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Cryptog ra phy

Wiley-Teubner Series in Computer Science Editorial Board

GunterHotz Fachbereich Angewandte Mathematik und Informatik, Universitat des Saar/andes, Saarbriicken, Germany Michael J. Fischer Yale University, Department of Computer Science, New Haven, Connecticut, USA Maurice Nivat U.E.R. de Mathematique et Informatique, Universite Paris VI/, Paris, France David W. Barron Department of Computer Science, University of Southampton, UK Kemp: Fundamentals of the Average Case Analysis of Particular Algorithms Loeckx, Sieber, Stansifer: The Foundations of Program Verification 2nd Edition Kranakis: Primality and Cryptography Wegener: The Complexity of Boolean Functions Kulisch: Pascal-SC

Primality

and

Cryptography

Evangelos Kranakis

Universiteit van Amsterdam Fakultaire Vakgroep Informatica Amsterdam, Netherlands AND

Yale University Department of Computer Science New Haven, USA

Springer Fachmedien Wiesbaden GmbH

© Springer Fachmedien Wiesbaden 1986 Originally published by John Wiley & Sons Ltd, and B.G. Teubner, Stutgart in 1986 Softcover reprint ofthe hardcover 1st edition 1986 Reprinted August 1987 Ali rights reserved. No part of this book may be reproduced by any means, or transmitted, or translated into a machi ne language without the written permission of the publisher. Library of Congress Cataloging in Publication Data: Kranakis, Evangelos Primality and cryptography. (Wiley-Teubner series in computer science) lncludes index. 1. Telecommunication-Security measures. 2. Numbers, Prime. 3. Cryptography. 1. Title. 11. Series. TK5102.5.K66 1986 005.8'2 85-29485 ISBN 978-3-322-96648-3 British Library Cataloguing in Publication Data: Kranakis, Evangelos Primality and crytography.-(Wiley-Teubner series in computer science) 1. Computers-Access control 2. Cryptography 1. Title 001.6 OA76.9.A25 ISBN 978-3-322-96648-3 CIP-Kurztitelufnahme der Deutschen Bibliothek: Kranakis, Evangelos: Primality and cryptography/Evangelos Kranakis.-Stuttgart: Teubner; Chichester; New York; Brisbane; Toronto; Singapore: Wiley, 1986. (Wiley Teubner series in computer science) ISBN 978-3-322-96648-3 ISBN 978-3-322-96647-6 (eBook) DOI 10.1007/978-3-322-96647-6

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Dedicated to Eda, my best friend and lifelong companion.

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C'est en forgeant que l'on devient forgeron. (Medieval Latin Proverb)

PROLOGUE

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PROLOGUE

The art of ciphering, hath for relative an art of deciphering, by supposition unprofitable, but as things are, of great use. (Francis Bacon) Ciphering has been widely used throughout history in military and diplomatic communication in order to make the meaning of transmitted messages incomprehensible to unauthorized users. According to Francis Bacon l the following must be among the preferred virtues of cipher systems: • that they be not laborious to write and read, • that they be impossible to decipher, and, • in some cases, that they be without suspicion. The three principles of Bacon listed above are still valid today. But, to quote Diffie and Hellman: the development of computer controlled communicati