Handbook of Applied Cryptography (Discrete Mathematics and Its Applications)

Handbook of Applied Cryptography (Discrete Mathematics and Its Applications)
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Alfred Menezes (Editor), Paul van Oorschot (Editor), Scott Vanstone (Editor)

Review
[This book] is an incredible achievement. … [T]he handbook is complete. If I want to check what problems there were with a proposed system, determine how the variations on a particular algorithm developed, see what research preceded and followed an idea, I go to the Handbook. The Handbook has accurate, clear, and correct information. It is wonderful. … If I were limited to only one cryptography text on my shelves, it would be the Handbook of Applied Cryptography.
- Bulletin of the AMS

[This book] is an incredible achievement. … [T]he handbook is complete. If I want to check what problems there were with a proposed system, determine how the variations on a particular algorithm developed, see what research preceded and followed an idea, I go to the Handbook. The Handbook has accurate, clear, and correct information. It is wonderful. … If I were limited to only one cryptography text on my shelves, it would be the Handbook of Applied Cryptography.
- Bulletin of the AMS

…very well suited for the reader who wants an encyclopedic description of the state of the art of applied modern cryptography.
-Mathematical Reviews, Issue 99g

…very well suited for the reader who wants an encyclopedic description of the state of the art of applied modern cryptography.
-Mathematical Reviews, Issue 99g


Product Description
Cryptography, in particular public-key cryptography, has emerged in the last 20 years as an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications. Standards are emerging to meet the demands for cryptographic protection in most areas of data communications. Public-key cryptographic techniques are now in widespread use, especially in the financial services industry, in the public sector, and by individuals for their personal privacy, such as in electronic mail. This Handbook will serve as a valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography. It is a necessary and timely guide for professionals who practice the art of cryptography. The Handbook of Applied Cryptography provides a treatment that is multifunctional:
Product Details

* Hardcover: 780 pages
* Publisher: CRC Press; 1 edition (December 16, 1996)
* Language: English
* ISBN-10: 0849385237
* ISBN-13: 978-0849385230

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Military Cryptanalysis - Part 1,2,3,4

Military Cryptanalysis - Part 1,2,3,4
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William F. Friedman

Product Description
Military Cryptanalysis - Part I: Monoalphabetic Substitution Systems is one of the most well-respected publications on cryptanalysis, as was written by William F. Friedman, one of the true experts in the field. Now declassified by the National Security Agency (NSA), this publication is key in helping individuals understand and solve cipher systems. Military Cryptanalysis - Part I is the first publication in a series of four and focuses on monoalphabetic substitution systems.
Product Details

* Paperback: 76 pages
* Publisher: Cryptanalysis Reprint Publications (July 20, 2009)
* Language: English
* ASIN: B002JCSPNQ

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Handbook of elliptic and hyperelliptic curve cryptography

Handbook of elliptic and hyperelliptic curve cryptography
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Henri Cohen (Editor), Gerhard Frey (Editor), Roberto Avanzi (Editor), Christophe Doche (Editor), Tanja Lange (Editor), Kim Nguyen (Editor), Frederik Vercauteren (Editor)

Review
… the book is designed for people who are working in the area and want to learn more about a specific issue. The chapters are written to be relatively independent so that readers can focus on the part of interest for them. Such readers will be grateful for the excellent index and extensive bibliography. … the handbook covers a wide range of topics and will be a valuable reference for researchers in curve-based cryptography.
— Steven D. Galbraith, in Mathematical Reviews, Issue 2007f


Product Description
The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications.

The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the group operations and computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method and provides the algorithms in an explicit manner. It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves. For some special curves the discrete logarithm problem can be transferred to an easier one; the consequences are explained and suggestions for good choices are given. The authors present applications to protocols for discrete-logarithm-based systems (including bilinear structures) and explain the use of elliptic and hyperelliptic curves in factorization and primality proving. Two chapters explore their design and efficient implementations in smart cards. Practical and theoretical aspects of side-channel attacks and countermeasures and a chapter devoted to (pseudo-)random number generation round off the exposition.

The broad coverage of all- important areas makes this book a complete handbook of elliptic and hyperelliptic curve cryptography and an invaluable reference to anyone interested in this exciting field.
Product Details

* Hardcover: 848 pages
* Publisher: Chapman & Hall/CRC; 1 edition (July 19, 2005)
* Language: English
* ISBN-10: 1584885181
* ISBN-13: 978-1584885184

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Elliptic Curves: Number Theory and Cryptography (Discrete Mathematics and Its Applications)

Elliptic Curves: Number Theory and Cryptography (Discrete Mathematics and Its Applications)
by: Lawrence C. Washington

Details

# Hardcover: 440 pages
# Publisher: Chapman & Hall/CRC; 1 edition (May 28, 2003)
# Language: English
# ISBN-10: 1584883650
# ISBN-13: 978-1584883654

Description

Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to senior undergraduate or beginning graduate students.Assuming only a modest background in elementary number theory, groups, and fields, Elliptic Curves: Number Theory and Cryptography introduces both the cryptographic and number theoretic sides of elliptic curves, interweaving the theory of elliptic curves with their applications. The author introduces elliptic curves over finite fields early in the treatment, leading readers directly to the intriguing cryptographic applications, but the book is structured so that readers can explore the number theoretic aspects independently if desired.By side-stepping algebraic geometry in favor an approach based on basic formulas, this book clearly demonstrates how elliptic curves are used and opens the doors to higher-level studies. Elliptic Curves offers a solid introduction to the mathematics and applications of elliptic curves that well prepares its readers to tackle more advanced problems in cryptography and number theory.

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Elementary Number Theory, Cryptography and Codes (Universitext)

Elementary Number Theory, Cryptography and Codes (Universitext)
by: M. Welleda Baldoni, Ciro Ciliberto, G.M. Piacentini Cattaneo

Details

* Publisher: Springer
* Number Of Pages: 522
* Publication Date: 2008-12-01
* ISBN-10 / ASIN: 3540691995
* ISBN-13 / EAN: 9783540691990
* Binding: Paperback

Description

In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic residues, primality tests, continued fractions, etc.) which in recent years have proven to be extremely useful for applications to cryptography and coding theory. Both cryptography and codes have crucial applications in our daily lives, and they are described here, while the complexity problems that arise in implementing the related numerical algorithms are also taken into due account. Cryptography has been developed in great detail, both in its classical and more recent aspects. In particular public key cryptography is extensively discussed, the use of algebraic geometry, specifically of elliptic curves over finite fields, is illustrated, and a final chapter is devoted to quantum cryptography, which is the new frontier of the field. Coding theory is not discussed in full; however a chapter, sufficient for a good introduction to the subject, has been devoted to linear codes. Each chapter ends with several complements and with an extensive list of exercises, the solutions to most of which are included in the last chapter.

Though the book contains advanced material, such as cryptography on elliptic curves, Goppa codes using algebraic curves over finite fields, and the recent AKS polynomial primality test, the authors' objective has been to keep the exposition as self-contained and elementary as possible. Therefore the book will be useful to students and researchers, both in theoretical (e.g. mathematicians) and in applied sciences (e.g. physicists, engineers, computer scientists, etc.) seeking a friendly introduction to the important subjects treated here. The book will also be useful for teachers who intend to give courses on these topics.
Written for: Students and researchers in theoretical (e.g. mathematicians) and in applied sciences (e.g. physicists, engineers, computer scientists, etc.); teachers who intend to give courses on these topics

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Cryptography: Theory and Practice, Third Edition (Discrete Mathematics and Its Applications)

Cryptography: Theory and Practice, Third Edition (Discrete Mathematics and Its Applications)
by: Douglas R. Stinson

Details

# Hardcover: 616 pages
# Publisher: Chapman & Hall/CRC; 3 edition (November 1, 2005)
# Language: English
# ISBN-10: 1584885084
# ISBN-13: 978-1584885085

Description

Douglas R. Stinson's Cryptography: Theory and Practice is a mathematically intensive examination of cryptography, including ciphers, the Data Encryption Standard (DES), public key cryptography, one-way hash functions, and digital signatures. Stinson's explication of "zero-sum proofs"--a process by which one person lets another person know that he or she has a password without actually revealing any information--is especially good.

If you are new to the math behind cryptography but want to tackle it, the author covers all of the required background to understand the real mathematics here. Cryptography includes extensive exercises with each chapter and makes an ideal introduction for any math-literate person willing to get acquainted with this material. --This text refers to an alternate Hardcover edition.

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