacks from adversaries, as well as the privacy intrusion. The key target in the development of next-generation wireless networks is to promote the integration of the human, cyber, and physical worlds. Previous work in Cyber Physical Systems (CPS) considered the connection between the cyber world and the physical world. In the recent studies, human involvement brings new channels and initiatives in this interconnection. In this integration process, security and privacy are critical issues to many wireless network applications, and it is a paramount concern for the growth of next-generation wireless networks. This is due to the open nature of wireless communication and the involvement of humans. New opportunities for tackling these security and privacy issues in next-generation wireless networks will be achieved by leveraging the properties of interaction among human, computers and things.

Managing Next Generation Networks and Services

Author : Shingo Ata
Publisher : Springer Science & Business Media
ISBN 13 : 354075475X
Total Pages : 634 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Managing Next Generation Networks and Services by : Shingo Ata

Download or read book Managing Next Generation Networks and Services written by Shingo Ata and published by Springer Science & Business Media. This book was released on 2007-09-20 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 9th Asia-Pacific Network Operations and Management Symposium, APNOMS 2007, held in Sapporo, Japan, October 2007. The 48 revised full papers and 30 revised short papers cover management of distributed networks, network configuration and planning, network security management, sensor and ad-hoc networks, network monitoring, routing and traffic engineering, management of wireless networks and security on wireless networks.

Mathematical Circle Diaries, Year 2

Author : Anna Burago
Publisher : American Mathematical Soc.
ISBN 13 : 147043718X
Total Pages : 378 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mathematical Circle Diaries, Year 2 by : Anna Burago

Download or read book Mathematical Circle Diaries, Year 2 written by Anna Burago and published by American Mathematical Soc.. This book was released on 2018-07-03 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical circles, with their question-driven approach and emphasis on problem solving, expose students to the type of mathematics that stimulates the development of logical thinking, creativity, analytical abilities, and mathematical reasoning. These skills, while scarcely introduced at school, are in high demand in the modern world. This book, a sequel to Mathematical Circle Diaries, Year 1, teaches how to think and solve problems in mathematics. The material, distributed among twenty-nine weekly lessons, includes detailed lectures and discussions, sets of problems with solutions, and contests and games. In addition, the book shares some of the know-how of running a mathematical circle. The book covers a broad range of problem-solving strategies and proofing techniques, as well as some more advanced topics that go beyond the limits of a school curriculum. The topics include invariants, proofs by contradiction, the Pigeonhole principle, proofs by coloring, double counting, combinatorics, binary numbers, graph theory, divisibility and remainders, logic, and many others. When students take science and computing classes in high school and college, they will be better prepared for both the foundations and advanced material. The book contains everything that is needed to run a successful mathematical circle for a full year. This book, written by an author actively involved in teaching mathematical circles for fifteen years, is intended for teachers, math coaches, parents, and math enthusiasts who are interested in teaching math that promotes critical thinking. Motivated students can work through this book on their own. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Implementing Data Analytics and Architectures for Next Generation Wireless Communications

Author : Bhatt, Chintan
Publisher : IGI Global
ISBN 13 : 1799869903
Total Pages : 227 pages
Book Rating : 4.7/5 (998 download)

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Book Synopsis Implementing Data Analytics and Architectures for Next Generation Wireless Communications by : Bhatt, Chintan

Download or read book Implementing Data Analytics and Architectures for Next Generation Wireless Communications written by Bhatt, Chintan and published by IGI Global. This book was released on 2021-08-13 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wireless communication is continuously evolving to improve and be a part of our daily communication. This leads to improved quality of services and applications supported by networking technologies. We are now able to use LTE, LTE-Advanced, and other emerging technologies due to the enormous efforts that are made to improve the quality of service in cellular networks. As the future of networking is uncertain, the use of deep learning and big data analytics is a point of focus as it can work in many capacities at a variety of levels for wireless communications. Implementing Data Analytics and Architectures for Next Generation Wireless Communications addresses the existing and emerging theoretical and practical challenges in the design, development, and implementation of big data algorithms, protocols, architectures, and applications for next generation wireless communications and their applications in smart cities. The chapters of this book bring together academics and industrial practitioners to exchange, discuss, and implement the latest innovations and applications of data analytics in advanced networks. Specific topics covered include key encryption techniques, smart home appliances, fog communication networks, and security in the internet of things. This book is valuable for technologists, data analysts, networking experts, practitioners, researchers, academicians, and students.

Building Next-Generation Converged Networks

Author : Al-Sakib Khan Pathan
Publisher : CRC Press
ISBN 13 : 1466507616
Total Pages : 606 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Building Next-Generation Converged Networks by : Al-Sakib Khan Pathan

Download or read book Building Next-Generation Converged Networks written by Al-Sakib Khan Pathan and published by CRC Press. This book was released on 2013-01-29 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supplying a comprehensive introduction to next-generation networks, Building Next-Generation Converged Networks: Theory and Practice strikes a balance between how and why things work and how to make them work. It compiles recent advancements along with basic issues from the wide range of fields related to next generation networks. Containing the contributions of 56 industry experts and researchers from 16 different countries, the book presents relevant theoretical frameworks and the latest research. It investigates new technologies such as IPv6 over Low Power Wireless Personal Area Network (6LoWPAN) architectures, standards, mobility, and security. Presenting the material in a manner that entry-level readers can easily grasp the fundamentals, the book is organized into five parts: Multimedia Streaming—deals with multimedia streaming in networks of the future—from basics to more in-depth information for the experts Safety and Security in Networks—addresses the issues related to security, including fundamental Internet and cyber-security concepts that will be relevant in any future network Network Management and Traffic Engineering—includes coverage of mathematical modeling-based works Information Infrastructure and Cloud Computing—integrates information about past achievements, present conditions, and future expectations in information infrastructure-related areas Wireless Networking—touches on the various aspects of wireless networks and technologies The text includes coverage of Internet architectures and protocols, embedded systems and sensor networks, web services, Cloud technologies, and next-generation wireless networking. Reporting on the latest advancements in the field, it provides you with the understanding required to contribute towards the materialization of future networks. This book is suitable for graduate students, researchers, academics, industry practitioners working in the area of wired or wireless networking, and basically anyone who wants to improve his or her understanding of the topics related to next-generation networks.

Post-Quantum Cryptography

Author : Jintai Ding
Publisher : Springer Nature
ISBN 13 : 3030442233
Total Pages : 562 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Post-Quantum Cryptography by : Jintai Ding

Download or read book Post-Quantum Cryptography written by Jintai Ding and published by Springer Nature. This book was released on 2020-04-10 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the proceedings of the 11th International Conference on post-quantum cryptography, PQCrypto 2020, held in Paris, France in April 2020. The 29 full papers presented in this volume were carefully reviewed and selected from 86 submissions. They cover a broad spectrum of research within the conference's scope, including code-, hash-, isogeny-, and lattice-based cryptography, multivariate cryptography, and quantum cryptanalysis.

Internet of Things, Smart Spaces, and Next Generation Networks and Systems

Author : Yevgeni Koucheryavy
Publisher : Springer Nature
ISBN 13 : 3031302583
Total Pages : 672 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Internet of Things, Smart Spaces, and Next Generation Networks and Systems by : Yevgeni Koucheryavy

Download or read book Internet of Things, Smart Spaces, and Next Generation Networks and Systems written by Yevgeni Koucheryavy and published by Springer Nature. This book was released on 2023-04-19 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 22nd International Conference on Internet of Things, Smart Spaces, and Next Generation Networks and Systems, NEW2AN 2022, held in Tashkent, Uzbekistan, in December 2022. The 58 regular papers presented in this volume were carefully reviewed and selected from 282 submissions. The papers of NEW2AN address various aspects of next-generation data networks, while special attention is given to advanced wireless networking and applications. In particular, the authors have demonstrated novel and innovative approaches to performance and efficiency analysis of 5G and beyond systems, employed game-theoretical formulations, advanced queuing theory, and machine learning. It is also worth mentioning the rich coverage of the Internet of Things, optics, signal processing, as well as digital economy and business aspects.

Securing Next-Generation Connected Healthcare Systems

Author : Deepak Gupta
Publisher : Elsevier
ISBN 13 : 0443139520
Total Pages : 254 pages
Book Rating : 4.4/5 (431 download)

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Book Synopsis Securing Next-Generation Connected Healthcare Systems by : Deepak Gupta

Download or read book Securing Next-Generation Connected Healthcare Systems written by Deepak Gupta and published by Elsevier. This book was released on 2024-05-14 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Securing Next-Generation Connected Healthcare Systems focuses on the crucial aspects of IoT security in a connected environment, which will not only benefit from cutting-edge methodological approaches but also assist in the rapid scalability and improvement of these systems. This book shows how to utilize technologies like blockchain and its integration with IoT for communication, data security, and trust management. This book will introduce the security aspect of next generation technologies for healthcare, covering a wide range of security and computing methodologies. Researchers, data scientists, students, and professionals interested in the application of artificial intelligence in healthcare management, data security of connected healthcare systems and related fields, specifically on data intensive secured systems and computing environments will finds this to be a welcomed resource. - Covers the latest next generation connected healthcare technologies using parallel computing - Presents all the security aspects in next-generation technologies for healthcare - Utilizes technologies such as blockchain and its integration with IoT for communication, data security, and trust management - Discusses privacy and security issues and challenges in data intensive cloud computing environment - Dives into the concept of parallel and distributed computing technologies and their applications in the real world

Secret History

Author : Craig Bauer
Publisher : CRC Press
ISBN 13 : 1351668498
Total Pages : 775 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Secret History by : Craig Bauer

Download or read book Secret History written by Craig Bauer and published by CRC Press. This book was released on 2021-04-20 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this award-winning book attracted a wide audience. This second edition is both a joy to read and a useful classroom tool. Unlike traditional textbooks, it requires no mathematical prerequisites and can be read around the mathematics presented. If used as a textbook, the mathematics can be prioritized, with a book both students and instructors will enjoy reading. Secret History: The Story of Cryptology, Second Edition incorporates new material concerning various eras in the long history of cryptology. Much has happened concerning the political aspects of cryptology since the first edition appeared. The still unfolding story is updated here. The first edition of this book contained chapters devoted to the cracking of German and Japanese systems during World War II. Now the other side of this cipher war is also told, that is, how the United States was able to come up with systems that were never broken. The text is in two parts. Part I presents classic cryptology from ancient times through World War II. Part II examines modern computer cryptology. With numerous real-world examples and extensive references, the author skillfully balances the history with mathematical details, providing readers with a sound foundation in this dynamic field. FEATURES Presents a chronological development of key concepts Includes the Vigenère cipher, the one-time pad, transposition ciphers, Jefferson’s wheel cipher, Playfair cipher, ADFGX, matrix encryption, Enigma, Purple, and other classic methods Looks at the work of Claude Shannon, the origin of the National Security Agency, elliptic curve cryptography, the Data Encryption Standard, the Advanced Encryption Standard, public-key cryptography, and many other topics New chapters detail SIGABA and SIGSALY, successful systems used during World War II for text and speech, respectively Includes quantum cryptography and the impact of quantum computers