An Introduction to Cryptology

TO CRYPTOLOGY by Henk C. A. van Tilborg Eindhoven University of Technology THE NETHERLANDS l1li. . . KLUWER ACADEMIC PUBLISHERS Boston / Dordrecht " / Lancaster Dlstrlbuton for North America Kluwer Academic Publishers 101 Philip Drive Assinippi Park Norwell, Massachusetts 02061 USA Dlstrlbuton for the VK and lreland Kluwer Academic Publishers Falcon House, Queen Square Lancaster LAI IRN, UNITED KINGDOM Dlstrlbuton for aII other countrles Kluwer Academic Publishers Group Distribution Centre Post Office Box 322 3300 AH Dordrecht, THE NETHERLANDS Library of Congress Cataloglng-in-Publication Data Tilborg, Henk C. A. van, 1947- An introduction to cryptology. (The Kluwer international series in engineering and computer science) Bibliography: p. Includes index. 1. Cryptology. 2. Cyrptography-Data processing. 1. Title. II. Series. Z103. T54 1987 652'. 8 88-616 ISBN-I3: 978-1-4612-8955-5 e-ISBN-I3: 978-1-4613-1693-0 DOI: 10. 1007/978-1-4613-1693-0 Copyright © 1988 by Kluwer Academic Publishers Softcover reprint ofthe hardcover lst edition 1988 AlI rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Kluwer Academic Publishers, 101 Philip Drive, Assinippi Park, Norwell, Massachusetts 02061. 10 Marijke, who afler so many years stiU is an enigma 10 me CONTENTS page vii Contents ix Preface 1. INTRODUCfION 2. CLASSICAL SYSTEMS 7 2. 1. Caesar, simple substitutions, Vigenere 7 2. 2. The incidence of coincidences 11 2. 3. Vemam, Playfair, Transpositions, Hagelin, Enigma 14 19 3. SHIFf REGISTER SEQUENCES 3. 1.

Contenu

2. Classical Systems.- 2.1. Caesar, simple substitutions, Vigenère.- 2.2. The incidence of coincidences.- 2.3. Vernam, Playfair, Transpositions, Hagelin, Enigma.- 3. Shift Register Sequences.- 3.1. Introduction.- 3.2. Linear feedback shift registers.- 3.3. Non-linear algorithms.- 4. Shannon Theory.- 5. Huffman Codes.- 6. Des.- 7. Public Key Cryptography.- 8. The Discrete Logarithm Problem.- 8.1. The discrete logarithm system.- 8.2. How to take discrete logarithms.- 9. RSA.- 9.1. The RSA system.- 9.2. The Solovay and Strassen primality test.- 9.3. The Cohen and Lenstra primality test.- 9.4. The Rabin variant.- 10. The Mceliece System.- 11. The Knapsack Problem.- 11.1. The knapsack system.- 11.2. The Shamir attack.- 11.3. The Lagarias and Odlyzko attack.- 12. Threshold Schemes.- 13. Other Directions.- Appendix A. Elementary Number Theory.- A.1. Introduction.- A.2. Euclid's Algorithm.- A.3. Congruences, Fermat, Euler, Chinese Remainder Theorem.- A.4. Quadratic residues.- A.5. Möbius inversion formula, the principle of inclusion and exclusion.- Appendix B. The Theory of Finite Fields.- B.1. Groups, rings, ideals and fields.- B.2. Constructions.- B.3. The number of irreducible polynomials over IFq.- B.4. The structure of finite fields.- References.- Notations.