Classical and Physical Security of Symmetric Key Cryptographic Algorithms

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Publisher :
ISBN 13 : 9789811665233
Total Pages : 0 pages
Book Rating : 4.6/5 (652 download)

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Book Synopsis Classical and Physical Security of Symmetric Key Cryptographic Algorithms by : Anubhab Baksi

Download or read book Classical and Physical Security of Symmetric Key Cryptographic Algorithms written by Anubhab Baksi and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consolidates several key aspects from the state-of-the-art research in symmetric key cryptography, which is among the cornerstones of digital security. It presents the content in an informative yet beginner-friendly, accompanied with toy examples and comprehensible graphics. In particular, it highlights the recent developments in tool-assisted analysis of ciphers. Furthermore, promising device-dependent attacks, such as fault attack and side channel attacks on symmetric key ciphers, are discussed in detail. One salient feature of this book is to present a detailed analysis of various fault countermeasures. The coverage of our book is quite diverse-it ranges from prerequisite information, latest research contribution as well as future research directions. It caters to students and researchers working in the field of cryptography. .

Classical and Physical Security of Symmetric Key Cryptographic Algorithms

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Publisher : Springer Nature
ISBN 13 : 9811665222
Total Pages : 295 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Classical and Physical Security of Symmetric Key Cryptographic Algorithms by : Anubhab Baksi

Download or read book Classical and Physical Security of Symmetric Key Cryptographic Algorithms written by Anubhab Baksi and published by Springer Nature. This book was released on 2022-01-01 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consolidates several key aspects from the state-of-the-art research in symmetric key cryptography, which is among the cornerstones of digital security. It presents the content in an informative yet beginner-friendly, accompanied with toy examples and comprehensible graphics. In particular, it highlights the recent developments in tool-assisted analysis of ciphers. Furthermore, promising device-dependent attacks, such as fault attack and side channel attacks on symmetric key ciphers, are discussed in detail. One salient feature of this book is to present a detailed analysis of various fault countermeasures. The coverage of our book is quite diverse—it ranges from prerequisite information, latest research contribution as well as future research directions. It caters to students and researchers working in the field of cryptography.

Understanding and Applying Cryptography and Data Security

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Publisher : CRC Press
ISBN 13 : 1420061615
Total Pages : 416 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Understanding and Applying Cryptography and Data Security by : Adam J. Elbirt

Download or read book Understanding and Applying Cryptography and Data Security written by Adam J. Elbirt and published by CRC Press. This book was released on 2009-04-09 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A How-to Guide for Implementing Algorithms and Protocols Addressing real-world implementation issues, Understanding and Applying Cryptography and Data Security emphasizes cryptographic algorithm and protocol implementation in hardware, software, and embedded systems. Derived from the author’s teaching notes and research publications, the text is designed for electrical engineering and computer science courses. Provides the Foundation for Constructing Cryptographic Protocols The first several chapters present various types of symmetric-key cryptographic algorithms. These chapters examine basic substitution ciphers, cryptanalysis, the Data Encryption Standard (DES), and the Advanced Encryption Standard (AES). Subsequent chapters on public-key cryptographic algorithms cover the underlying mathematics behind the computation of inverses, the use of fast exponentiation techniques, tradeoffs between public- and symmetric-key algorithms, and the minimum key lengths necessary to maintain acceptable levels of security. The final chapters present the components needed for the creation of cryptographic protocols and investigate different security services and their impact on the construction of cryptographic protocols. Offers Implementation Comparisons By examining tradeoffs between code size, hardware logic resource requirements, memory usage, speed and throughput, power consumption, and more, this textbook provides students with a feel for what they may encounter in actual job situations. A solutions manual is available to qualified instructors with course adoptions.

A Classical Introduction to Cryptography Exercise Book

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Publisher : Springer Science & Business Media
ISBN 13 : 038728835X
Total Pages : 262 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis A Classical Introduction to Cryptography Exercise Book by : Thomas Baigneres

Download or read book A Classical Introduction to Cryptography Exercise Book written by Thomas Baigneres and published by Springer Science & Business Media. This book was released on 2007-08-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: TO CRYPTOGRAPHY EXERCISE BOOK Thomas Baignkres EPFL, Switzerland Pascal Junod EPFL, Switzerland Yi Lu EPFL, Switzerland Jean Monnerat EPFL, Switzerland Serge Vaudenay EPFL, Switzerland Springer - Thomas Baignbres Pascal Junod EPFL - I&C - LASEC Lausanne, Switzerland Lausanne, Switzerland Yi Lu Jean Monnerat EPFL - I&C - LASEC EPFL-I&C-LASEC Lausanne, Switzerland Lausanne, Switzerland Serge Vaudenay Lausanne, Switzerland Library of Congress Cataloging-in-Publication Data A C.I.P. Catalogue record for this book is available from the Library of Congress. A CLASSICAL INTRODUCTION TO CRYPTOGRAPHY EXERCISE BOOK by Thomas Baignkres, Palcal Junod, Yi Lu, Jean Monnerat and Serge Vaudenay ISBN- 10: 0-387-27934-2 e-ISBN-10: 0-387-28835-X ISBN- 13: 978-0-387-27934-3 e-ISBN- 13: 978-0-387-28835-2 Printed on acid-free paper. O 2006 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if the are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America.

Implementation and Analysis of Ciphers in Quantum Computing

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Publisher : Springer Nature
ISBN 13 : 9819700256
Total Pages : 160 pages
Book Rating : 4.8/5 (197 download)

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Book Synopsis Implementation and Analysis of Ciphers in Quantum Computing by : Anubhab Baksi

Download or read book Implementation and Analysis of Ciphers in Quantum Computing written by Anubhab Baksi and published by Springer Nature. This book was released on with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Classical and Modern Cryptography for Beginners

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Publisher : Springer Nature
ISBN 13 : 3031329597
Total Pages : 230 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Classical and Modern Cryptography for Beginners by : Rajkumar Banoth

Download or read book Classical and Modern Cryptography for Beginners written by Rajkumar Banoth and published by Springer Nature. This book was released on 2023-06-24 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers the knowledge and the mathematical background or techniques that are required to implement encryption/decryption algorithms or security techniques. It also provides the information on the cryptography and a cryptosystem used by organizations and applications to protect their data and users can explore classical and modern cryptography. The first two chapters are dedicated to the basics of cryptography and emphasize on modern cryptography concepts and algorithms. Cryptography terminologies such as encryption, decryption, cryptology, cryptanalysis and keys and key types included at the beginning of this textbook . The subsequent chapters cover basic phenomenon of symmetric and asymmetric cryptography with examples including the function of symmetric key encryption of websites and asymmetric key use cases. This would include security measures for websites, emails, and other types of encryptions that demand key exchange over a public network. Cryptography algorithms (Caesar cipher, Hill cipher, Playfair cipher, Vigenere cipher, DES, AES, IDEA, TEA, CAST, etc.) which are varies on algorithmic criteria like- scalability, flexibility, architecture, security, limitations in terms of attacks of adversary. They are the core consideration on which all algorithms differs and applicable as per application environment. The modern cryptography starts from invent of RSA (Rivest-Shamir-Adleman) which is an asymmetric key algorithm based on prime numbers. Nowadays it is enabled with email and digital transaction over the Internet. This textbook covers Chinese remainder theorem, Legendre, Jacobi symbol, Rabin cryptosystem, generalized ElGamal public key cryptosystem, key management, digital signatures, message authentication, differential cryptanalysis, linear cryptanalysis, time-memory trade-off attack, network security, cloud security, blockchain, bitcoin, etc. as well as accepted phenomenon under modern cryptograph. Advanced level students will find this textbook essential for course work and independent study. Computer scientists and engineers and researchers working within these related fields will also find this textbook useful.

Advances in Data-Driven Computing and Intelligent Systems

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Publisher : Springer Nature
ISBN 13 : 9819995248
Total Pages : 553 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Advances in Data-Driven Computing and Intelligent Systems by : Swagatam Das

Download or read book Advances in Data-Driven Computing and Intelligent Systems written by Swagatam Das and published by Springer Nature. This book was released on with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Why Cryptography Should Not Rely on Physical Attack Complexity

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Publisher : Springer
ISBN 13 : 9812877878
Total Pages : 122 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Why Cryptography Should Not Rely on Physical Attack Complexity by : Juliane Krämer

Download or read book Why Cryptography Should Not Rely on Physical Attack Complexity written by Juliane Krämer and published by Springer. This book was released on 2015-09-05 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents two practical physical attacks. It shows how attackers can reveal the secret key of symmetric as well as asymmetric cryptographic algorithms based on these attacks, and presents countermeasures on the software and the hardware level that can help to prevent them in the future. Though their theory has been known for several years now, since neither attack has yet been successfully implemented in practice, they have generally not been considered a serious threat. In short, their physical attack complexity has been overestimated and the implied security threat has been underestimated. First, the book introduces the photonic side channel, which offers not only temporal resolution, but also the highest possible spatial resolution. Due to the high cost of its initial implementation, it has not been taken seriously. The work shows both simple and differential photonic side channel analyses. Then, it presents a fault attack against pairing-based cryptography. Due to the need for at least two independent precise faults in a single pairing computation, it has not been taken seriously either. Based on these two attacks, the book demonstrates that the assessment of physical attack complexity is error-prone, and as such cryptography should not rely on it. Cryptographic technologies have to be protected against all physical attacks, whether they have already been successfully implemented or not. The development of countermeasures does not require the successful execution of an attack but can already be carried out as soon as the principle of a side channel or a fault attack is sufficiently understood.

Information Security and Cryptology - ICISC 2010

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Publisher : Springer
ISBN 13 : 364224209X
Total Pages : 435 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Information Security and Cryptology - ICISC 2010 by : Kyung-Hyune Rhee

Download or read book Information Security and Cryptology - ICISC 2010 written by Kyung-Hyune Rhee and published by Springer. This book was released on 2011-08-30 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 13th International Conference on Information Security and Cryptology, held in Seoul, Korea, in December 2010. The 28 revised full papers presented were carefully selected from 99 submissions during two rounds of reviewing. The conference provides a forum for the presentation of new results in research, development, and applications in the field of information security and cryptology. The papers are organized in topical sections on cryptanalysis, cryptographic algorithms, implementation, network and mobile security, symmetric key cryptography, cryptographic protocols, and side channel attack.

Fault Analysis in Cryptography

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Publisher : Springer Science & Business Media
ISBN 13 : 3642296564
Total Pages : 352 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Fault Analysis in Cryptography by : Marc Joye

Download or read book Fault Analysis in Cryptography written by Marc Joye and published by Springer Science & Business Media. This book was released on 2012-06-21 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 1970s researchers noticed that radioactive particles produced by elements naturally present in packaging material could cause bits to flip in sensitive areas of electronic chips. Research into the effect of cosmic rays on semiconductors, an area of particular interest in the aerospace industry, led to methods of hardening electronic devices designed for harsh environments. Ultimately various mechanisms for fault creation and propagation were discovered, and in particular it was noted that many cryptographic algorithms succumb to so-called fault attacks. Preventing fault attacks without sacrificing performance is nontrivial and this is the subject of this book. Part I deals with side-channel analysis and its relevance to fault attacks. The chapters in Part II cover fault analysis in secret key cryptography, with chapters on block ciphers, fault analysis of DES and AES, countermeasures for symmetric-key ciphers, and countermeasures against attacks on AES. Part III deals with fault analysis in public key cryptography, with chapters dedicated to classical RSA and RSA-CRT implementations, elliptic curve cryptosystems and countermeasures using fault detection, devices resilient to fault injection attacks, lattice-based fault attacks on signatures, and fault attacks on pairing-based cryptography. Part IV examines fault attacks on stream ciphers and how faults interact with countermeasures used to prevent power analysis attacks. Finally, Part V contains chapters that explain how fault attacks are implemented, with chapters on fault injection technologies for microprocessors, and fault injection and key retrieval experiments on a widely used evaluation board. This is the first book on this topic and will be of interest to researchers and practitioners engaged with cryptographic engineering.

Physical-Layer Security

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Publisher : Cambridge University Press
ISBN 13 : 1139496298
Total Pages : 347 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Physical-Layer Security by : Matthieu Bloch

Download or read book Physical-Layer Security written by Matthieu Bloch and published by Cambridge University Press. This book was released on 2011-09-22 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This complete guide to physical-layer security presents the theoretical foundations, practical implementation, challenges and benefits of a groundbreaking new model for secure communication. Using a bottom-up approach from the link level all the way to end-to-end architectures, it provides essential practical tools that enable graduate students, industry professionals and researchers to build more secure systems by exploiting the noise inherent to communications channels. The book begins with a self-contained explanation of the information-theoretic limits of secure communications at the physical layer. It then goes on to develop practical coding schemes, building on the theoretical insights and enabling readers to understand the challenges and opportunities related to the design of physical layer security schemes. Finally, applications to multi-user communications and network coding are also included.

A Classical Introduction to Cryptography

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Publisher : Springer
ISBN 13 : 9780387254647
Total Pages : 336 pages
Book Rating : 4.2/5 (546 download)

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Book Synopsis A Classical Introduction to Cryptography by : Serge Vaudenay

Download or read book A Classical Introduction to Cryptography written by Serge Vaudenay and published by Springer. This book was released on 2005-09-16 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Classical Introduction to Cryptography: Applications for Communications Security introduces fundamentals of information and communication security by providing appropriate mathematical concepts to prove or break the security of cryptographic schemes. This advanced-level textbook covers conventional cryptographic primitives and cryptanalysis of these primitives; basic algebra and number theory for cryptologists; public key cryptography and cryptanalysis of these schemes; and other cryptographic protocols, e.g. secret sharing, zero-knowledge proofs and undeniable signature schemes. A Classical Introduction to Cryptography: Applications for Communications Security is designed for upper-level undergraduate and graduate-level students in computer science. This book is also suitable for researchers and practitioners in industry. A separate exercise/solution booklet is available as well, please go to www.springeronline.com under author: Vaudenay for additional details on how to purchase this booklet.

Modern Cryptography Volume 1

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Publisher : Springer Nature
ISBN 13 : 9811909202
Total Pages : 364 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Modern Cryptography Volume 1 by : Zhiyong Zheng

Download or read book Modern Cryptography Volume 1 written by Zhiyong Zheng and published by Springer Nature. This book was released on 2022 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas. [Resumen de la editorial]

Foundations of Cryptography

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Publisher : Now Publishers Inc
ISBN 13 : 1933019026
Total Pages : 133 pages
Book Rating : 4.9/5 (33 download)

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Book Synopsis Foundations of Cryptography by : Oded Goldreich

Download or read book Foundations of Cryptography written by Oded Goldreich and published by Now Publishers Inc. This book was released on 2005 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revolutionary developments which took place in the 1980's have transformed cryptography from a semi-scientific discipline to a respectable field in theoretical Computer Science. In particular, concepts such as computational indistinguishability, pseudorandomness and zero-knowledge interactive proofs were introduced and classical notions as secure encryption and unforgeable signatures were placed on sound grounds. The resulting field of cryptography, reviewed in this survey, is strongly linked to complexity theory (in contrast to 'classical' cryptography which is strongly related to information theory).

Secret Key Cryptography

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Publisher : Simon and Schuster
ISBN 13 : 1638351244
Total Pages : 552 pages
Book Rating : 4.6/5 (383 download)

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Book Synopsis Secret Key Cryptography by : Frank Rubin

Download or read book Secret Key Cryptography written by Frank Rubin and published by Simon and Schuster. This book was released on 2022-08-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore the fascinating and rich world of Secret Key cryptography! This book provides practical methods for encrypting messages, an interesting and entertaining historical perspective, and an incredible collection of ciphers and codes—including 30 unbreakable methods. In Secret Key Cryptography: Ciphers, from simple to unbreakable you will: Measure the strength of your ciphers and learn how to guarantee their security Construct and incorporate data-compression codes Generate true random numbers in bulk Construct huge primes and safe primes Add an undetectable backdoor to a cipher Defeat hypothetical ultracomputers that could be developed decades from now Construct 30 unbreakable ciphers Secret Key Cryptography gives you a toolbox of cryptographic techniques and Secret Key methods. The book’s simple, non-technical language is easy to understand and accessible for any reader, even without the advanced mathematics normally required for cryptography. You’ll learn how to create and solve ciphers, as well as how to measure their strength. As you go, you’ll explore both historic ciphers and groundbreaking new approaches—including a never-before-seen way to implement the uncrackable One-Time Pad algorithm. Whoever you are, this book is for you! History buffs will love seeing the evolution of sophisticated cryptographic methods, hobbyists will get a gentle introduction to cryptography, and engineers and computer scientists will learn the principles of constructing secure ciphers. Even professional cryptographers will find a range of new methods and concepts never published before. About the technology From the Roman empire’s Caesar cipher to the WWII Enigma machine, secret messages have influenced the course of history. Today, Secret Key cryptography is the backbone of all modern computing infrastructure. Properly designed, these algorithms are efficient and practical. Some are actually unbreakable, even using supercomputers or quantum technology! About the book Secret Key Cryptography teaches you how to create Secret Key ciphers, ranging from simple pen-and-paper methods to advanced techniques used in modern computer-based cryptography. It reveals both historic examples and current innovations. You’ll learn how to efficiently encrypt large files with fast stream ciphers, discover alternatives to AES encryption, and avoid strong-looking but weak ciphers. Simple language and fun-to-solve mini-ciphers make learning serious concepts easy and engaging. What's inside Construct 30 unbreakable ciphers Measure the strength of your ciphers and guarantee their security Add an undetectable backdoor to a cipher Defeat hypothetical ultracomputers of the future About the reader For professional engineers, computer scientists, and cryptography hobbyists. No advanced math knowledge is required. About the author Frank Rubin has been doing cryptography for over 50 years. He holds an MS in Mathematics, and a PhD in Computer Science. Table of Contents 1 Introduction 2 What is cryptography? 3 Preliminary concepts 4 Cryptographer’s toolbox 5 Substitution ciphers 6 Countermeasures 7 Transposition 8 Jefferson Wheel Cypher 9 Fractionation 10 Variable-length fractionation 11 Block ciphers 12 Principles for secure encryption 13 Stream ciphers 14 One-time pad 15 Matrix methods 16 Three pass protocol 17 Codes 18 Quantum computers

Cryptography Algorithms

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Publisher : Packt Publishing Ltd
ISBN 13 : 1789618576
Total Pages : 358 pages
Book Rating : 4.7/5 (896 download)

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Book Synopsis Cryptography Algorithms by : Massimo Bertaccini

Download or read book Cryptography Algorithms written by Massimo Bertaccini and published by Packt Publishing Ltd. This book was released on 2022-03-03 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Build your real-world cryptography knowledge, from understanding the fundamentals to implementing the most popular modern-day algorithms to excel in your cybersecurity career Key FeaturesLearn modern algorithms such as zero-knowledge, elliptic curves, and quantum cryptographyExplore vulnerability and new logical attacks on the most-used algorithmsUnderstand the practical implementation of algorithms and protocols in cybersecurity applicationsBook Description Cryptography Algorithms is designed to help you get up and running with modern cryptography algorithms. You'll not only explore old and modern security practices but also discover practical examples of implementing them effectively. The book starts with an overview of cryptography, exploring key concepts including popular classical symmetric and asymmetric algorithms, protocol standards, and more. You'll also cover everything from building crypto codes to breaking them. In addition to this, the book will help you to understand the difference between various types of digital signatures. As you advance, you will become well-versed with the new-age cryptography algorithms and protocols such as public and private key cryptography, zero-knowledge protocols, elliptic curves, quantum cryptography, and homomorphic encryption. Finally, you'll be able to apply the knowledge you've gained with the help of practical examples and use cases. By the end of this cryptography book, you will be well-versed with modern cryptography and be able to effectively apply it to security applications. What you will learnUnderstand key cryptography concepts, algorithms, protocols, and standardsBreak some of the most popular cryptographic algorithmsBuild and implement algorithms efficientlyGain insights into new methods of attack on RSA and asymmetric encryptionExplore new schemes and protocols for blockchain and cryptocurrencyDiscover pioneering quantum cryptography algorithmsPerform attacks on zero-knowledge protocol and elliptic curvesExplore new algorithms invented by the author in the field of asymmetric, zero-knowledge, and cryptocurrencyWho this book is for This hands-on cryptography book is for IT professionals, cybersecurity enthusiasts, or anyone who wants to develop their skills in modern cryptography and build a successful cybersecurity career. Working knowledge of beginner-level algebra and finite fields theory is required.

Cryptographic Hardware and Embedded Systems - CHES 2000

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 354041455X
Total Pages : 366 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Cryptographic Hardware and Embedded Systems - CHES 2000 by : Cetin K. Koc

Download or read book Cryptographic Hardware and Embedded Systems - CHES 2000 written by Cetin K. Koc and published by Springer Science & Business Media. This book was released on 2000-12-13 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems, CHES 2000, held in Worcester, MA, USA in August 2000. The 25 revised full papers presented together with two invited contributions were carefully reviewed and selected from 51 submissions. The papers are organized in topical sections on implementation of elliptic curve cryptosystems, power and timing analysis attacks, hardware implementation of block ciphers, hardware architectures, power analysis attacks, arithmetic architectures, physical security and cryptanalysis, and new schemes and algorithms.