The Mathematics of Secrets

Author: Joshua Holden
Publisher: Princeton University Press
ISBN: 0691184550
Format: PDF, ePub, Docs
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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 Secrets

Author: Joshua Holden
Publisher:
ISBN: 9780691183312
Format: PDF, ePub, Docs
Download Now
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 Secrets

Author: Joshua Holden
Publisher: Princeton University Press
ISBN: 1400885620
Format: PDF, ePub, Mobi
Download Now
The Mathematics of Secrets takes readers on a fascinating tour of the mathematics behind cryptography—the science of sending secret messages. Most books about cryptography are organized historically, or around how codes and ciphers have been used, such as in government and military intelligence or bank transactions. Joshua Holden instead shows how mathematical principles underpin the ways that different codes and ciphers operate. Holden focuses on both code making and code breaking and he discusses the majority of ancient and modern ciphers currently known. Holden begins by looking at substitution ciphers, built by substituting one letter or block of letters for another. Explaining one of the simplest and historically well-known ciphers, the Caesar cipher, Holden establishes the key mathematical idea behind the cipher and discusses how to introduce flexibility and additional notation. Holden goes on to explore polyalphabetic substitution ciphers, transposition ciphers, including one developed by the Spartans, connections between ciphers and computer encryption, stream ciphers, and ciphers involving exponentiation. He also examines public-key ciphers, where the methods used to encrypt messages are public knowledge, and yet, intended recipients are still the only ones who are able to read the message. He concludes with a look at the future of ciphers and where cryptography might be headed. Only basic mathematics up to high school algebra is needed to understand and enjoy the book. With a plethora of historical anecdotes and real-world examples, The Mathematics of Secrets reveals the mathematics working stealthily in the science of coded messages.

Secret History

Author: Craig P. Bauer
Publisher: CRC Press
ISBN: 1466561874
Format: PDF
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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.

Mathematics of Public Key Cryptography

Author: Steven D. Galbraith
Publisher: Cambridge University Press
ISBN: 1107013925
Format: PDF, Docs
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This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.

Decrypted Secrets

Author: Friedrich L. Bauer
Publisher: Springer Science & Business Media
ISBN: 3662034522
Format: PDF
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Cryptology, for millennia a "secret science", is rapidly gaining in practical importance for the protection of communication channels, databases, and software. Beside its role in computerized information systems, cryptology is finding more and more applications inside computer systems and networks, extending to access rights and source file protection. The first part of this book treats secret codes and their uses - cryptography - before moving on to the process of covertly decrypting a secret code - cryptanalysis. Spiced with a wealth of exciting, amusing, and occasionally personal stories from the history of cryptology, and presupposing only elementary mathematical knowledge, this book will also stimulate general readers.

Codes and Ciphers

Author: R. F. Churchhouse
Publisher: Cambridge University Press
ISBN: 9780521008907
Format: PDF, ePub
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This book describes and analyses many cipher systems ranging from the earliest and most elementary to the most recent and sophisticated(RSA and DES).

CryptoSchool

Author: Joachim von zur Gathen
Publisher: Springer
ISBN: 3662484250
Format: PDF, Kindle
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This book offers an introduction to cryptology, the science that makes secure communications possible, and addresses its two complementary aspects: cryptography—--the art of making secure building blocks—--and cryptanalysis—--the art of breaking them. The text describes some of the most important systems in detail, including AES, RSA, group-based and lattice-based cryptography, signatures, hash functions, random generation, and more, providing detailed underpinnings for most of them. With regard to cryptanalysis, it presents a number of basic tools such as the differential and linear methods and lattice attacks. This text, based on lecture notes from the author’s many courses on the art of cryptography, consists of two interlinked parts. The first, modern part explains some of the basic systems used today and some attacks on them. However, a text on cryptology would not be complete without describing its rich and fascinating history. As such, the colorfully illustrated historical part interspersed throughout the text highlights selected inventions and episodes, providing a glimpse into the past of cryptology. The first sections of this book can be used as a textbook for an introductory course to computer science or mathematics students. Other sections are suitable for advanced undergraduate or graduate courses. Many exercises are included. The emphasis is on providing reasonably complete explanation of the background for some selected systems.

Techniques for Cryptanalysis of Block Ciphers

Author: Eli Biham
Publisher: Springer
ISBN: 9783642172311
Format: PDF, Mobi
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Block ciphers are widely used to protect information over the Internet, so assessing their strength in the case of malicious adversaries is critical to public trust. Such security evaluations, called cryptanalysis, expose weak points of the ciphers and can be used to develop attack techniques, thus cryptanalytic techniques also direct designers on ways to develop more secure block ciphers. In this book the authors describe the cryptanalytic toolbox for block ciphers. The book starts with the differential and linear attacks, and their extensions and generalizations. Then the more advanced attacks such as the boomerang and rectangle attacks are discussed, along with their related-key variants. Finally, other attacks are explored, in particular combined attacks that are built on top of other attacks. The book covers both the underlying concepts at the heart of these attacks and the mathematical foundations of the analysis itself. These are complemented by an extensive bibliography and numerous examples, mainly involving widely deployed block ciphers. The book is intended as a reference book for graduate students and researchers in the field of cryptography. Block ciphers are widely used to protect information over the Internet, so assessing their strength in the case of malicious adversaries is critical to public trust. Such security evaluations, called cryptanalysis, expose weak points of the ciphers and can be used to develop attack techniques, thus cryptanalytic techniques also direct designers on ways to develop more secure block ciphers. In this book the authors describe the cryptanalytic toolbox for block ciphers. The book starts with the differential and linear attacks, and their extensions and generalizations. Then the more advanced attacks such as the boomerang and rectangle attacks are discussed, along with their related-key variants. Finally, other attacks are explored, in particular combined attacks that are built on top of other attacks. The book covers both the underlying concepts at the heart of these attacks and the mathematical foundations of the analysis itself. These are complemented by an extensive bibliography and numerous examples, mainly involving widely deployed block ciphers. The book is intended as a reference book for graduate students and researchers in the field of cryptography.

A Cryptography Primer

Author: Philip N. Klein
Publisher: Cambridge University Press
ISBN: 1139916106
Format: PDF, ePub
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Cryptography has been employed in war and diplomacy from the time of Julius Caesar. In our Internet age, cryptography's most widespread application may be for commerce, from protecting the security of electronic transfers to guarding communication from industrial espionage. This accessible introduction for undergraduates explains the cryptographic protocols for achieving privacy of communication and the use of digital signatures for certifying the validity, integrity, and origin of a message, document, or program. Rather than offering a how-to on configuring web browsers and e-mail programs, the author provides a guide to the principles and elementary mathematics underlying modern cryptography, giving readers a look under the hood for security techniques and the reasons they are thought to be secure.