Cryptological Mathematics

Author: Robert Lewand

Publisher: MAA

ISBN: 9780883857199

Category: Mathematics

Page: 199

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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.
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Mathematical Ciphers

From Caesar to RSA

Author: Anne L. Young

Publisher: American Mathematical Soc.

ISBN: 0821837303

Category: Mathematics

Page: 159

View: 3314

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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.
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All the Math That's Fit to Print

Articles from The Guardian

Author: Keith Devlin

Publisher: Cambridge University Press

ISBN: 9780883855157

Category: Mathematics

Page: 330

View: 8884

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Do you expect to find articles about mathematics in your daily newspaper? If you are a reader of The Guardian you do, or at least you did during the second half of the 1980s. This volume collects many of the columns Keith Devlin wrote for The Guardian. Read them and assign them to your students to read. This is a book for delving in, and is accessible to anyone with an interest in things mathematical. Devlin takes mathematical discoveries and explains them to the interested lay reader. The topics range from computer discoveries dealing with large prime numbers to much deeper results, such as Fermat's Last Theorem. You will find articles on the traveling salesman problem, on cryptology, and on procedures for working out claims for traveling expenses. Although the individual pieces are short and easily read, many contain references to mathematical articles and can form the basis for student research papers.
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Cryptology

Author: Albrecht Beutelspacher

Publisher: MAA

ISBN: 9780883855041

Category: Business & Economics

Page: 156

View: 5093

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The art & science of secret writing. Provides ideal methods to solve the problems of transmitting information secretly & securely.
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Secret History

The Story of Cryptology

Author: Craig P. Bauer

Publisher: CRC Press

ISBN: 1466561874

Category: Computers

Page: 620

View: 6105

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Winner of an Outstanding Academic Title Award from CHOICE Magazine Most available cryptology books primarily focus on either mathematics or history. Breaking this mold, Secret History: The Story of Cryptology gives a thorough yet accessible treatment of both the mathematics and history of cryptology. Requiring minimal mathematical prerequisites, the book presents the mathematics in sufficient detail and weaves the history throughout the chapters. In addition to the fascinating historical and political sides of cryptology, the author—a former Scholar-in-Residence at the U.S. National Security Agency (NSA) Center for Cryptologic History—includes interesting instances of codes and ciphers in crime, literature, music, and art. Following a mainly chronological development of concepts, the book focuses on classical cryptology in the first part. It covers Greek and Viking cryptography, the Vigenère cipher, the one-time pad, transposition ciphers, Jefferson’s cipher wheel, the Playfair cipher, ADFGX, matrix encryption, World War II cipher systems (including a detailed examination of Enigma), and many other classical methods introduced before World War II. The second part of the book examines modern cryptology. The author looks at the work of Claude Shannon and the origin and current status of the NSA, including some of its Suite B algorithms such as elliptic curve cryptography and the Advanced Encryption Standard. He also details the controversy that surrounded the Data Encryption Standard and the early years of public key cryptography. The book not only provides the how-to of the Diffie-Hellman key exchange and RSA algorithm, but also covers many attacks on the latter. Additionally, it discusses Elgamal, digital signatures, PGP, and stream ciphers and explores future directions such as quantum cryptography and DNA computing. With numerous real-world examples and extensive references, this book skillfully balances the historical aspects of cryptology with its mathematical details. It provides readers with a sound foundation in this dynamic field.
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Cryptology and Computational Number Theory

Author: Carl Pomerance,Shafi Goldwasser

Publisher: American Mathematical Soc.

ISBN: 9780821801550

Category: Computers

Page: 171

View: 8204

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In the past dozen or so years, cryptology and computational number theory have become increasingly intertwined. Because the primary cryptologic application of number theory is the apparent intractability of certain computations, these two fields could part in the future and again go their separate ways. But for now, their union is continuing to bring ferment and rapid change in both subjects. This book contains the proceedings of an AMS Short Course in Cryptology and Computational Number Theory, held in August 1989 during the Joint Mathematics Meetings in Boulder, Colorado. These eight papers by six of the top experts in the field will provide readers with a thorough introduction to some of the principal advances in cryptology and computational number theory over the past fifteen years. In addition to an extensive introductory article, the book contains articles on primality testing, discrete logarithms, integer factoring, knapsack cryptosystems, pseudorandom number generators, the theoretical underpinnings of cryptology, and other number theory-based cryptosystems. Requiring only background in elementary number theory, this book is aimed at nonexperts, including graduate students and advanced undergraduates in mathematics and computer science.
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