McAndrew Introduction to Cryptography with Open-Source Software

Erscheinungsjahr 2012
ISBN: 978-1-4398-2571-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: 0 - No protection

E-Book, Englisch, 461 Seiten

Reihe: Discrete Mathematics and Its Applications

Once the privilege of a secret few, cryptography is now taught at universities around the world. Introduction to Cryptography with Open-Source Software illustrates algorithms and cryptosystems using examples and the open-source computer algebra system of Sage. The author, a noted educator in the field, provides a highly practical learning experience by progressing at a gentle pace, keeping mathematics at a manageable level, and including numerous end-of-chapter exercises.

Focusing on the cryptosystems themselves rather than the means of breaking them, the book first explores when and how the methods of modern cryptography can be used and misused. It then presents number theory and the algorithms and methods that make up the basis of cryptography today. After a brief review of "classical" cryptography, the book introduces information theory and examines the public-key cryptosystems of RSA and Rabin’s cryptosystem. Other public-key systems studied include the El Gamal cryptosystem, systems based on knapsack problems, and algorithms for creating digital signature schemes.

The second half of the text moves on to consider bit-oriented secret-key, or symmetric, systems suitable for encrypting large amounts of data. The author describes block ciphers (including the Data Encryption Standard), cryptographic hash functions, finite fields, the Advanced Encryption Standard, cryptosystems based on elliptical curves, random number generation, and stream ciphers. The book concludes with a look at examples and applications of modern cryptographic systems, such as multi-party computation, zero-knowledge proofs, oblivious transfer, and voting protocols.

Zielgruppe

Undergraduate and postgraduate students in cryptography or computer and network security.

Autoren/Hrsg.

McAndrew, Alasdair

Fachgebiete

• Mathematik | Informatik EDV | Informatik Technische Informatik Computersicherheit Kryptographie, Datenverschlüsselung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Kryptologie, Informationssicherheit
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

Introduction to Cryptography
Hiding information: confidentiality

Some basic definitions

Attacks on a cryptosystem

Some cryptographic problems

Cryptographic protocols

Some simple ciphers

Cryptography and computer security

Basic Number Theory

Introduction

Some basic definitions

Some number theoretic calculations

Primality testing

Classical Cryptosystems

Introduction

The Caesar cipher

Translation ciphers
Transposition ciphers

The Vigenère cipher

The one-time pad

Permutation ciphers

Matrix ciphers

Introduction to Information Theory
Entropy and uncertainty

Perfect secrecy

Estimating the entropy of English

Unicity distance

Public-Key Cryptosystems Based on Factoring

Introduction

The RSA cryptosystem

Attacks against RSA

RSA in Sage

Rabin’s cryptosystem

Rabin’s cryptosystem in Sage

Some notes on security
Factoring

Public-Key Cryptosystems Based on Logarithms and Knapsacks
El Gamal’s cryptosystem

El Gamal in Sage

Computing discrete logarithms

Diffie-Hellman key exchange

Knapsack cryptosystems

Breaking the knapsack

Digital Signatures

Introduction

RSA signature scheme

Rabin digital signatures

The El Gamal digital signature scheme

The Digital Signature Standard

Block Ciphers and the Data Encryption Standard

Block ciphers

Some definitions

Substitution/permutation ciphers
Modes of encryption

Exploring modes of encryption

The Data Encryption Standard (DES)

Feistel ciphers

Simplified DES: sDES

The DES algorithm

Security of S-boxes

Security of DES

Using DES

Experimenting with DES

Lightweight ciphers

Finite Fields

Groups and rings

Introduction to fields

Fundamental algebra of finite fields

Polynomials mod 2

A field of order 8

Other fields GF(2n)

Multiplication and inversion

Multiplication without power tables

The Advanced Encryption Standard

Introduction and some history

Basic structure

The layers in detail

Decryption

Experimenting with AES

A simplified Rijndael

Security of the AES

Hash Functions
Uses of hash functions

Security of hash functions

Constructing a hash function

Provably secure hash functions

New hash functions

Message authentication codes

Using a MAC

Elliptic Curves and Cryptosystems
Basic definitions
The group on an elliptic curve

Background and history

Multiplication

Elliptic curve cryptosystems

Elliptic curve signature schemes

Elliptic curves over binary fields

Pairing based cryptography

Exploring pairings in Sage

Random Numbers and Stream Ciphers

Introduction

Pseudo-random number generators
Some cryptographically strong generators

The shrinking generator

ISAAC and Fortuna

Stream ciphers

RC4

The Blum-Goldwasser cryptosystem

Advanced Applications and Protocols
Secure multi-party computation

Zero knowledge proofs

Oblivious transfer

Digital cash

Voting protocols

Appendix A: Introduction to Sage

Appendix B: Advanced Computational Number Theory

Bibliography
Index

Exercises appear at the end of each chapter.

Über Autor(innen)

Alasdair McAndrew is a senior lecturer in the School of Engineering and Science at Victoria University in Melbourne, Australia.