Invitation to Cryptology / Edition 1

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Overview

This book introduces a wide range of up-to-date cryptological concepts along with the mathematical ideas that are behind them. The new and old are organized around a historical framework. A variety of mathematical topics that are germane to cryptology (e.g., modular arithmetic, Boolean functions, complexity theory, etc.) are developed, but they do not overshadow the main focus of the book. Chapter topics cover origins, examples, and ideas in cryptology; classical cryptographic techniques; symmetric computer-based cryptology; public-key cryptography; and present practice, issues, and the future. For individuals seeking an up-close and accurate idea of how current-day cryptographic methods work.

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Editorial Reviews

From The Critics
Incorporating discussions of the history of cryptology and mathematical concepts related to cryptology, Barr (Rhodes College) has produced an introductory work that manages to touch upon a number of topics while not attempting to be a single comprehensive treatment of the subject. Both classical and modern cryptologies are covered, and the use of statistical analysis, matrix manipulation, modular arithmetic, number theory, and other mathematical methods are discussed. The material is organized into sections that treat the origins of cryptology, classical cryptographic techniques, symmetric computer-based cryptology, and public-key cryptography. The last chapter offers a couple of case studies on the Data Encryption Standard and the Pretty Good Privacy software, as well as discussing legal and infrastructure issues. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780130889768
  • Publisher: Pearson
  • Publication date: 8/28/2001
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 396
  • Sales rank: 840,028
  • Product dimensions: 7.00 (w) x 9.10 (h) x 1.00 (d)

Read an Excerpt

In 1994, my colleague Terri Lindquester had a pedagogical inspiration: to teach cryptology. The lack of unified resources to teach an introductory course with mathematical themes, historical content, and current cryptographic relevance required her to piece together material from various sources. She had considerable success with The Science of Secret Writing: more students requested it at registration time than could be accommodated, her own insights and teaching abilities made the course itself lively and appealing to the students enrolled, and students from a wide range of academic disciplines learned some mathematics and cryptology. The experience convinced her that there was a genuine need for an up-to-date introductory cryptology text, and this prompted her to seek National Science Foundation (NSF) funding to develop materials for such a course. A guiding principle was to introduce mathematics in the context of cryptology. This book is the result of Terri's application for that funding, of the foundation's awarding it, and of a great deal of work, teaching, and writing in the interim. Unfortunately for those who use this text, very little of it is Terri's writing. Almost coincident with the awarding of funding for the project, Terri was called to serve in an administrative capacity at Rhodes College. The demands of this post were such that it would be extraordinarily difficult for her to work on the cryptology project, and indeed its fate was, for a time, in question. In 1997, through conversations with and encouragement from Terri, I embarked on the project: teaching the second offering of Secret Writing, doing research, and writing materials based on her course notes from the first offering of Secret Writing. I became "Chief Staff Mathematician" on the project. With her continuing consultation and reviewing of early drafts, the book has evolved into its present form.

This book is directed toward those whose mathematical background includes college-preparatory courses such as high school algebra and geometry. In earlier drafts, I have used it as the basis for a course for which there were no formal mathematical prerequisites at the college level. Students majoring in areas ranging from Art History to Zoology took the course. Many had not taken mathematics in four or five years.

The purpose of the book is to introduce students to segments of history and current cryptological practice that have mathematical content or underpinnings. This is not a mathematics text in the strictest sense because it does not begin with a few definitions and axioms and build up a mathematical edifice on that. However, a variety of mathematical topics are developed here: modular arithmetic, probability and statistics, matrix arithmetic, Boolean functions, complexity theory, and number theory. In each case, the topic is germane to cryptology.

The concepts introduced in this book may also be a springboard for those who may not be drawn into technical careers but who instead may be headed toward careers in public service or industry where important policy or strategic decisions regarding information security will be made. The more technical background the policymakers and managers have, the better. With any luck, these pages may provide some of that background.

The treatment here is not comprehensive, but the concepts discussed cover a number of the current uses of cryptographic methods. The mathematical basis of cryptography has been a theme throughout this exposition, and what is here can provide an entree to a range of mathematical areas. Readers may find their way into the general mathematical literature as well by following the links provided in the mathematical references in this book.

The academic and popular literature on cryptology is large and growing rapidly. It represents a considerable body of general knowledge about cryptology and specific information on implementations in hardware and software. In the bibliography of this book you will find a number of book and journal references on the subject. However, this merely scratches the surface. If you want to explore the literature more deeply, go to the references in these books.

A few words of advice about the book are in order. First, there is more material here than can be used in a one-semester course. One possible pathway through the material is this: Chapter 1, Chapter 2, Chapter 3 (possibly skipping 3.2), and Sections 4.1, 4.3, 4.4, 4.6, and 5.4. This sort of option covers conventional substitutions and transpositions, block ciphers and hash functions, public-key cryptography and related mathematics, applications of public-key cryptography such as key agreement and digital signatures, and finally a look at public policy issues relating to cryptography. Several mathematical topics arise naturally with this approach: modular arithmetic, functions, probability, matrix arithmetic, and number theory. In a more technically oriented course, a closer focus on 4.7, 5.1, or 5.3 may be appropriate.

There is a second caveat. An instructor is unlikely to be able to cover all this material at a uniform pages-per-unit-time rate: Some of the mathematical topics here are inherently more challenging than others to absorb. Consequently, while many sections can be dealt with effectively in one lecture, some may require more time to cover adequately. Instructors should be prepared to use their best judgment about this issue, taking into account the background of the students enrolled in the course.

In this material, opportunities abound for implementing encryption, decryption, and cryptanalytic methods on a computer. Depending on the method, students and instructors may wish to use a spreadsheet, computer algebra system, or compiled language such as C++ or Java. A few explicit examples and pseudocode and a range of hints throughout the text provide some indications how this can be done, though programming is not a focus in this text.

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Table of Contents

1. Origins, Examples, and Ideas in Cryptology.

A Crypto-Chronology. Cryptology and Mathematics: Functions. Crypto: Models, Maxims, and Mystique.

2. Classical Cryptographic Techniques.

Shift Ciphers and Modular Arithmetic. Affine Ciphers; More Modular Arithmetic. Substitution Ciphers. Transposition Ciphers. Polyalphabetic Substitutions. Probability and Expectation. The Friedman and Kasiski Tests. Cryptanalysis of the Vingenere Cipher. The Hill Cipher; Matrices.

3. Symmetric Computer-Based Cryptology.

Number Representation. Boolean and Numerical Functions. Computational Complexity. Stream Ciphers and Feedback Shift Registers. Block Ciphers. Hash Functions.

4. Public-Key Cryptography.

Primes, Factorization, and the Euclidean Algorithm. The Merkle-Hellman Knapsack. Fermat's Little Theorem. The RSA Public-Key Cryptosystem. Key Agreement. Digital Signatures. Zero-Knowledge Identification Protocols.

5. Case Studies and Issues.

Case Study I: DES. Case Study II: PGP. Public-Key Infrastructure. Law and Issues Regarding Cryptography.

Glossary.

Bibliography.

Table of Primes.

Answers to Selected Exercises.

Index.

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Preface

In 1994, my colleague Terri Lindquester had a pedagogical inspiration: to teach cryptology. The lack of unified resources to teach an introductory course with mathematical themes, historical content, and current cryptographic relevance required her to piece together material from various sources. She had considerable success with The Science of Secret Writing: more students requested it at registration time than could be accommodated, her own insights and teaching abilities made the course itself lively and appealing to the students enrolled, and students from a wide range of academic disciplines learned some mathematics and cryptology. The experience convinced her that there was a genuine need for an up-to-date introductory cryptology text, and this prompted her to seek National Science Foundation (NSF) funding to develop materials for such a course. A guiding principle was to introduce mathematics in the context of cryptology. This book is the result of Terri's application for that funding, of the foundation's awarding it, and of a great deal of work, teaching, and writing in the interim. Unfortunately for those who use this text, very little of it is Terri's writing. Almost coincident with the awarding of funding for the project, Terri was called to serve in an administrative capacity at Rhodes College. The demands of this post were such that it would be extraordinarily difficult for her to work on the cryptology project, and indeed its fate was, for a time, in question. In 1997, through conversations with and encouragement from Terri, I embarked on the project: teaching the second offering of Secret Writing, doing research, and writing materials based on her course notes from the first offering of Secret Writing. I became "Chief Staff Mathematician" on the project. With her continuing consultation and reviewing of early drafts, the book has evolved into its present form.

This book is directed toward those whose mathematical background includes college-preparatory courses such as high school algebra and geometry. In earlier drafts, I have used it as the basis for a course for which there were no formal mathematical prerequisites at the college level. Students majoring in areas ranging from Art History to Zoology took the course. Many had not taken mathematics in four or five years.

The purpose of the book is to introduce students to segments of history and current cryptological practice that have mathematical content or underpinnings. This is not a mathematics text in the strictest sense because it does not begin with a few definitions and axioms and build up a mathematical edifice on that. However, a variety of mathematical topics are developed here: modular arithmetic, probability and statistics, matrix arithmetic, Boolean functions, complexity theory, and number theory. In each case, the topic is germane to cryptology.

The concepts introduced in this book may also be a springboard for those who may not be drawn into technical careers but who instead may be headed toward careers in public service or industry where important policy or strategic decisions regarding information security will be made. The more technical background the policymakers and managers have, the better. With any luck, these pages may provide some of that background.

The treatment here is not comprehensive, but the concepts discussed cover a number of the current uses of cryptographic methods. The mathematical basis of cryptography has been a theme throughout this exposition, and what is here can provide an entree to a range of mathematical areas. Readers may find their way into the general mathematical literature as well by following the links provided in the mathematical references in this book.

The academic and popular literature on cryptology is large and growing rapidly. It represents a considerable body of general knowledge about cryptology and specific information on implementations in hardware and software. In the bibliography of this book you will find a number of book and journal references on the subject. However, this merely scratches the surface. If you want to explore the literature more deeply, go to the references in these books.

A few words of advice about the book are in order. First, there is more material here than can be used in a one-semester course. One possible pathway through the material is this: Chapter 1, Chapter 2, Chapter 3 (possibly skipping 3.2), and Sections 4.1, 4.3, 4.4, 4.6, and 5.4. This sort of option covers conventional substitutions and transpositions, block ciphers and hash functions, public-key cryptography and related mathematics, applications of public-key cryptography such as key agreement and digital signatures, and finally a look at public policy issues relating to cryptography. Several mathematical topics arise naturally with this approach: modular arithmetic, functions, probability, matrix arithmetic, and number theory. In a more technically oriented course, a closer focus on 4.7, 5.1, or 5.3 may be appropriate.

There is a second caveat. An instructor is unlikely to be able to cover all this material at a uniform pages-per-unit-time rate: Some of the mathematical topics here are inherently more challenging than others to absorb. Consequently, while many sections can be dealt with effectively in one lecture, some may require more time to cover adequately. Instructors should be prepared to use their best judgment about this issue, taking into account the background of the students enrolled in the course.

In this material, opportunities abound for implementing encryption, decryption, and cryptanalytic methods on a computer. Depending on the method, students and instructors may wish to use a spreadsheet, computer algebra system, or compiled language such as C++ or Java. A few explicit examples and pseudocode and a range of hints throughout the text provide some indications how this can be done, though programming is not a focus in this text.

Read More Show Less

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