After introducing the basic mathematical and computational complexity concepts, and some historical context, including the story of Enigma, the authors explain symmetric and asymmetric cryptography, electronic signatures and hash functions, PGP systems, public key infrastructures, cryptographic protocols, and applications in network security. In each case the text presents the key technologies, algorithms, and protocols, along with methods of design and analysis, while the content is characterized by a visual style and all algorithms are presented in readable pseudocode or using simple graphics and diagrams.
The book is suitable for undergraduate and graduate courses in computer science and engineering, particularly in the area of networking, and it is also a suitable reference text for self-study by practitioners and researchers. The authors assume only basic elementary mathematical experience, the text covers the foundational mathematics and computational complexity theory.
A distinctive feature of the author's approach is the use of Maple as a programming environment in which not just the cryptographic primitives but also the most important cryptographic schemes are implemented following the recommendations of standards bodies such as NIST, with many of the known cryptanalytic attacks implemented as well. The purpose of the Maple implementations is to let the reader experiment and learn, and for this reason the author includes numerous examples. The book discusses important recent subjects such as homomorphic encryption, identity-based cryptography and elliptic curve cryptography. The algorithms and schemes which are treated in detail and implemented in Maple include AES and modes of operation, CMAC, GCM/GMAC, SHA-256, HMAC, RSA, Rabin, Elgamal, Paillier, Cocks IBE, DSA and ECDSA. In addition, some recently introduced schemes enjoying strong security properties, such as RSA-OAEP, Rabin-SAEP, Cramer--Shoup, and PSS, are also discussed and implemented. On the cryptanalysis side, Maple implementations and examples are used to discuss many important algorithms, including birthday and man-in-the-middle attacks, integer factorization algorithms such as Pollard's rho and the quadratic sieve, and discrete log algorithms such as baby-step giant-step, Pollard's rho, Pohlig--Hellman and the index calculus method.
This textbook is suitable for advanced undergraduate and graduate students of computer science, engineering and mathematics, satisfying the requirements of various types of courses: a basic introductory course; a theoretically oriented course whose focus is on the precise definition of security concepts and on cryptographic schemes with reductionist security proofs; a practice-oriented course requiring little mathematical background and with an emphasis on applications; or a mathematically advanced course addressed to students with a stronger mathematical background. The main prerequisite is a basic knowledge of linear algebra and elementary calculus, and while some knowledge of probability and abstract algebra would be helpful, it is not essential because the book includes the necessary background from these subjects and, furthermore, explores the number-theoretic material in detail. The book is also a comprehensive reference and is suitable for self-study by practitioners and programmers.
The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include:
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 Introductionto 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.
Cryptography is not just for specialists. Now every wireless message, wireless phone call, online transaction, and email is encrypted at one end and decrypted at the other. “Crypto” is part of the job description for network designers, network engineers, and telecom developers. If you need cryptography basics—but dread the thick tomes that are your only other option—help is at hand. Cryptography Demystified puts the fundamentals into a 35-module, learn-by-doing package that’s actually fun to use.
You must read this book if—
* You prefer your simplifications from an expert who understands the complexities
* 6 years of success as a short course for students and professionals works for you
* you enjoy hearing the phrase “nothing to memorize”
* ecommerce, email, network security, or wireless communications is part of your bailiwick
* cracking cryptography means a jump up the career ladder
* the words “public-key cryptography,” “channel-based cryptography,” and “prime numbers” pique your interest
* best-practices cryptography is the only secure way for you—and your company—to go
One of the most complex subjects in Information Technology, cryptography gets its due in this down-to-earth, self-teaching tutorial—the first to make the basics of the science truly accessible.
This is the third of several volumes serving as the collected documentation of Rudolf Ahlswede’s lectures on information theory. Each volume includes comments from an invited well-known expert. In the supplement to the present volume, Rüdiger Reischuk contributes his insights.
Classical information processing concerns the main tasks of gaining knowledge and the storage, transmission and hiding of data. The first task is the prime goal of Statistics. For transmission and hiding data, Shannon developed an impressive mathematical theory called Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presented in this work are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs.
". . .the best introduction to cryptography I've ever seen. . . .The book the National Security Agency wanted never to be published. . . ." -Wired Magazine
". . .monumental . . . fascinating . . . comprehensive . . . the definitive work on cryptography for computer programmers . . ." -Dr. Dobb's Journal
". . .easily ranks as one of the most authoritative in its field." -PC Magazine
The book details how programmers and electronic communications professionals can use cryptography-the technique of enciphering and deciphering messages-to maintain the privacy of computer data. It describes dozens of cryptography algorithms, gives practical advice on how to implement them into cryptographic software, and shows how they can be used to solve security problems. The book shows programmers who design computer applications, networks, and storage systems how they can build security into their software and systems.
With a new Introduction by the author, this premium edition will be a keepsake for all those committed to computer and cyber security.
This book offers a comprehensive introduction to the fundamental structures and applications of a wide range of contemporary coding operations. This text focuses on the ways to structure information so that its transmission will be in the safest, quickest, and most efficient and error-free manner possible. All coding operations are covered in a single framework, with initial chapters addressing early mathematical models and algorithmic developments which led to the structure of code. After discussing the general foundations of code, chapters proceed to cover individual topics such as notions of compression, cryptography, detection, and correction codes. Both classical coding theories and the most cutting-edge models are addressed, along with helpful exercises of varying complexities to enhance comprehension.Explains how to structure coding information so that its transmission is safe, error-free, efficient, and fast Includes a pseudo-code that readers may implement in their preferential programming language Features descriptive diagrams and illustrations, and almost 150 exercises, with corrections, of varying complexity to enhance comprehension
Foundations of Coding: Compression, Encryption, Error-Correction is an invaluable resource for understanding the various ways information is structured for its secure and reliable transmission in the 21st-century world.
Besides the classical methods of symmetric and private key encryption, the book treats the mathematics of cryptographic protocols and several unique topics such asGroup-Based Cryptography Gröbner Basis Methods in Cryptography Lattice-Based Cryptography
The book contains approximately ten examples with detailed solutions, while each chapter includes forty to fifty problems with full solutions for odd-numbered problems provided in the Appendix. Public Key Cryptography:
• Explains fundamentals of public key cryptography
• Offers numerous examples and exercises
• Provides excellent study tools for those preparing to take the Certified Information Systems Security Professional (CISSP) exam
• Provides solutions to the end-of-chapter problems
Public Key Cryptography provides a solid background for anyone who is employed by or seeking employment with a government organization, cloud service provider, or any large enterprise that uses public key systems to secure data.
Modern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for achieving these aims. In both theory and practice it requires notions and constructions from three major disciplines: computer science, electronic engineering and mathematics. Within mathematics, group theory, the theory of finite fields, and elementary number theory as well as some topics not normally covered in courses in algebra, such as the theory of Boolean functions and Shannon theory, are involved.Although essentially self-contained, a degree of mathematical maturity on the part of the reader is assumed, corresponding to his or her background in computer science or engineering. Algebra for Cryptologists is a textbook for an introductory course in cryptography or an upper undergraduate course in algebra, or for self-study in preparation for postgraduate study in cryptology.