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Handbook of Applied Cryptography
, 1997
"... As we draw near to closing out the twentieth century, we see quite clearly that the informationprocessing and telecommunications revolutions now underway will continue vigorously into the twentyfirst. We interact and transact by directing flocks of digital packets towards each other through cybers ..."
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Cited by 2724 (33 self)
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As we draw near to closing out the twentieth century, we see quite clearly that the informationprocessing and telecommunications revolutions now underway will continue vigorously into the twentyfirst. We interact and transact by directing flocks of digital packets towards each other through cyberspace, carrying love notes, digital cash, and secret corporate documents. Our personal and economic lives rely more and more on our ability to let such ethereal carrier pigeons mediate at a distance what we used to do with facetoface meetings, paper documents, and a firm handshake. Unfortunately, the technical wizardry enabling remote collaborations is founded on broadcasting everything as sequences of zeros and ones that one's own dog wouldn't recognize. What is to distinguish a digital dollar when it is as easily reproducible as the spoken word? How do we converse privately when every syllable is bounced off a satellite and smeared over an entire continent? How should a bank know that it really is Bill Gates requesting from his laptop in Fiji a transfer of $10,000,000,000 to another bank? Fortunately, the magical mathematics of cryptography can help. Cryptography provides techniques for keeping information secret, for determining that information
This is a Chapter from the Handbook of Applied Cryptography, by A. Menezes, P. van
"... For further information, see www.cacr.math.uwaterloo.ca/hac CRC Press has granted the following specific 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 ..."
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For further information, see www.cacr.math.uwaterloo.ca/hac CRC Press has granted the following specific 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 overridden by the specific 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, microfilming, 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. Specific permission must be obtained in writing from CRC Press for such copying. c○1997 by CRC Press, Inc.
The Probability Advantages of Two Linear Expressions in Symmetric Ciphers
, 2006
"... In this paper, we prove the probability advantages of two linear expressions which are summarized from the ABC stream cipher submitted to ECRPYT Estream Project. Two linear expressions with probability advantages reflect the linear correlations among Modular Addition equations. Corresponding to each ..."
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In this paper, we prove the probability advantages of two linear expressions which are summarized from the ABC stream cipher submitted to ECRPYT Estream Project. Two linear expressions with probability advantages reflect the linear correlations among Modular Addition equations. Corresponding to each linear expression and its advantage, a large amount of weak keys are derived under which all the ABC main keys can be retrieved successively. The first linear expression is a generic bit linear correlation between two Modular Addition equations. The second is a linear correlation of bit carries derived from three Modular Addition equations and the linear equation of LFSR in ABC. It is remarked that the second is found by Wu and Preneel, and has been used to find 2 weak keys. In the cryptanalysis of ABC, Wu and Preneel only utilized its estimated probability advantage which is concluded by experimental data, and they did not give its strict proof. Modular Addition and XOR operations are widely used in designing symmetric ciphers. We believe that these types of linear expressions with probability advantages not only can be used to analyze some other symmetric ciphers, but also are important criteria in designing secure symmetric ciphers.
3. The Categories of Solicited Cryptographic Technique.................................... 3
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PILINGUP LEMMA FOR MARKOV CHAINS
"... The Pilingup Lemma for binary independent random variables is a very useful tool in linear cryptanalysis of block ciphers and in cryptanalysis of stream ciphers, especially when fast correlation attacks are used. Also, it was shown that, for some block ciphers, the sequence of differences at each r ..."
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The Pilingup Lemma for binary independent random variables is a very useful tool in linear cryptanalysis of block ciphers and in cryptanalysis of stream ciphers, especially when fast correlation attacks are used. Also, it was shown that, for some block ciphers, the sequence of differences at each round output forms a Markov chain. We give here a corresponding Pilingup lemma for Markov chains. Key words: Pilingup lemma; Markov chains; stream and block ciphers; linear and differential cryptanalysis.