Mathematical Ciphers

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Mathematical Ciphers

Anne L. Young
Mathematical Ciphers Book PDF

Author : Anne L. Young
Publisher : American Mathematical Soc.
Page : 170 pages
File Size : 45,7 Mb
Release : 2006
Category : Ciphers
ISBN : 9780821837306

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Mathematical Ciphers by Anne L. Young Pdf

A cipher is a scheme for creating coded messages for the secure exchange of information. Throughout history, many different coding schemes have been devised. One of the oldest and simplest mathematical systems was used by Julius Caesar. This is where Mathematical Ciphers begins. Building on that simple system, Young moves on to more complicated schemes, ultimately ending with the RSA cipher, which is used to provide security for the internet. This book is structured differently from most mathematics texts. It does not begin with a mathematical topic, but rather with a cipher. The mathematics is developed as it is needed; the applications motivate the mathematics. As is typical in mathematics textbooks, most chapters end with exercises. Many of these problems are similar to solved examples and are designed to assist the reader in mastering the basic material. A few of the exercises are one-of-a-kind, intended to challenge the interested reader. Implementing encryption schemes is considerably easier with the use of the computer. For all the ciphers introduced in this book, JavaScript programs are available from the web. In addition to developing various encryption schemes, this book also introduces the reader to number theory. Here, the study of integers and their properties is placed in the exciting and modern context of cryptology. Mathematical Ciphers can be used as a textbook for an introductory course in mathematics for all majors. The only prerequisite is high school mathematics.

The Mathematics of Secrets

Joshua Holden
The Mathematics of Secrets Book PDF

Author : Joshua Holden
Publisher : Princeton University Press
Page : 390 pages
File Size : 44,5 Mb
Release : 2018-10-02
Category : Computers
ISBN : 9780691183312

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The Mathematics of Secrets by Joshua Holden Pdf

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.

The Mathematics of Encryption: An Elementary Introduction

Margaret Cozzens, Steven J. Miller
The Mathematics of Encryption An Elementary Introduction Book PDF

Author : Margaret Cozzens, Steven J. Miller
Publisher : American Mathematical Soc.
Page : 332 pages
File Size : 48,9 Mb
Release : 2013-09-05
Category : Mathematics
ISBN : 9780821883211

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The Mathematics of Encryption: An Elementary Introduction by Margaret Cozzens, Steven J. Miller Pdf

How quickly can you compute the remainder when dividing by 120143? Why would you even want to compute this? And what does this have to do with cryptography? Modern cryptography lies at the intersection of mathematics and computer sciences, involving number theory, algebra, computational complexity, fast algorithms, and even quantum mechanics. Many people think of codes in terms of spies, but in the information age, highly mathematical codes are used every day by almost everyone, whether at the bank ATM, at the grocery checkout, or at the keyboard when you access your email or purchase products online. This book provides a historical and mathematical tour of cryptography, from classical ciphers to quantum cryptography. The authors introduce just enough mathematics to explore modern encryption methods, with nothing more than basic algebra and some elementary number theory being necessary. Complete expositions are given of the classical ciphers and the attacks on them, along with a detailed description of the famous Enigma system. The public-key system RSA is described, including a complete mathematical proof that it works. Numerous related topics are covered, such as efficiencies of algorithms, detecting and correcting errors, primality testing and digital signatures. The topics and exposition are carefully chosen to highlight mathematical thinking and problem solving. Each chapter ends with a collection of problems, ranging from straightforward applications to more challenging problems that introduce advanced topics. Unlike many books in the field, this book is aimed at a general liberal arts student, but without losing mathematical completeness.

The Mathematics of Secrets

Joshua Holden
The Mathematics of Secrets Book PDF

Author : Joshua Holden
Publisher : Princeton University Press
Page : 390 pages
File Size : 45,6 Mb
Release : 2018-10-02
Category : Computers
ISBN : 9780691183312

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The Mathematics of Secrets by Joshua Holden Pdf

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.

An Introduction to Mathematical Cryptography

Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman
An Introduction to Mathematical Cryptography Book PDF

Author : Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman
Publisher : Springer
Page : 538 pages
File Size : 54,6 Mb
Release : 2014-09-11
Category : Mathematics
ISBN : 9781493917112

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An Introduction to Mathematical Cryptography by Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman Pdf

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.

A Course in Mathematical Cryptography

Gilbert Baumslag,Benjamin Fine,Martin Kreuzer,Gerhard Rosenberger
A Course in Mathematical Cryptography Book PDF

Author : Gilbert Baumslag,Benjamin Fine,Martin Kreuzer,Gerhard Rosenberger
Publisher : Walter de Gruyter GmbH & Co KG
Page : 389 pages
File Size : 51,8 Mb
Release : 2015-06-16
Category : Computers
ISBN : 9783110386165

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A Course in Mathematical Cryptography by Gilbert Baumslag,Benjamin Fine,Martin Kreuzer,Gerhard Rosenberger Pdf

The subject of this book is mathematical cryptography. By this we mean the mathematics involved in cryptographic protocols. As the field has expanded, using both commutative and noncommutative algebraic objects as cryptographic platforms, a book describing and explaining all these mathematical methods is of immeasurable value.

Cryptanalysis of Number Theoretic Ciphers

Samuel S. Wagstaff, Jr.
Cryptanalysis of Number Theoretic Ciphers Book PDF

Author : Samuel S. Wagstaff, Jr.
Publisher : CRC Press
Page : 340 pages
File Size : 41,8 Mb
Release : 2019-08-22
Category : Mathematics
ISBN : 9781351991940

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Cryptanalysis of Number Theoretic Ciphers by Samuel S. Wagstaff, Jr. Pdf

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

Samuel S. Wagstaff, Jr.
Cryptanalysis of Number Theoretic Ciphers Book PDF

Author : Samuel S. Wagstaff, Jr.
Publisher : CRC Press
Page : 336 pages
File Size : 49,9 Mb
Release : 2019-08-22
Category : Mathematics
ISBN : 9781420057690

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Cryptanalysis of Number Theoretic Ciphers by Samuel S. Wagstaff, Jr. Pdf

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.

Introduction to Cryptography

Johannes Buchmann
Introduction to Cryptography Book PDF

Author : Johannes Buchmann
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 42,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781441990037

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Introduction to Cryptography by Johannes Buchmann Pdf

This book explains the basic methods of modern cryptography. It is written for readers with only basic mathematical knowledge who are interested in modern cryptographic algorithms and their mathematical foundation. Several exercises are included following each chapter. From the reviews: "Gives a clear and systematic introduction into the subject whose popularity is ever increasing, and can be recommended to all who would like to learn about cryptography." --ZENTRALBLATT MATH

Elementary Cryptanalysis

Abraham Sinkov,Todd Feil
Elementary Cryptanalysis Book PDF

Author : Abraham Sinkov,Todd Feil
Publisher : MAA
Page : 240 pages
File Size : 42,5 Mb
Release : 2009-08-06
Category : Business & Economics
ISBN : 0883856476

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Elementary Cryptanalysis by Abraham Sinkov,Todd Feil Pdf

An introduction to the basic mathematical techniques involved in cryptanalysis.

Cryptology

Richard Klima,Richard E. Klima,Neil Sigmon,Neil P. Sigmon
Cryptology Book PDF

Author : Richard Klima,Richard E. Klima,Neil Sigmon,Neil P. Sigmon
Publisher : CRC Press
Page : 482 pages
File Size : 49,5 Mb
Release : 2018-12-07
Category : Computers
ISBN : 9781351692540

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Cryptology by Richard Klima,Richard E. Klima,Neil Sigmon,Neil P. Sigmon Pdf

Cryptology: Classical and Modern, Second Edition proficiently introduces readers to the fascinating field of cryptology. The book covers classical methods including substitution, transposition, Alberti, Vigenère, and Hill ciphers. It also includes coverage of the Enigma machine, Turing bombe, and Navajo code. Additionally, the book presents modern methods like RSA, ElGamal, and stream ciphers, as well as the Diffie-Hellman key exchange and Advanced Encryption Standard. When possible, the book details methods for breaking both classical and modern methods. The new edition expands upon the material from the first edition which was oriented for students in non-technical fields. At the same time, the second edition supplements this material with new content that serves students in more technical fields as well. Thus, the second edition can be fully utilized by both technical and non-technical students at all levels of study. The authors include a wealth of material for a one-semester cryptology course, and research exercises that can be used for supplemental projects. Hints and answers to selected exercises are found at the end of the book. Features: Requires no prior programming knowledge or background in college-level mathematics Illustrates the importance of cryptology in cultural and historical contexts, including the Enigma machine, Turing bombe, and Navajo code Gives straightforward explanations of the Advanced Encryption Standard, public-key ciphers, and message authentication Describes the implementation and cryptanalysis of classical ciphers, such as substitution, transposition, shift, affine, Alberti, Vigenère, and Hill

The Mathematics of Ciphers

S.C. Coutinho
The Mathematics of Ciphers Book PDF

Author : S.C. Coutinho
Publisher : CRC Press
Page : 213 pages
File Size : 49,8 Mb
Release : 1999-01-15
Category : Mathematics
ISBN : 9781439863893

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The Mathematics of Ciphers by S.C. Coutinho Pdf

This book is an introduction to the algorithmic aspects of number theory and its applications to cryptography, with special emphasis on the RSA cryptosys-tem. It covers many of the familiar topics of elementary number theory, all with an algorithmic twist. The text also includes many interesting historical notes.

Stream Ciphers and Number Theory

T.W. Cusick,C. Ding,Ari R. Renvall
Stream Ciphers and Number Theory Book PDF

Author : T.W. Cusick,C. Ding,Ari R. Renvall
Publisher : Elsevier
Page : 446 pages
File Size : 49,6 Mb
Release : 1998-04-20
Category : Computers
ISBN : 9780080541846

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Stream Ciphers and Number Theory by T.W. Cusick,C. Ding,Ari R. Renvall Pdf

This book is almost entirely concerned with stream ciphers, concentrating on a particular mathematical model for such ciphers which are called additive natural stream ciphers. These ciphers use a natural sequence generator to produce a periodic keystream. Full definitions of these concepts are given in Chapter 2. This book focuses on keystream sequences which can be analysed using number theory. It turns out that a great deal of information can be deducted about the cryptographic properties of many classes of sequences by applying the terminology and theorems of number theory. These connections can be explicitly made by describing three kinds of bridges between stream ciphering problems and number theory problems. A detailed summary of these ideas is given in the introductory Chapter 1. Many results in the book are new, and over seventy percent of these results described in this book are based on recent research results.

Mathematical Principles of the Internet, Volume 1

Nirdosh Bhatnagar
Mathematical Principles of the Internet Volume 1 Book PDF

Author : Nirdosh Bhatnagar
Publisher : CRC Press
Page : 1022 pages
File Size : 48,7 Mb
Release : 2018-11-20
Category : Computers
ISBN : 9781351379151

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Mathematical Principles of the Internet, Volume 1 by Nirdosh Bhatnagar Pdf

This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, they cover a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.

Cryptography and Computational Number Theory

Kwok Yan Lam
Cryptography and Computational Number Theory Book PDF

Author : Kwok Yan Lam
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 53,8 Mb
Release : 2001
Category : Computers
ISBN : 3764365102

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Cryptography and Computational Number Theory by Kwok Yan Lam Pdf

The fields of cryptography and computational number theory have recently witnessed a rapid development, which was the subject of the CCNT workshop in Singapore in November 1999. Its aim was to stimulate further research in information and computer security as well as the design and implementation of number theoretic cryptosystems and other related areas. Another achievement of the meeting was the collaboration of mathematicians, computer scientists, practical cryptographers and engineers in academia, industry and government. The present volume comprises a selection of refereed papers originating from this event, presenting either a survey of some area or original and new results. They concern many different aspects of the field such as theory, techniques, applications and practical experience. It provides a state-of-the-art report on some number theoretical issues of significance to cryptography.