Introduction to Cryptography with Coding Theory

Description

• 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.

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

• 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

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.

• 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.

 

 

 

Additional information

Dimensions	1.50 × 7.40 × 9.55 in
Imprint	Pearson
Format	gen
ISBN-13	09780131862395
ISBN-10	0131862391
Author	Lawrence C. Washington, Wade Trappe
BISAC	MAT000000
Subjects	cryptography, mathematics, MAT000000, higher education, Calculus, Applied & Advanced Math, Advanced Math