Cryptanalysis of Number Theoretic Ciphers

Cryptanalysis of Number Theoretic Ciphers
Author: Samuel S. Wagstaff, Jr.
Publisher: CRC Press
Total Pages: 340
Release: 2019-08-22
Genre: Mathematics
ISBN: 1351991949

At the heart of modern cryptographic algorithms lies computational number theory. Whether you're encrypting or decrypting ciphers, a solid background in number theory is essential for success. Written by a number theorist and practicing cryptographer, Cryptanalysis of Number Theoretic Ciphers takes you from basic number theory to the inner workings of ciphers and protocols. First, the book provides the mathematical background needed in cryptography as well as definitions and simple examples from cryptography. It includes summaries of elementary number theory and group theory, as well as common methods of finding or constructing large random primes, factoring large integers, and computing discrete logarithms. Next, it describes a selection of cryptographic algorithms, most of which use number theory. Finally, the book presents methods of attack on the cryptographic algorithms and assesses their effectiveness. For each attack method the author lists the systems it applies to and tells how they may be broken with it. Computational number theorists are some of the most successful cryptanalysts against public key systems. Cryptanalysis of Number Theoretic Ciphers builds a solid foundation in number theory and shows you how to apply it not only when breaking ciphers, but also when designing ones that are difficult to break.

Cryptanalysis of Number Theoretic Ciphers

Cryptanalysis of Number Theoretic Ciphers
Author: Samuel S. Wagstaff, Jr.
Publisher: CRC Press
Total Pages: 336
Release: 2019-08-22
Genre: Mathematics
ISBN: 1420057693

At the heart of modern cryptographic algorithms lies computational number theory. Whether you're encrypting or decrypting ciphers, a solid background in number theory is essential for success. Written by a number theorist and practicing cryptographer, Cryptanalysis of Number Theoretic Ciphers takes you from basic number theory to the inner workings of ciphers and protocols. First, the book provides the mathematical background needed in cryptography as well as definitions and simple examples from cryptography. It includes summaries of elementary number theory and group theory, as well as common methods of finding or constructing large random primes, factoring large integers, and computing discrete logarithms. Next, it describes a selection of cryptographic algorithms, most of which use number theory. Finally, the book presents methods of attack on the cryptographic algorithms and assesses their effectiveness. For each attack method the author lists the systems it applies to and tells how they may be broken with it. Computational number theorists are some of the most successful cryptanalysts against public key systems. Cryptanalysis of Number Theoretic Ciphers builds a solid foundation in number theory and shows you how to apply it not only when breaking ciphers, but also when designing ones that are difficult to break.

An Introduction to Mathematical Cryptography

An Introduction to Mathematical Cryptography
Author: Jeffrey Hoffstein
Publisher: Springer
Total Pages: 549
Release: 2014-09-11
Genre: Mathematics
ISBN: 1493917110

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.

Modern Cryptanalysis

Modern Cryptanalysis
Author: Christopher Swenson
Publisher: John Wiley & Sons
Total Pages: 336
Release: 2012-06-27
Genre: Computers
ISBN: 1118428625

As an instructor at the University of Tulsa, Christopher Swenson could find no relevant text for teaching modern cryptanalysis?so he wrote his own. This is the first book that brings the study of cryptanalysis into the 21st century. Swenson provides a foundation in traditional cryptanalysis, examines ciphers based on number theory, explores block ciphers, and teaches the basis of all modern cryptanalysis: linear and differential cryptanalysis. This time-honored weapon of warfare has become a key piece of artillery in the battle for information security.

Group Theoretic Cryptography

Group Theoretic Cryptography
Author: Maria Isabel Gonzalez Vasco
Publisher: CRC Press
Total Pages: 244
Release: 2015-04-01
Genre: Computers
ISBN: 1584888377

Group theory appears to be a promising source of hard computational problems for deploying new cryptographic constructions. This reference focuses on the specifics of using groups, including in particular non-Abelian groups, in the field of cryptography. It provides an introduction to cryptography with emphasis on the group theoretic perspective, making it one of the first books to use this approach. The authors provide the needed cryptographic and group theoretic concepts, full proofs of essential theorems, and formal security evaluations of the cryptographic schemes presented. They also provide references for further reading and exercises at the end of each chapter.

Computational Number Theory and Modern Cryptography

Computational Number Theory and Modern Cryptography
Author: Song Y. Yan
Publisher: John Wiley & Sons
Total Pages: 432
Release: 2013-01-29
Genre: Computers
ISBN: 1118188586

The only book to provide a unified view of the interplay between computational number theory and cryptography Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yang combines knowledge of these two critical fields, providing a unified view of the relationships between computational number theory and cryptography. The author takes an innovative approach, presenting mathematical ideas first, thereupon treating cryptography as an immediate application of the mathematical concepts. The book also presents topics from number theory, which are relevant for applications in public-key cryptography, as well as modern topics, such as coding and lattice based cryptography for post-quantum cryptography. The author further covers the current research and applications for common cryptographic algorithms, describing the mathematical problems behind these applications in a manner accessible to computer scientists and engineers. Makes mathematical problems accessible to computer scientists and engineers by showing their immediate application Presents topics from number theory relevant for public-key cryptography applications Covers modern topics such as coding and lattice based cryptography for post-quantum cryptography Starts with the basics, then goes into applications and areas of active research Geared at a global audience; classroom tested in North America, Europe, and Asia Incudes exercises in every chapter Instructor resources available on the book’s Companion Website Computational Number Theory and Modern Cryptography is ideal for graduate and advanced undergraduate students in computer science, communications engineering, cryptography and mathematics. Computer scientists, practicing cryptographers, and other professionals involved in various security schemes will also find this book to be a helpful reference.

Algorithmic Cryptanalysis

Algorithmic Cryptanalysis
Author: Antoine Joux
Publisher: CRC Press
Total Pages: 516
Release: 2009-06-15
Genre: Computers
ISBN: 1420070037

Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program.Divided into three parts, the book begins with a

Mathematics of Public Key Cryptography

Mathematics of Public Key Cryptography
Author: Steven D. Galbraith
Publisher: Cambridge University Press
Total Pages: 631
Release: 2012-03-15
Genre: Computers
ISBN: 1107013925

This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.

Cryptography

Cryptography
Author: Simon Rubinstein-Salzedo
Publisher: Springer
Total Pages: 259
Release: 2018-09-27
Genre: Mathematics
ISBN: 3319948180

This text introduces cryptography, from its earliest roots to cryptosystems used today for secure online communication. Beginning with classical ciphers and their cryptanalysis, this book proceeds to focus on modern public key cryptosystems such as Diffie-Hellman, ElGamal, RSA, and elliptic curve cryptography with an analysis of vulnerabilities of these systems and underlying mathematical issues such as factorization algorithms. Specialized topics such as zero knowledge proofs, cryptographic voting, coding theory, and new research are covered in the final section of this book. Aimed at undergraduate students, this book contains a large selection of problems, ranging from straightforward to difficult, and can be used as a textbook for classes as well as self-study. Requiring only a solid grounding in basic mathematics, this book will also appeal to advanced high school students and amateur mathematicians interested in this fascinating and topical subject.

Applied Cryptography

Applied Cryptography
Author: Bruce Schneier
Publisher: John Wiley & Sons
Total Pages: 926
Release: 2017-05-25
Genre: Computers
ISBN: 1119439027

From the world's most renowned security technologist, Bruce Schneier, this 20th Anniversary Edition is the most definitive reference on cryptography ever published and is the seminal work on cryptography. Cryptographic techniques have applications far beyond the obvious uses of encoding and decoding information. For developers who need to know about capabilities, such as digital signatures, that depend on cryptographic techniques, there's no better overview than Applied Cryptography, the definitive book on the subject. Bruce Schneier covers general classes of cryptographic protocols and then specific techniques, detailing the inner workings of real-world cryptographic algorithms including the Data Encryption Standard and RSA public-key cryptosystems. The book includes source-code listings and extensive advice on the practical aspects of cryptography implementation, such as the importance of generating truly random numbers and of keeping keys secure. ". . .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.