# Computer Security and Cryptography

# Computer Security and Cryptography

ISBN: 978-0-470-08398-7

May 2006

544 pages

## Description

**Gain the skills and knowledge needed to create effective data security systems**

This book updates readers with all the tools, techniques, and concepts needed to understand and implement data security systems. It presents a wide range of topics for a thorough understanding of the factors that affect the efficiency of secrecy, authentication, and digital signature schema. Most importantly, readers gain hands-on experience in cryptanalysis and learn how to create effective cryptographic systems.

The author contributed to the design and analysis of the Data Encryption Standard (DES), a widely used symmetric-key encryption algorithm. His recommendations are based on firsthand experience of what does and does not work.

Thorough in its coverage, the book starts with a discussion of the history of cryptography, including a description of the basic encryption systems and many of the cipher systems used in the twentieth century. The author then discusses the theory of symmetric- and public-key cryptography. Readers not only discover what cryptography can do to protect sensitive data, but also learn the practical limitations of the technology. The book ends with two chapters that explore a wide range of cryptography applications.

Three basic types of chapters are featured to facilitate learning:

- Chapters that develop technical skills
- Chapters that describe a cryptosystem and present a method of analysis
- Chapters that describe a cryptosystem, present a method of analysis, and provide problems to test your grasp of the material and your ability to implement practical solutions

With consumers becoming increasingly wary of identity theft and companies struggling to develop safe, secure systems, this book is essential reading for professionals in e-commerce and information technology. Written by a professor who teaches cryptography, it is also ideal for students.

## Related Resources

### Instructor

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PREFACE.

ABOUT THE AUTHOR.

**CHAPTER 1: APERITIFS.**

1.1 The Lexicon of Cryptography.

1.2 Cryptographic Systems.

1.3 Cryptanalysis.

1.4 Side Information.

1.5 Thomas Jefferson and the M-94.

1.6 Cryptography and History.

1.7 Cryptography and Computers.

1.8 The National Security Agency.

1.9 The Giants.

1.10 No Sex, Money, Crime or . . . Love.

1.11 An Example of the Inference Process in Cryptanalysis.

1.12 Warning!

**CHAPTER 2: COLUMNAR TRANSPOSITION.**

2.1 Shannon’s Classification of Secrecy Transformations.

2.2 The Rules of Columnar Transposition Encipherment.

2.3 Cribbing.

2.4 Examples of Cribbing.

2.5 Plaintext Language Models.

2.6 Counting k-Grams.

2.7 Deriving the Parameters of a Markov Model from Sliding Window Counts.

2.8 Markov Scoring.

2.9 The ADFGVX Transposition System.

2.10 CODA.

2.11 Columnar Transposition Problems.

**CHAPTER 3: MONOALPHABETIC SUBSTITUTION.**

3.1 Monoalphabetic Substitution.

3.2 Caesar’s Cipher.

3.3 Cribbing Using Isomorphs.

3.4 The x^{2}-Test of a Hypothesis.

3.5 Pruning from the Table of Isomorphs.

3.6 Partial Maximum Likelihood Estimation of a Monoalphabetic Substitution.

3.7 The Hidden Markov Model (HMM).

3.8 Hill Encipherment of ASCII N-Grams.

3.9 Gaussian Elimination.

3.10 Monoalphabetic Substitution Problems.

**CHAPTER 4: POLYALPHABETIC SUBSTITUTION.**

4.1 Running Keys.

4.2 Blaise de Vigene're.

4.3 Gilbert S. Vernam.

4.4 The One-Time Pad.

4.5 Finding the Key of Vernam–Vigene're Ciphertext with Known Period by Correlation.

4.6 Coincidence.

4.7 Venona.

4.8 Polyalphabetic Substitution Problems.

**CHAPTER 5: STATISTICAL TESTS.**

5.1 Weaknesses in a Cryptosystem.

5.2 The Kolmogorov–Smirnov Test.

5.3 NIST’s Proposed Statistical Tests.

5.4 Diagnosis.

5.5 Statistical Tests Problems.

**CHAPTER 6: THE EMERGENCE OF CIPHER MACHINES.**

6.1 The Rotor.

6.2 Rotor Systems.

6.3 Rotor Patents.

6.4 A Characteristic Property of Conjugacy.

6.5 Analysis of a 1-Rotor System: Ciphertext Only.

6.6 The Displacement Sequence of a Permutation.

6.7 Arthur Scherbius.

6.8 Enigma Key Distribution Protocol.

6.9 Cryptanalysis of the Enigma.

6.10 Cribbing Enigma Ciphertext.

6.11 The Lorenz Schlu¨sselzusatz.

6.12 The SZ40 Pin Wheels.

6.13 SZ40 Cryptanalysis Problems.

6.14 Cribbing SZ40 Ciphertext.

**CHAPTER 7: THE JAPANESE CIPHER MACHINES.**

7.1 Japanese Signaling Conventions.

7.2 Half-Rotors.

7.3 Components of the RED Machine.

7.4 Cribbing RED Ciphertext.

7.5 Generalized Vowels and Consonants.

7.6 “Climb Mount Itaka” – War!

7.7 Components of the PURPLE Machine.

7.8 The PURPLE Keys.

7.9 Cribbing PURPLE: Finding the V-Stepper.

7.10 Cribbing PURPLE: Finding the C-Steppers.

**CHAPTER 8: STREAM CIPHERS.**

8.1 Stream Ciphers.

8.2 Feedback Shift Registers.

8.3 The Algebra of Polynomials over Z_{2}.

8.4 The Characteristic Polynomial of a Linear Feedback Shift Register.

8.5 Properties of Maximal Length LFSR Sequences.

8.6 Linear Equivalence.

8.7 Combining Multiple Linear Feedback Shift Registers.

8.8 Matrix Representation of the LFSR.

8.9 Cribbing of Stream Enciphered ASCII Plaintext.

8.10 Nonlinear Feedback Shift Registers.

8.11 Nonlinear Key Stream Generation.

8.12 Irregular Clocking.

8.13 RC4.

8.14 Stream Encipherment Problems.

**CHAPTER 9: BLOCK-CIPHERS: LUCIFER, DES, AND AES.**

9.1 LUCIFER.

9.2 DES.

9.3 The DES S-Boxes, P-Box, and Initial Permutation (IP).

9.4 DES Key Schedule.

9.5 Sample DES Encipherment.

9.6 Chaining.

9.7 Is DES a Random Mapping?

9.8 DES in the Output-Feedback Mode (OFB).

9.9 Cryptanalysis of DES.

9.10 Differential Cryptanalysis.

9.11 The EFS DES-Cracker.

9.12 What Now?

9.13 The Future Advanced Data Encryption Standard.

9.14 And the Winner Is!

9.15 The Rijndael Operations.

9.16 The Rijndael Cipher.

9.17 Rijndael’s Strength: Propagation of Patterns.

9.18 When is a Product Block-Cipher Secure?

9.19 Generating the Symmetric Group.

9.20 A Class of Block Ciphers.

9.21 The IDEA Block Cipher.

**CHAPTER 10: THE PARADIGM OF PUBLIC KEY CRYPTOGRAPHY.**

10.1 In the Beginning. . . .

10.2 Key Distribution.

10.3 E-Commerce.

10.4 Public-Key Cryptosystems: Easy and Hard Computational Problems.

10.5 Do PKCS Solve the Problem of Key Distribution?

10.6 P.S.

**CHAPTER 11: THE KNAPSACK CRYPTOSYSTEM.**

11.1 Subset Sum and Knapsack Problems.

11.2 Modular Arithmetic and the Euclidean Algorithm.

11.3 A Modular Arithmetic Knapsack Problem.

11.4 Trap-Door Knapsacks.

11.5 Knapsack Encipherment and Decipherment of ASCII-Plaintext.

11.6 Cryptanalysis of the Merkle–Hellman Knapsack System (Modular Mapping).

11.7 Diophantine Approximation.

11.8 Short Vectors in a Lattice.

11.9 Knapsack-Like Cryptosystems.

11.10 Knapsack Cryptosystem Problems.

**CHAPTER 12: THE RSA CRYPTOSYSTEM.**

12.1 A Short Number-Theoretic Digression.

12.2 RSA.

12.3 The RSA Encipherment and Decipherment of ASCII-Plaintext.

12.4 Attack on RSA.

12.5 Williams Variation of RSA.

12.6 Multiprecision Modular Arithmetic.

**CHAPTER 13: PRIME NUMBERS AND FACTORIZATION.**

13.1 Number Theory and Cryptography.

13.2 Prime Numbers and the Sieve of Eratosthenes.

13.3 Pollard’s p 2 1 Method.

13.4 Pollard’s r-Algorithm.

13.5 Quadratic Residues.

13.6 Random Factorization.

13.7 The Quadratic Sieve (QS).

13.8 Testing if an Integer is a Prime.

13.9 The RSA Challenge.

13.10 Perfect Numbers and the Mersenne Primes.

13.11 Multiprecision Arithmetic.

13.12 Prime Number Testing and Factorization Problems.

**CHAPTER 14: THE DISCRETE LOGARITHM PROBLEM.**

14.1 The Discrete Logarithm Problem Modulo *p*.

14.2 Solution of the DLP Modulo *p* Given a Factorization of *p* - 1.

14.3 Adelman’s Subexponential Algorithm for the Discrete Logarithm Problem.

14.4 The Baby-Step, Giant-Step Algorithm.

14.5 The Index-Calculus Method.

14.6 Pollard’s ρ-Algorithm.

14.7 Extension Fields.

14.8 The Current State of Discrete Logarithm Research.

**CHAPTER 15: ELLIPTIC CURVE CRYPTOGRAPHY.**

15.1 Elliptic Curves.

15.2 The Elliptic Group over the Reals.

15.3 Lenstra’s Factorization Algorithm.

15.4 The Elliptic Group over Z_{p} ( *p* > 3).

15.5 Elliptic Groups over the Field Z_{m,2}.

15.6 Computations in the Elliptic Group E_{Zm,2}(a, b).

15.7 Supersingular Elliptic Curves.

15.8 Diffie–Hellman Key Exchange Using an Elliptic Curve.

15.9 The Menezes–Vanstone Elliptic Curve Cryptosystem.

15.10 The Elliptic Curve Digital Signature Algorithm.

15.11 The Certicom Challenge.

15.12 NSA and Elliptic Curve Cryptography.

**CHAPTER 16: KEY EXCHANGE IN A NETWORK.**

16.1 Key Distribution in a Network.

16.2 U.S. Patent ’770.

16.3 Spoofing.

16.4 El Gamal’s Extension of Diffie–Hellman.

16.5 Shamir’s Autonomous Key Exchange.

16.6 X9.17 Key Exchange Architecture.

16.7 The Needham–Schroeder Key Distribution Protocol.

**CHAPTER 17: DIGITAL SIGNATURES AND AUTHENTICATION.**

17.1 The Need for Signatures.

17.2 Threats to Network Transactions.

17.3 Secrecy, Digital Signatures, and Authentication.

17.4 The Desiderata of a Digital Signature.

17.5 Public-Key Cryptography and Signature Systems.

17.6 Rabin’s Quadratic Residue Signature Protocol.

17.7 Hash Functions.

17.8 MD5.

17.9 The Secure Hash Algorithm.

17.10 NIST’s Digital Signature Algorithm.

17.11 El Gamal’s Signature Protocol.

17.12 The Fiat–Shamir Identification and Signature Schema.

17.13 The Oblivious Transfer.

**CHAPTER 18: APPLICATIONS OF CRYPTOGRAPHY.**

18.1 UNIX Password Encipherment.

18.2 Magnetic Stripe Technology.

18.3 Protecting ATM Transactions.

18.4 Keyed-Access Cards.

18.5 Smart Cards.

18.6 Who Can You Trust?: Kohnfelder’s Certificates.

18.7 X.509 Certificates.

18.8 The Secure Socket Layer (SSL).

18.9 Making a Secure Credit Card Payment on the Web.

**CHAPTER 19: CRYPTOGRAPHIC PATENTS.**

19.1 What is a Patent?

19.2 Patentability of Ideas.

19.3 The Format of a Patent.

19.4 Patentable versus Nonpatentable Subjects.

19.5 Infringement.

19.6 The Role of Patents in Cryptography.

19.7 U.S. Patent 3,543,904.

19.8 U.S. Patent 4,200,770.

19.9 U.S. Patent 4,218,582.

19.10 U.S. Patent 4,405,829.

19.11 PKS/RSADSI Litigation.

19.12 Leon Stambler.

**INDEX.**

*IEEE Computer Magazine*, March 2007)

- Exercises and problems are presented to test students' understanding
- Solutions manual is available for adoptees of the book
- Parts of the book have been used by the author to teach the course Introduction to Cryptology at UC Santa Barbara
- Book is encyclopedic in the sense that it covers all the past and current developments in encryption algorithm design
- Author was involved in the design of the Data Encryption Standard (DES), which is perhaps the most widely used symmetric-key encryption algorithm in public use. DES is thoroughly discussed in one of the book's chapters.
- An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.