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by Wade Trappe and Lawrence Washington

Cover type: HardbackEdition: 2ND 06

Copyright: 2006

Publisher: Prentice Hall, Inc.

Published: 2006

International: No

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With its lively, conversational tone and practical focus, this new edition mixes applied and theoretical aspects for a solid introduction to cryptography and security, including the latest significant advancements in the field.

**Features**

- Balances applied and theoretical aspects of security--Presents applications and protocols where cryptographic primitives are used in practice, such as SET and SSL.
- Coverage of Rijndael and AES--Provides a detailed explanation of AES, which has replaced Feistel-based ciphers (DES) as the standard block cipher algorithm.
- Coverage of practical applications of cryptography to security protocols--Connects the cryptographic tools developed earlier in the book to the building of real security tools, demonstrating to students that there is more to security and cryptography than just math.
- Friendly, story-like discussion of security concepts--Uses historical examples to illustrate the concepts of security and cryptanalysis by relating theory to easier-to-grasp events.
- Modern methods such as Elliptic curves, Lattice methods, and Quantum Techniques--Provides thorough coverage of topics that are becoming increasingly prominent in the field.
- Major coverage of coding theory--Offers a discussion of coding theory, which is often covered in today's cryptology courses.
- Numerous example calculations--Includes many examples, especially in purely mathematical chapters such as Ch. 3.
- Public key certificate--Provides an example of what an actual public key certificate looks like, rather than just describing it.
- Mathematica/Maple/Matlab problems and notebooks--Allow students to work with realistic sized examples in RSA and Digital Signatures, as well as classical cryptosystems and those with elliptic curves.
- Practical examples and applications--Give students hands-on experience with the large-numbered cryptography of today's security systems, and provides a discussion of security protocols.

**New To This Edition**

- New problems in Chs. 3 and 6--Offers instructors an expanded problem set.
- Sections on Legendre and Jacobi symbols and Continued Fractions in Ch. 3--Allows instructors to cover more advanced material (such as an attack on RSA) in later chapters.
- More modes of operation in Ch. 4--Completes the discussion of block ciphers.
- Additional attacks on RSA--Makes students aware of the strengths and shortcomings of this popular scheme.
- New material on hash functions--Expands the coverage of these important cryptographic primitives, including recent advancements relevant to the security profession.
- Updated discussion of multicollisions--Keeps students up-to-date on events that will have a significant impact on security systems over the next few years.

**1 Overview **

Secure Communications. Cryptographic Applications

**2 Classical Cryptosystems.**

Shift Ciphers. Affine Ciphers. The Vigen`ere Cipher. Substitution Ciphers. Sherlock Holmes. The Playfair and ADFGX Ciphers. Block Ciphers. Binary Numbers and ASCII. One-Time Pads. Pseudo-random Bit Generation. LFSR Sequences. Enigma. Exercises. Computer Problems.

**3 Basic Number Theory.**

Basic Notions. Solving ax + by = d. Congruences. The Chinese Remainder Theorem. Modular Exponentiation. Fermat and Euler. Primitive Roots. Inverting Matrices Mod n. Square Roots Mod n. Legendre and Jacobi Symbols. Finite Fields. Continued Fractions. Exercises. Computer Problems.

**4 The Data Encryption Standard **

Introduction. A Simplified DES-Type Algorithm. Differential Cryptanalysis. DES. Modes of Operation. Breaking DES. Meet-in-the-Middle Attacks. Password Security. Exercises.

**5 AES: Rijndael **

The Basic Algorithm. The Layers. Decryption. Design Considerations.

**6 The RSA Algorithm**

The RSA Algorithm. Attacks on RSA. Primality Testing. Factoring. The RSA Challenge. An Application to Treaty Verification. The Public Key Concept. Exercises. Computer Problems

**7 Discrete Logarithms **

Discrete Logarithms. Computing Discrete Logs. Bit Commitment Diffie-Hellman Key Exchange. ElGamal Public Key Cryptosystems. Exercises. Computer Problems.

**8 Hash Functions **

Hash Functions. A Simple Hash Example. The Secure Hash Algorithm. Birthday Attacks. Multicollisions. The Random Oracle Model. Using Hash Functions to Encrypt.

**9 Digital Signatures **

RSA Signatures. The ElGamal Signature Scheme. Hashing and Signing. Birthday Attacks on Signatures. The Digital Signature Algorithm. Exercises. Computer Problems.

**10 Security Protocols **

Intruders-in-the-Middle and Impostors. Key Distribution. Kerberos Public Key Infrastructures (PKI). X.509 Certificates. Pretty Good Privacy. SSL and TLS. Secure Electronic Transaction. Exercises.

**11 Digital Cash **

Digital Cash. Exercises.

**12 Secret Sharing Schemes **

Secret Splitting. Threshold Schemes. Exercises. Computer Problems.

**13 Games **

Flipping Coins over the Telephone. Poker over the Telephone. Exercises.

**14 Zero-Knowledge Techniques **

The Basic Setup. The Feige-Fiat-Shamir Identification Scheme. Exercises.

**15 Information Theory **

Probability Review. Entropy. Huffman Codes. Perfect Secrecy. The Entropy of English. Exercises.

**16 Elliptic Curves **

The Addition Law. Elliptic Curves Mod n. Factoring with Elliptic Curves. Elliptic Curves in Characteristic 2. Elliptic Curve Cryptosystems. Identity-Based Encryption. Exercises. Computer Problems.

**17 Lattice Methods **

Lattices. Lattice Reduction. An Attack on RSA. NTRU. Exercises

**18 Error Correcting Codes **

Introduction. Error Correcting Codes. Bounds on General Codes. Linear Codes. Hamming Codes. Golay Codes. Cyclic Codes. BCH Codes. Reed-Solomon Codes. The McEliece Cryptosystem. Other Topics. Exercises. Computer Problems.

**19 Quantum Techniques in Cryptography **

A Quantum Experiment. Quantum Key Distribution. Shor's Algorithm. 4 Exercises.

Mathematica Examples

Maple Examples

MATLAB Examples

Further Reading

Bibliography

Index

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Summary

With its lively, conversational tone and practical focus, this new edition mixes applied and theoretical aspects for a solid introduction to cryptography and security, including the latest significant advancements in the field.

**Features**

- Balances applied and theoretical aspects of security--Presents applications and protocols where cryptographic primitives are used in practice, such as SET and SSL.
- Coverage of Rijndael and AES--Provides a detailed explanation of AES, which has replaced Feistel-based ciphers (DES) as the standard block cipher algorithm.
- Coverage of practical applications of cryptography to security protocols--Connects the cryptographic tools developed earlier in the book to the building of real security tools, demonstrating to students that there is more to security and cryptography than just math.
- Friendly, story-like discussion of security concepts--Uses historical examples to illustrate the concepts of security and cryptanalysis by relating theory to easier-to-grasp events.
- Modern methods such as Elliptic curves, Lattice methods, and Quantum Techniques--Provides thorough coverage of topics that are becoming increasingly prominent in the field.
- Major coverage of coding theory--Offers a discussion of coding theory, which is often covered in today's cryptology courses.
- Numerous example calculations--Includes many examples, especially in purely mathematical chapters such as Ch. 3.
- Public key certificate--Provides an example of what an actual public key certificate looks like, rather than just describing it.
- Mathematica/Maple/Matlab problems and notebooks--Allow students to work with realistic sized examples in RSA and Digital Signatures, as well as classical cryptosystems and those with elliptic curves.
- Practical examples and applications--Give students hands-on experience with the large-numbered cryptography of today's security systems, and provides a discussion of security protocols.

**New To This Edition**

- New problems in Chs. 3 and 6--Offers instructors an expanded problem set.
- Sections on Legendre and Jacobi symbols and Continued Fractions in Ch. 3--Allows instructors to cover more advanced material (such as an attack on RSA) in later chapters.
- More modes of operation in Ch. 4--Completes the discussion of block ciphers.
- Additional attacks on RSA--Makes students aware of the strengths and shortcomings of this popular scheme.
- New material on hash functions--Expands the coverage of these important cryptographic primitives, including recent advancements relevant to the security profession.
- Updated discussion of multicollisions--Keeps students up-to-date on events that will have a significant impact on security systems over the next few years.

Table of Contents

**1 Overview **

Secure Communications. Cryptographic Applications

**2 Classical Cryptosystems.**

Shift Ciphers. Affine Ciphers. The Vigen`ere Cipher. Substitution Ciphers. Sherlock Holmes. The Playfair and ADFGX Ciphers. Block Ciphers. Binary Numbers and ASCII. One-Time Pads. Pseudo-random Bit Generation. LFSR Sequences. Enigma. Exercises. Computer Problems.

**3 Basic Number Theory.**

Basic Notions. Solving ax + by = d. Congruences. The Chinese Remainder Theorem. Modular Exponentiation. Fermat and Euler. Primitive Roots. Inverting Matrices Mod n. Square Roots Mod n. Legendre and Jacobi Symbols. Finite Fields. Continued Fractions. Exercises. Computer Problems.

**4 The Data Encryption Standard **

Introduction. A Simplified DES-Type Algorithm. Differential Cryptanalysis. DES. Modes of Operation. Breaking DES. Meet-in-the-Middle Attacks. Password Security. Exercises.

**5 AES: Rijndael **

The Basic Algorithm. The Layers. Decryption. Design Considerations.

**6 The RSA Algorithm**

The RSA Algorithm. Attacks on RSA. Primality Testing. Factoring. The RSA Challenge. An Application to Treaty Verification. The Public Key Concept. Exercises. Computer Problems

**7 Discrete Logarithms **

Discrete Logarithms. Computing Discrete Logs. Bit Commitment Diffie-Hellman Key Exchange. ElGamal Public Key Cryptosystems. Exercises. Computer Problems.

**8 Hash Functions **

Hash Functions. A Simple Hash Example. The Secure Hash Algorithm. Birthday Attacks. Multicollisions. The Random Oracle Model. Using Hash Functions to Encrypt.

**9 Digital Signatures **

RSA Signatures. The ElGamal Signature Scheme. Hashing and Signing. Birthday Attacks on Signatures. The Digital Signature Algorithm. Exercises. Computer Problems.

**10 Security Protocols **

Intruders-in-the-Middle and Impostors. Key Distribution. Kerberos Public Key Infrastructures (PKI). X.509 Certificates. Pretty Good Privacy. SSL and TLS. Secure Electronic Transaction. Exercises.

**11 Digital Cash **

Digital Cash. Exercises.

**12 Secret Sharing Schemes **

Secret Splitting. Threshold Schemes. Exercises. Computer Problems.

**13 Games **

Flipping Coins over the Telephone. Poker over the Telephone. Exercises.

**14 Zero-Knowledge Techniques **

The Basic Setup. The Feige-Fiat-Shamir Identification Scheme. Exercises.

**15 Information Theory **

Probability Review. Entropy. Huffman Codes. Perfect Secrecy. The Entropy of English. Exercises.

**16 Elliptic Curves **

The Addition Law. Elliptic Curves Mod n. Factoring with Elliptic Curves. Elliptic Curves in Characteristic 2. Elliptic Curve Cryptosystems. Identity-Based Encryption. Exercises. Computer Problems.

**17 Lattice Methods **

Lattices. Lattice Reduction. An Attack on RSA. NTRU. Exercises

**18 Error Correcting Codes **

Introduction. Error Correcting Codes. Bounds on General Codes. Linear Codes. Hamming Codes. Golay Codes. Cyclic Codes. BCH Codes. Reed-Solomon Codes. The McEliece Cryptosystem. Other Topics. Exercises. Computer Problems.

**19 Quantum Techniques in Cryptography **

A Quantum Experiment. Quantum Key Distribution. Shor's Algorithm. 4 Exercises.

Mathematica Examples

Maple Examples

MATLAB Examples

Further Reading

Bibliography

Index

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 2006

International: No

Published: 2006

International: No

With its lively, conversational tone and practical focus, this new edition mixes applied and theoretical aspects for a solid introduction to cryptography and security, including the latest significant advancements in the field.

**Features**

- Balances applied and theoretical aspects of security--Presents applications and protocols where cryptographic primitives are used in practice, such as SET and SSL.
- Coverage of Rijndael and AES--Provides a detailed explanation of AES, which has replaced Feistel-based ciphers (DES) as the standard block cipher algorithm.
- Coverage of practical applications of cryptography to security protocols--Connects the cryptographic tools developed earlier in the book to the building of real security tools, demonstrating to students that there is more to security and cryptography than just math.
- Friendly, story-like discussion of security concepts--Uses historical examples to illustrate the concepts of security and cryptanalysis by relating theory to easier-to-grasp events.
- Modern methods such as Elliptic curves, Lattice methods, and Quantum Techniques--Provides thorough coverage of topics that are becoming increasingly prominent in the field.
- Major coverage of coding theory--Offers a discussion of coding theory, which is often covered in today's cryptology courses.
- Numerous example calculations--Includes many examples, especially in purely mathematical chapters such as Ch. 3.
- Public key certificate--Provides an example of what an actual public key certificate looks like, rather than just describing it.
- Mathematica/Maple/Matlab problems and notebooks--Allow students to work with realistic sized examples in RSA and Digital Signatures, as well as classical cryptosystems and those with elliptic curves.
- Practical examples and applications--Give students hands-on experience with the large-numbered cryptography of today's security systems, and provides a discussion of security protocols.

**New To This Edition**

- New problems in Chs. 3 and 6--Offers instructors an expanded problem set.
- Sections on Legendre and Jacobi symbols and Continued Fractions in Ch. 3--Allows instructors to cover more advanced material (such as an attack on RSA) in later chapters.
- More modes of operation in Ch. 4--Completes the discussion of block ciphers.
- Additional attacks on RSA--Makes students aware of the strengths and shortcomings of this popular scheme.
- New material on hash functions--Expands the coverage of these important cryptographic primitives, including recent advancements relevant to the security profession.
- Updated discussion of multicollisions--Keeps students up-to-date on events that will have a significant impact on security systems over the next few years.

**1 Overview **

Secure Communications. Cryptographic Applications

**2 Classical Cryptosystems.**

Shift Ciphers. Affine Ciphers. The Vigen`ere Cipher. Substitution Ciphers. Sherlock Holmes. The Playfair and ADFGX Ciphers. Block Ciphers. Binary Numbers and ASCII. One-Time Pads. Pseudo-random Bit Generation. LFSR Sequences. Enigma. Exercises. Computer Problems.

**3 Basic Number Theory.**

Basic Notions. Solving ax + by = d. Congruences. The Chinese Remainder Theorem. Modular Exponentiation. Fermat and Euler. Primitive Roots. Inverting Matrices Mod n. Square Roots Mod n. Legendre and Jacobi Symbols. Finite Fields. Continued Fractions. Exercises. Computer Problems.

**4 The Data Encryption Standard **

Introduction. A Simplified DES-Type Algorithm. Differential Cryptanalysis. DES. Modes of Operation. Breaking DES. Meet-in-the-Middle Attacks. Password Security. Exercises.

**5 AES: Rijndael **

The Basic Algorithm. The Layers. Decryption. Design Considerations.

**6 The RSA Algorithm**

The RSA Algorithm. Attacks on RSA. Primality Testing. Factoring. The RSA Challenge. An Application to Treaty Verification. The Public Key Concept. Exercises. Computer Problems

**7 Discrete Logarithms **

Discrete Logarithms. Computing Discrete Logs. Bit Commitment Diffie-Hellman Key Exchange. ElGamal Public Key Cryptosystems. Exercises. Computer Problems.

**8 Hash Functions **

Hash Functions. A Simple Hash Example. The Secure Hash Algorithm. Birthday Attacks. Multicollisions. The Random Oracle Model. Using Hash Functions to Encrypt.

**9 Digital Signatures **

RSA Signatures. The ElGamal Signature Scheme. Hashing and Signing. Birthday Attacks on Signatures. The Digital Signature Algorithm. Exercises. Computer Problems.

**10 Security Protocols **

Intruders-in-the-Middle and Impostors. Key Distribution. Kerberos Public Key Infrastructures (PKI). X.509 Certificates. Pretty Good Privacy. SSL and TLS. Secure Electronic Transaction. Exercises.

**11 Digital Cash **

Digital Cash. Exercises.

**12 Secret Sharing Schemes **

Secret Splitting. Threshold Schemes. Exercises. Computer Problems.

**13 Games **

Flipping Coins over the Telephone. Poker over the Telephone. Exercises.

**14 Zero-Knowledge Techniques **

The Basic Setup. The Feige-Fiat-Shamir Identification Scheme. Exercises.

**15 Information Theory **

Probability Review. Entropy. Huffman Codes. Perfect Secrecy. The Entropy of English. Exercises.

**16 Elliptic Curves **

The Addition Law. Elliptic Curves Mod n. Factoring with Elliptic Curves. Elliptic Curves in Characteristic 2. Elliptic Curve Cryptosystems. Identity-Based Encryption. Exercises. Computer Problems.

**17 Lattice Methods **

Lattices. Lattice Reduction. An Attack on RSA. NTRU. Exercises

**18 Error Correcting Codes **

Introduction. Error Correcting Codes. Bounds on General Codes. Linear Codes. Hamming Codes. Golay Codes. Cyclic Codes. BCH Codes. Reed-Solomon Codes. The McEliece Cryptosystem. Other Topics. Exercises. Computer Problems.

**19 Quantum Techniques in Cryptography **

A Quantum Experiment. Quantum Key Distribution. Shor's Algorithm. 4 Exercises.

Mathematica Examples

Maple Examples

MATLAB Examples

Further Reading

Bibliography

Index