Mathematics of Post-quantum Cryptography PDF Download
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Author: Tsuyoshi Takagi
Publisher: Springer
ISBN: 9784431550150
Category : Computers
Languages : en
Pages : 300
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Book Description
This book offers an introduction to post-quantum cryptography for students, engineers and researchers in the field of information security. Above all, it describes the mathematical concepts underlying the security of post-quantum cryptographic schemes. The first part of the book provides essential background information by briefly introducing the core elements of quantum computation and presenting Shor’s algorithm, which solves the factoring problem and the discrete logarithm problem in polynomial time. In turn, the second part presents a number of candidates for post-quantum public-key encryption and digital signature schemes. The security of these schemes is based on mathematical problems in coding theory, multivariate quadratic equations, and lattices, respectively. The book provides an essential guide for students, researchers and engineers, helping them to quickly grasp this highly promising area of cryptography.
Author: Tsuyoshi Takagi
Publisher: Springer
ISBN: 9784431550150
Category : Computers
Languages : en
Pages : 300
Get Book Here
Book Description
This book offers an introduction to post-quantum cryptography for students, engineers and researchers in the field of information security. Above all, it describes the mathematical concepts underlying the security of post-quantum cryptographic schemes. The first part of the book provides essential background information by briefly introducing the core elements of quantum computation and presenting Shor’s algorithm, which solves the factoring problem and the discrete logarithm problem in polynomial time. In turn, the second part presents a number of candidates for post-quantum public-key encryption and digital signature schemes. The security of these schemes is based on mathematical problems in coding theory, multivariate quadratic equations, and lattices, respectively. The book provides an essential guide for students, researchers and engineers, helping them to quickly grasp this highly promising area of cryptography.
Author: Tsuyoshi Takagi
Publisher: Springer Nature
ISBN: 981155191X
Category : Technology & Engineering
Languages : en
Pages : 275
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Book Description
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.
Author: Tsuyoshi Takagi
Publisher: Springer
ISBN: 9811050651
Category : Computers
Languages : en
Pages : 363
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Book Description
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.
Author: Heiko Knospe
Publisher: American Mathematical Soc.
ISBN: 1470450550
Category : Computers
Languages : en
Pages : 344
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Book Description
This book provides a compact course in modern cryptography. The mathematical foundations in algebra, number theory and probability are presented with a focus on their cryptographic applications. The text provides rigorous definitions and follows the provable security approach. The most relevant cryptographic schemes are covered, including block ciphers, stream ciphers, hash functions, message authentication codes, public-key encryption, key establishment, digital signatures and elliptic curves. The current developments in post-quantum cryptography are also explored, with separate chapters on quantum computing, lattice-based and code-based cryptosystems. Many examples, figures and exercises, as well as SageMath (Python) computer code, help the reader to understand the concepts and applications of modern cryptography. A special focus is on algebraic structures, which are used in many cryptographic constructions and also in post-quantum systems. The essential mathematics and the modern approach to cryptography and security prepare the reader for more advanced studies. The text requires only a first-year course in mathematics (calculus and linear algebra) and is also accessible to computer scientists and engineers. This book is suitable as a textbook for undergraduate and graduate courses in cryptography as well as for self-study.
Author: Jeffrey Hoffstein
Publisher: Springer
ISBN: 1493917110
Category : Mathematics
Languages : en
Pages : 549
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Book Description
This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.
Author: Neal Koblitz
Publisher: Springer Science & Business Media
ISBN: 1441985921
Category : Mathematics
Languages : en
Pages : 245
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Book Description
This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.
Author: Steven D. Galbraith
Publisher: Cambridge University Press
ISBN: 1107013925
Category : Computers
Languages : en
Pages : 631
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Book Description
This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.
Author: David Wong
Publisher: Simon and Schuster
ISBN: 1617296716
Category : Computers
Languages : en
Pages : 398
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Book Description
If you''re browsing the web, using public APIs, making and receiving electronic payments, registering and logging in users, or experimenting with blockchain, you''re relying on cryptography. And you''re probably trusting a collection of tools, frameworks, and protocols to keep your data, users, and business safe. It''s important to understand these tools so you can make the best decisions about how, where, and why to use them. Real-World Cryptography teaches you applied cryptographic techniques to understand and apply security at every level of your systems and applications. about the technology Cryptography is the foundation of information security. This simultaneously ancient and emerging science is based on encryption and secure communication using algorithms that are hard to crack even for high-powered computer systems. Cryptography protects privacy, secures online activity, and defends confidential information, such as credit cards, from attackers and thieves. Without cryptographic techniques allowing for easy encrypting and decrypting of data, almost all IT infrastructure would be vulnerable. about the book Real-World Cryptography helps you understand the cryptographic techniques at work in common tools, frameworks, and protocols so you can make excellent security choices for your systems and applications. There''s no unnecessary theory or jargon--just the most up-to-date techniques you''ll need in your day-to-day work as a developer or systems administrator. Cryptography expert David Wong takes you hands-on with cryptography building blocks such as hash functions and key exchanges, then shows you how to use them as part of your security protocols and applications. Alongside modern methods, the book also anticipates the future of cryptography, diving into emerging and cutting-edge advances such as cryptocurrencies, password-authenticated key exchange, and post-quantum cryptography. Throughout, all techniques are fully illustrated with diagrams and real-world use cases so you can easily see how to put them into practice. what''s inside Best practices for using cryptography Diagrams and explanations of cryptographic algorithms Identifying and fixing cryptography bad practices in applications Picking the right cryptographic tool to solve problems about the reader For cryptography beginners with no previous experience in the field. about the author David Wong is a senior engineer working on Blockchain at Facebook. He is an active contributor to internet standards like Transport Layer Security and to the applied cryptography research community. David is a recognized authority in the field of applied cryptography; he''s spoken at large security conferences like Black Hat and DEF CON and has delivered cryptography training sessions in the industry.
Author: Neha Sharma
Publisher: Springer Nature
ISBN: 9811629374
Category : Technology & Engineering
Languages : en
Pages : 530
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Book Description
This book presents the latest findings in the areas of data management and smart computing, machine learning, big data management, artificial intelligence, and data analytics, along with advances in network technologies. The book is a collection of peer-reviewed research papers presented at Fifth International Conference on Data Management, Analytics and Innovation (ICDMAI 2021), held during January 15–17, 2021, in a virtual mode. It addresses state-of-the-art topics and discusses challenges and solutions for future development. Gathering original, unpublished contributions by scientists from around the globe, the book is mainly intended for a professional audience of researchers and practitioners in academia and industry.
Author: Joshua Holden
Publisher: Princeton University Press
ISBN: 0691183317
Category : Computers
Languages : en
Pages : 390
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Book Description
Explaining the mathematics of cryptography The Mathematics of Secrets takes readers on a fascinating tour of the mathematics behind cryptography—the science of sending secret messages. Using a wide range of historical anecdotes and real-world examples, Joshua Holden shows how mathematical principles underpin the ways that different codes and ciphers work. He focuses on both code making and code breaking and discusses most of the ancient and modern ciphers that are currently known. He begins by looking at substitution ciphers, and then discusses how to introduce flexibility and additional notation. Holden goes on to explore polyalphabetic substitution ciphers, transposition ciphers, connections between ciphers and computer encryption, stream ciphers, public-key ciphers, and ciphers involving exponentiation. He concludes by looking at the future of ciphers and where cryptography might be headed. The Mathematics of Secrets reveals the mathematics working stealthily in the science of coded messages. A blog describing new developments and historical discoveries in cryptography related to the material in this book is accessible at http://press.princeton.edu/titles/10826.html.
