The Mathematics Of Encryption An Elementary Introduction

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The Mathematics of Encryption

Author : Margaret Cozzens
Publisher : American Mathematical Soc.
ISBN 13 : 0821883216
Total Pages : 355 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Mathematics of Encryption by : Margaret Cozzens

Download or read book The Mathematics of Encryption written by Margaret Cozzens and published by American Mathematical Soc.. This book was released on 2013-09-05 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Mathematical Cryptography

Author : Jeffrey Hoffstein
Publisher : Springer
ISBN 13 : 1493917110
Total Pages : 538 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis An Introduction to Mathematical Cryptography by : Jeffrey Hoffstein

Download or read book An Introduction to Mathematical Cryptography written by Jeffrey Hoffstein and published by Springer. This book was released on 2014-09-11 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Cryptography

Author : Johannes Buchmann
Publisher : Springer Science & Business Media
ISBN 13 : 1441990038
Total Pages : 342 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Introduction to Cryptography by : Johannes Buchmann

Download or read book Introduction to Cryptography written by Johannes Buchmann and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Introduction to Cryptography with Mathematical Foundations and Computer Implementations

Author : Alexander Stanoyevitch
Publisher : CRC Press
ISBN 13 : 1439817634
Total Pages : 646 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Introduction to Cryptography with Mathematical Foundations and Computer Implementations by : Alexander Stanoyevitch

Download or read book Introduction to Cryptography with Mathematical Foundations and Computer Implementations written by Alexander Stanoyevitch and published by CRC Press. This book was released on 2010-08-09 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the exciting history of its development in ancient times to the present day, Introduction to Cryptography with Mathematical Foundations and Computer Implementations provides a focused tour of the central concepts of cryptography. Rather than present an encyclopedic treatment of topics in cryptography, it delineates cryptographic concepts in chronological order, developing the mathematics as needed. Written in an engaging yet rigorous style, each chapter introduces important concepts with clear definitions and theorems. Numerous examples explain key points while figures and tables help illustrate more difficult or subtle concepts. Each chapter is punctuated with "Exercises for the Reader;" complete solutions for these are included in an appendix. Carefully crafted exercise sets are also provided at the end of each chapter, and detailed solutions to most odd-numbered exercises can be found in a designated appendix. The computer implementation section at the end of every chapter guides students through the process of writing their own programs. A supporting website provides an extensive set of sample programs as well as downloadable platform-independent applet pages for some core programs and algorithms. As the reliance on cryptography by business, government, and industry continues and new technologies for transferring data become available, cryptography plays a permanent, important role in day-to-day operations. This self-contained sophomore-level text traces the evolution of the field, from its origins through present-day cryptosystems, including public key cryptography and elliptic curve cryptography.

An Introduction to Mathematical Cryptography

Author : Jeffrey Hoffstein
Publisher : Springer
ISBN 13 : 9781493917129
Total Pages : 538 pages
Book Rating : 4.9/5 (171 download)

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Book Synopsis An Introduction to Mathematical Cryptography by : Jeffrey Hoffstein

Elementary Cryptanalysis

Author : Abraham Sinkov
Publisher : MAA
ISBN 13 : 9780883856475
Total Pages : 240 pages
Book Rating : 4.8/5 (564 download)

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Book Synopsis Elementary Cryptanalysis by : Abraham Sinkov

Download or read book Elementary Cryptanalysis written by Abraham Sinkov and published by MAA. This book was released on 2009-08-06 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the basic mathematical techniques involved in cryptanalysis.

An Introduction to Mathematical Cryptography

Author : Jeffrey Hoffstein
Publisher : Springer Science & Business Media
ISBN 13 : 0387779949
Total Pages : 533 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis An Introduction to Mathematical Cryptography by : Jeffrey Hoffstein

Download or read book An Introduction to Mathematical Cryptography written by Jeffrey Hoffstein and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Mathematical Cryptography provides an introduction to public key cryptography and underlying mathematics that is required for the subject. Each of the eight chapters expands on a specific area of mathematical cryptography and provides an extensive list of exercises. It is a suitable text for advanced students in pure and applied mathematics and computer science, or the book may be used as a self-study. This book also provides a self-contained treatment of mathematical cryptography for the reader with limited mathematical background.

Mathematics of Public Key Cryptography

Author : Steven D. Galbraith
Publisher : Cambridge University Press
ISBN 13 : 1107013925
Total Pages : 631 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Mathematics of Public Key Cryptography by : Steven D. Galbraith

Download or read book Mathematics of Public Key Cryptography written by Steven D. Galbraith and published by Cambridge University Press. This book was released on 2012-03-15 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.

Discrete Mathematics With Cryptographic Applications

Author : Alexander I. Kheyfits
Publisher : Mercury Learning and Information
ISBN 13 : 1683927613
Total Pages : 402 pages
Book Rating : 4.6/5 (839 download)

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Book Synopsis Discrete Mathematics With Cryptographic Applications by : Alexander I. Kheyfits

Download or read book Discrete Mathematics With Cryptographic Applications written by Alexander I. Kheyfits and published by Mercury Learning and Information. This book was released on 2021-09-20 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers discrete mathematics both as it has been established after its emergence since the middle of the last century and as its elementary applications to cryptography. It can be used by any individual studying discrete mathematics, finite mathematics, and similar subjects. Any necessary prerequisites are explained and illustrated in the book. As a background of cryptography, the textbook gives an introduction into number theory, coding theory, information theory, that obviously have discrete nature. FEATURES: Designed in a “self-teaching” format, the book includes about 600 problems (with and without solutions) and numerous examples of cryptography Covers cryptography topics such as CRT, affine ciphers, hashing functions, substitution ciphers, unbreakable ciphers, Discrete Logarithm Problem (DLP), and more.

Introduction to Cryptography with Open-Source Software

Author : Alasdair McAndrew
Publisher : CRC Press
ISBN 13 : 1439825718
Total Pages : 456 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Introduction to Cryptography with Open-Source Software by : Alasdair McAndrew

Download or read book Introduction to Cryptography with Open-Source Software written by Alasdair McAndrew and published by CRC Press. This book was released on 2016-04-19 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Once the privilege of a secret few, cryptography is now taught at universities around the world. Introduction to Cryptography with Open-Source Software illustrates algorithms and cryptosystems using examples and the open-source computer algebra system of Sage. The author, a noted educator in the field, provides a highly practical learning experienc

Group-based Cryptography

Author : Alexei Myasnikov
Publisher : Springer Science & Business Media
ISBN 13 : 3764388277
Total Pages : 183 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Group-based Cryptography by : Alexei Myasnikov

Download or read book Group-based Cryptography written by Alexei Myasnikov and published by Springer Science & Business Media. This book was released on 2008-11-04 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering relations between three different areas of mathematics and theoretical computer science, this book explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography.

Introduction to Modern Cryptography

Author : Jonathan Katz
Publisher : CRC Press
ISBN 13 : 1351133012
Total Pages : 435 pages
Book Rating : 4.3/5 (511 download)

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Book Synopsis Introduction to Modern Cryptography by : Jonathan Katz

Download or read book Introduction to Modern Cryptography written by Jonathan Katz and published by CRC Press. This book was released on 2020-12-21 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now the most used texbook for introductory cryptography courses in both mathematics and computer science, the Third Edition builds upon previous editions by offering several new sections, topics, and exercises. The authors present the core principles of modern cryptography, with emphasis on formal definitions, rigorous proofs of security.

Cryptology

Author : Richard E. Klima
Publisher : CRC Press
ISBN 13 : 1439872414
Total Pages : 558 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Cryptology by : Richard E. Klima

Download or read book Cryptology written by Richard E. Klima and published by CRC Press. This book was released on 2012-06-20 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: Easily Accessible to Students with Nontechnical Backgrounds In a clear, nontechnical manner, Cryptology: Classical and Modern with Maplets explains how fundamental mathematical concepts are the bases of cryptographic algorithms. Designed for students with no background in college-level mathematics, the book assumes minimal mathematical prerequisites and incorporates student-friendly Maplets throughout that provide practical examples of the techniques used. Technology Resource By using the Maplets, students can complete complicated tasks with relative ease. They can encrypt, decrypt, and cryptanalyze messages without the burden of understanding programming or computer syntax. The authors explain topics in detail first before introducing one or more Maplets. All Maplet material and exercises are given in separate, clearly labeled sections. Instructors can omit the Maplet sections without any loss of continuity and non-Maplet examples and exercises can be completed with, at most, a simple hand-held calculator. The Maplets are available for download at www.radford.edu/~npsigmon/cryptobook.html. A Gentle, Hands-On Introduction to Cryptology After introducing elementary methods and techniques, the text fully develops the Enigma cipher machine and Navajo code used during World War II, both of which are rarely found in cryptology textbooks. The authors then demonstrate mathematics in cryptology through monoalphabetic, polyalphabetic, and block ciphers. With a focus on public-key cryptography, the book describes RSA ciphers, the Diffie–Hellman key exchange, and ElGamal ciphers. It also explores current U.S. federal cryptographic standards, such as the AES, and explains how to authenticate messages via digital signatures, hash functions, and certificates.

Cryptological Mathematics

Author : Robert Edward Lewand
Publisher : American Mathematical Society
ISBN 13 : 1470471558
Total Pages : 215 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Cryptological Mathematics by : Robert Edward Lewand

Download or read book Cryptological Mathematics written by Robert Edward Lewand and published by American Mathematical Society. This book was released on 2023-01-19 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to the mathematics involved in the intriguing field of cryptology, the science of writing and reading secret messages which are designed to be read only by their intended recipients. It is written at an elementary level, suitable for beginning undergraduates, with careful explanations of all the concepts used. The basic branches of mathematics required, including number theory, abstract algebra and probability, are used to show how to encipher and decipher messages, and why this works, giving a practical as well as theoretical basis to the subject. Challenging computer programming exercises are also included. The book is written in an engaging style which will appeal to all, and also includes historical background on some of the founders of the subject. It will be of interest both to students wishing to learn cryptology per se, and also to those searching for practical applications of seemingly abstract mathematics.

Codes: An Introduction to Information Communication and Cryptography

Author : Norman L. Biggs
Publisher : Springer Science & Business Media
ISBN 13 : 1848002734
Total Pages : 274 pages
Book Rating : 4.8/5 (48 download)

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Book Synopsis Codes: An Introduction to Information Communication and Cryptography by : Norman L. Biggs

Download or read book Codes: An Introduction to Information Communication and Cryptography written by Norman L. Biggs and published by Springer Science & Business Media. This book was released on 2008-12-16 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many people do not realise that mathematics provides the foundation for the devices we use to handle information in the modern world. Most of those who do know probably think that the parts of mathematics involvedare quite ‘cl- sical’, such as Fourier analysis and di?erential equations. In fact, a great deal of the mathematical background is part of what used to be called ‘pure’ ma- ematics, indicating that it was created in order to deal with problems that originated within mathematics itself. It has taken many years for mathema- cians to come to terms with this situation, and some of them are still not entirely happy about it. Thisbookisanintegratedintroductionto Coding.Bythis Imeanreplacing symbolic information, such as a sequence of bits or a message written in a naturallanguage,byanother messageusing (possibly) di?erentsymbols.There are three main reasons for doing this: Economy (data compression), Reliability (correction of errors), and Security (cryptography). I have tried to cover each of these three areas in su?cient depth so that the reader can grasp the basic problems and go on to more advanced study. The mathematical theory is introduced in a way that enables the basic problems to bestatedcarefully,butwithoutunnecessaryabstraction.Theprerequisites(sets andfunctions,matrices,?niteprobability)shouldbefamiliartoanyonewhohas taken a standard course in mathematical methods or discrete mathematics. A course in elementary abstract algebra and/or number theory would be helpful, but the book contains the essential facts, and readers without this background should be able to understand what is going on. vi Thereareafewplaceswherereferenceismadetocomputeralgebrasystems.

Cryptography Made Simple

Author : Nigel Smart
Publisher : Springer
ISBN 13 : 3319219367
Total Pages : 481 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Cryptography Made Simple by : Nigel Smart

Download or read book Cryptography Made Simple written by Nigel Smart and published by Springer. This book was released on 2015-11-12 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this introductory textbook the author explains the key topics in cryptography. He takes a modern approach, where defining what is meant by "secure" is as important as creating something that achieves that goal, and security definitions are central to the discussion throughout. The author balances a largely non-rigorous style — many proofs are sketched only — with appropriate formality and depth. For example, he uses the terminology of groups and finite fields so that the reader can understand both the latest academic research and "real-world" documents such as application programming interface descriptions and cryptographic standards. The text employs colour to distinguish between public and private information, and all chapters include summaries and suggestions for further reading. This is a suitable textbook for advanced undergraduate and graduate students in computer science, mathematics and engineering, and for self-study by professionals in information security. While the appendix summarizes most of the basic algebra and notation required, it is assumed that the reader has a basic knowledge of discrete mathematics, probability, and elementary calculus.

Introduction to Cryptography with Maple

Author : José Luis Gómez Pardo
Publisher : Springer Science & Business Media
ISBN 13 : 3642321666
Total Pages : 726 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Introduction to Cryptography with Maple by : José Luis Gómez Pardo

Download or read book Introduction to Cryptography with Maple written by José Luis Gómez Pardo and published by Springer Science & Business Media. This book was released on 2012-12-19 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to cryptography employs a programming-oriented approach to study the most important cryptographic schemes in current use and the main cryptanalytic attacks against them. Discussion of the theoretical aspects, emphasizing precise security definitions based on methodological tools such as complexity and randomness, and of the mathematical aspects, with emphasis on number-theoretic algorithms and their applications to cryptography and cryptanalysis, is integrated with the programming approach, thus providing implementations of the algorithms and schemes as well as examples of realistic size. 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.