Cryptographic Boolean Functions and Applications
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Authors(Editors):
Thomas W. Cusick
Pantelimon Stanica
Publisher: Apress
Pub Date: 2009
Pages: 245
ISBN: 978-0-1237-4890-4
Preface
Boolean functions have been an object of study in cryptography for over 50 years,
beginning with their use in linear feedback shift registers. It was in the late 1940s that
Shannon published the concepts of confusion and diffusion as fundamental concepts for
achieving security in cryptosystems. Confusion is reflected in the nonlinearity of parts
of the cryptosystem; linear systems are generally easy to break. Diffusion is achieved by
ensuring that a small change in the input is spread out to make a large change in the
output. Boolean functions can easily provide both confusion and diffusion. One goal of
this book is to show how to choose good Boolean functions for this purpose.
The book is designed to serve as a reference for various applications of Boolean
functions in modern cryptography, which we can say is about 35 years old. The relevant
material in the literature is scattered over hundreds of journal articles, conference
proceedings, books, reports and notes (some of them only available online). Until this
book, there has been no attempt to gather the gist of this material in one place. Our goal
is to present the major concepts and associated theorems, with proofs, except in those
cases where the proofs would be too long or too technical. The book is expository and
we have attempted to be accurate in assigning credit for the many results quoted here.
There is some original research in the book, and we have made quite a few corrections
and improvements to earlier work.
The bibliography is extensive, but is not intended to be all-inclusive. In particular, it is
common in cryptography for research which has been first published in the proceedings
of a conference (‘conference version’) to be published later (perhaps with refinements or
improvements) in a journal (‘journal version’). Many authors seem to fear that publishing
only a conference version will lead to their results not being as widely read or referred
to. In some cases where a more complete journal version of an article is available, we
have not listed the earlier, less polished, conference version. Of course this justifies the
fear that some of the authors had! We have not hesitated to give online references where
these are the only possible ones. We believe that the problem of long-term archiving of
online materials will be solved.
We have tried to avoid any errors, but in a book of this size it is likely that some
remain. The authors at first thought to resolve this issue by having each one blame the
other for any mistakes, but then decided instead to request that readers notify at least
one of us of any errors. We will then correct them in later editions, or via a posting of
online errata.
We would like to thank our institutions, the State University of New York at Buffalo
(T.W.C.), and Naval Postgraduate School and Institute of Mathematics of the Romanian
Academy (P.S.), for their excellent working conditions, and for allowing us to take some
time off, while this book was written.
The authors express their gratitude to the following people who undertook the task
of going through the various parts of this book in its incipient form: Anna Bernasconi,
David Canright, Claude Carlet, Bruno Codenotti, Ed Dawson, Hal Fredricksen,
Subhamoy Maitra, and Yuliang Zheng. The second author also thanks the group of students
in the ‘Cryptographic Boolean Functions’ course at Naval Postgraduate School
who diligently went through the manuscript in the Fall of 2008.
Thomas W. Cusick
Buffalo, NY
Pantelimon St?anic?a
Monterey, CA
September 2008
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Cryptographic Boolean Functions and Applications.Thomas W. Cusick.Apress.2009.pdf
Cryptographic Boolean Functions and Applications.Thomas W. Cusick.Apress.2009.pdf
Cryptographic Boolean Functions and Applications.Thomas W. Cusick.Apress.2009.pdf
Cryptographic Boolean Functions and Applications.Thomas W. Cusick.Apress.2009.pdf
Cryptographic Boolean Functions and Applications.Thomas W. Cusick.Apress.2009.pdf
Cryptographic Boolean Functions and Applications.Thomas W. Cusick.Apress.2009.pdf
Cryptographic Boolean Functions and Applications.Thomas W. Cusick.Apress.2009.pdf
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