TAILIEUCHUNG - Handbook of Applied Cryptography - chap2

This chapter is a collection of basic material on probability theory, information theory, complexity theory, number theory, abstract algebra, and finite fields that will be used throughout this book. Further background and proofs of the facts presented here can be found in the references given in . The following standard notation will be used throughout: | This is a Chapter from the Handbook of Applied Cryptography by A. Menezes P. van Oorschot and S. Vanstone CRC Press 1996. For further information see hac CRC Press has granted the following specihc permissions for the electronic version of this book Permission is granted to retrieve print and store a single copy of this chapter for personal use. This permission does not extend to binding multiple chapters of the book photocopying or producing copies for other than personal use of the person creating the copy or making electronic copies available for retrieval by others without prior permission in writing from CRC Press. Except where over-ridden by the specihc permission above the standard copyright notice from CRC Press applies to this electronic version Neither this book nor any part may be reproduced or transmitted in any form or by any means electronic or mechanical including photocopying microhlming and recording or by any information storage or retrieval system without prior permission in writing from the publisher. The consent of CRC Press does not extend to copying for general distribution for promotion for creating new works or for resale. Specihc permission must be obtained in writing from CRC Press for such copying. @1997 by CRC Press Inc. 48 Ch. 1 OverviewofCryptography One approach to distributing public-keys is the so-called Merkle channel see Simmons 1144 . Merkle proposed that public keys be distributed over so many independent public channels newspaper radio television etc. that it would be improbable for an adversary to compromise all of them. In 1979 Kohnfelder 702 suggested the idea of using public-key certificates to facilitate the distribution of public keys over unsecured channels such that their authenticity can be verified. Essentially the same idea but by on-line requests was proposed by Needham and Schroeder ses Wilkes 1244 . A provably secure key agreement protocol has been proposed whose security is

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