Cryptography and Network Security

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2 Cryptography and Network Security

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4 CRYPTOGRAPHY AND NETWORK SECURITY PRAKASH C. GUPTA Former Head Department of Information Technology Maharashtra Institute of Technology Pune Delhi

5 CRYPTOGRAPHY AND NETWORK SECURITY Prakash C. Gupta 2015 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN The export rights of this book are vested solely with the publisher. Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi and Printed by Mohan Makhijani at Rekha Printers Private Limited, New Delhi

6 Contents Preface...xvii Abbreviations...xix 1. Introduction to Network Security Security Goals The Cast Adversarial Attacks Security Services Security Mechanisms Organization of the Book Summing Up...10 Recommended Reading...10 Problems Mathematical Foundations I (Modular Arithmetic) Modular Arithmetic Modulo Operator Set of Residues Congruence Modular Arithmetic Operations Properties of Modular Arithmetic for Integers in Z n Properties of Modular Arithmetic for Integers in Z Additive Inverse Encryption and Decryption Using Additive Inverse Multiplicative Inverse Encryption and Decryption Using Multiplicative Inverse Matrices Modular Arithmetic of Matrices...17 v

7 vi Contents 2.5 Greatest Common Divisor (GCD) Euclid s Algorithm Bezout s Identity Extended Euclid s Algorithm Summing Up...20 Recommended Reading...21 Problems Classical Encryption Techniques Terminology of Cryptography Symmetric-key and Asymmetric-key Encryption Cryptanalysis Classical Encryption Methods Substitution Ciphers Shift Cipher Monoalphabetic Substitution Cipher Statistical Attack Playfair Cipher Hill Cipher Polyalphabetic Substitution Ciphers Vigenere Cipher One-time Pad Transposition Ciphers Cryptanalytic Attacks Ciphertext-only Attack Known-plaintext Attack Chosen-plaintext Attack Chosen-ciphertext Attack Summing Up...33 Recommended Reading...34 Problems Symmetric-key Ciphers I (Data Encryption Standard) Block Ciphers Block Ciphers Using Multiple Rounds Diffusion and Confusion Structure of Round Function R Feistel Cipher Structure Data Encryption Standard (DES) Scrambling Function g Round Key Generation Weak and Semi-weak Keys Strength of DES...49

8 Contents vii Double DES Triple DES Summing Up...52 Recommended Reading...53 Problems Mathematical Foundations II (Finite Fields) Binary Operation Properties of Binary Operation Group Cyclic Group Abelian Group Ring Commutative Ring Field Galois Finite Fields Finite Fields of Type GF(p) Finite Fields of Type GF(2 n ) Algebraic Polynomial Polynomials over a Field Representation of Binary Data by Polynomials Set of Polynomials Modular Arithmetic for Set of Polynomials Irreducible Polynomial Finite Field GF(2 n ) Generator for GF(2 n ) Summing Up...69 Recommended Reading...70 Problems Symmetric-key Ciphers II (Advanced Encryption Standard) Advanced Encryption Standard (AES) State Array and Word Overall Structure of AES Encryption Round Substitute Bytes (SubBytes) Transformation Shift Rows Transformation (ShiftRows) Mix Columns Transformation (MixColumns) Add Round Key (AddRoundKey) Decryption Round Inverse Shift Rows Transformation (InvShiftRows) Inverse Substitute Bytes Transformation (InvSubBytes) Inverse Mix Columns (InvMixColumns)...81

9 viii Contents 6.4 Key Expansion in AES Characteristic Features of the Key Expansion Algorithm Security and Implementation Aspects of AES Summing Up...84 Recommended Reading...85 Problems Symmetric-key Ciphers III (Stream Ciphers, Modes of Operation) Stream Ciphers Synchronous Stream Ciphers Characteristic Features of Synchronous Stream Cipher Self Synchronizing Stream Cipher Characteristic Features of Self Synchronizing Stream Cipher RC Analysis of RC Modes of Operation of Block Ciphers Electronic Codebook Mode (ECB) Cipher Block Chaining Mode (CBC) Cipher Feedback Mode (CFB) Output Feedback Mode (OFB) Counter Mode (CTR) Summing Up Recommended Reading Problems Mathematical Foundations III (Prime Numbers) Prime, Coprime and Composite Numbers Number of Primes Fermat s and Euler s Theorems Fermat s Little Theorem Euler s Totient Function Euler s Theorem Testing for Primality Divisibility Test Fermat s Primality Test Square Root Primality Test Miller Rabin Algorithm for Primality Testing AKS (Agrawal, Kayal, Saxena) Algorithm Chinese Remainder Theorem (CRT) Applications of CRT in Cryptography Quadratic Congruence Quadratic Congruence Modulo a Prime p Quadratic Congruence Modulo a Composite...118

10 Contents ix 8.5 Discrete Logarithm Multiplicative Group Multiplicative Group G = {Z * p, } Discrete Logarithm over G = {Z p *, } Properties and Applications of Discrete Logarithm Summing Up Recommended Reading Problems Asymmetric-key Cryptosystems Asymmetric-Key Cryptography Requirements for Asymmetric-key Cryptography Asymmetric-key Cryptography vs. Symmetric-key Cryptography RSA Cryptosystem RSA Algorithm Proof of RSA Algorithm Security of RSA Cryptosystem RSA Implementation Applications of RSA Rabin Cyptosystem Algorithm of Rabin Cryptosystem Security of Rabin Cryptosystem Operational Aspects of Rabin Cryptosystem ElGamal Cryptosystem Algorithm of ElGamal Cryptosystem Operational Aspects of ElGamal Cryptosystem Security of ElGamal Generalized ElGamal Cryptosystem Applications of ElGamal Cryptosystem Summing Up Recommended Reading Problems Elliptic Curve Cryptography Elliptic Curve Elliptic Curve as an Abelian Group Algebraic Expression for 2P Elliptic Curves over Z p E p (a, b) as Cyclic Group Elliptic Curves over Galois Field GF(2 n ) E 2 n (a, b) as Cyclic Group Elliptic Curve Cryptography (ECC) ElGamal Asymmetric-key Cryptosystem Using ECC Diffie Hellman Secret Key Exchange Using ECC...154

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