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Unformatted text preview: ivate key. (1) Alice chooses a large random number, x, and encrypts it in Bob’s public key. c = EB(x) (2) Alice computes c  i and sends the result to Bob. (3) Bob computes the following 100 numbers: yu = DB(c  i + u), for 1 d u d 100 DB is the decryption algorithm with Bob’s private key. He chooses a large random prime, p. (The size of p should be somewhat smaller than x. Bob doesn’t know x, but Alice could easily tell him the size of x.) He then computes the following 100 numbers: zu = (yu mod p), for 1 d u d 100 He then verifies that, for all u ` v zu  zv e 2 and that for all u 0 < zu < p  1 If this is not true, Bob chooses another prime and tries again. (4) Bob sends Alice this sequence of numbers in this exact order: z1 , z2 , ..., zj, zj+1 + 1, zj+2 + 1,..., z100 + 1, p (5) Alice checks whether the ith number in the sequence is congruent to x mod p. If it is, she concludes that i d j. If it is not, she concludes that i > j. (6) Alice tells Bob the conclusion. Previous Table of Contents Next Products  Contact Us  About Us  Privacy  Ad Info  Home Use of this site is subject to certain Terms & Conditions, Copyright © 19962000 EarthWeb Inc. All rights reserved. Reproduction whole or in part in any form or medium without express written permission of EarthWeb is prohibited. Read EarthWeb's privacy statement. To access the contents, click the chapter and section titles. Applied Cryptography, Second Edition: Protocols, Algorthms, and Source Code in C (cloth)
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Brief Full Advanced Search Search Tips (Publisher: John Wiley & Sons, Inc.) Author(s): Bruce Schneier ISBN: 0471128457 Publication Date: 01/01/96 Search this book:
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 All the verification that Bob goes through in step (3) is to guarantee that no number appears twice in the sequence generated in step (4). Otherwise, if za =zb, Alice knows that a dj <b. The one drawback to this protocol is that Alice learns the result of the computation before Bob does. No...
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This note was uploaded on 10/18/2010 for the course MATH CS 301 taught by Professor Aliulger during the Fall '10 term at Koç University.
 Fall '10
 ALIULGER
 Cryptography

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