HASHING IN COMPUTER SCIENCE FIFTY YEARS OF SLICING AND DICING

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1 HASHING IN COMPUTER SCIENCE FIFTY YEARS OF SLICING AND DICING Alan G. Konheim JOHN WILEY & SONS, INC., PUBLICATION

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3 HASHING IN COMPUTER SCIENCE

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5 HASHING IN COMPUTER SCIENCE FIFTY YEARS OF SLICING AND DICING Alan G. Konheim JOHN WILEY & SONS, INC., PUBLICATION

6 Copyright 2010 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) , fax (978) , or on the web at Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) , fax (201) , or online at Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) , outside the United States at (317) or fax (317) Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at Library of Congress Cataloging-in-Publication Data Konheim, Alan G., 1934 Hashing in computer science : fifty years of slicing and dicing / Alan G. Konheim. p. cm. ISBN Hashing (Computer science) 2. Cryptography. 3. Data encryption (Computer science) 4. Computer security. I. Title. QA76.9.H36K dc Printed in the United States of America

7 To my grandchildren Madelyn, David, Joshua, and Karlina

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9 CONTENTS PREFACE xiii PART I: MATHEMATICAL PRELIMINARIES 1 1. Counting 3 1.1: The Sum and Product Rules 4 1.2: Mathematical Induction 5 1.3: Factorial 6 1.4: Binomial Coefficients 8 1.5: Multinomial Coefficients : Permutations : Combinations : The Principle of Inclusion-Exclusion : Partitions : Relations : Inverse Relations 20 Appendix 1: Summations Involving Binomial Coefficients Recurrence and Generating Functions : Recursions : Generating Functions : Linear Constant Coefficient Recursions : Solving Homogeneous LCCRs Using Generating Functions : The Catalan Recursion : The Umbral Calculus : Exponential Generating Functions : Partitions of a Set: The Bell and Stirling Numbers : Rouché s Theorem and the Lagrange s Inversion Formula Asymptotic Analysis : Growth Notation for Sequences : Asymptotic Sequences and Expansions : Saddle Points 45 vii

10 viii CONTENTS 3.4: Laplace s Method : The Saddle Point Method : When Will the Saddle Point Method Work? : The Saddle Point Bounds : Examples of Saddle Point Analysis Discrete Probability Theory : The Origins of Probability Theory : Chance Experiments, Sample Points, Spaces, and Events : Random Variables : Moments Expectation and Variance : The Birthday Paradox : Conditional Probability and Independence : The Law of Large Numbers (LLN) : The Central Limit Theorem (CLT) : Random Processes and Markov Chains Number Theory and Modern Algebra : Prime Numbers : Modular Arithmetic and the Euclidean Algorithm : Modular Multiplication : The Theorems of Fermat and Euler : Fields and Extension Fields : Factorization of Integers : Testing Primality Basic Concepts of Cryptography : The Lexicon of Cryptography : Stream Ciphers : Block Ciphers : Secrecy Systems and Cryptanalysis : Symmetric and Two-Key Cryptographic Systems : The Appearance of Public Key Cryptographic systems : A Multitude of Keys : The RSA Cryptosystem : Does PKC Solve the Problem of Key Distribution? : Elliptic Groups Over the Reals : Elliptic Groups Over the Field Z m, : Elliptic Group Cryptosystems : The Menezes-Vanstone Elliptic Curve Cryptosystem : Super-Singular Elliptic Curves 112 PART II: HASHING FOR STORAGE: DATA MANAGEMENT Basic Concepts : Overview of the Records Management Problem 119

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