Algebraic Cryptanalysis
Algebraic Cryptanalysis bridges the gap between a course in cryptography, and being able to read the cryptanalytic literature. This book is divided into three parts: Part One covers the process of turning a cipher into a system of equations; Part Two cove
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Gregory V. Bard
Algebraic Cryptanalysis
Gregory V. Bard Department of Mathematics Fordham University Bronx, NY 10458 USA [email protected]
ISBN 978-0-387-88756-2 e-ISBN 978-0-387-88757-9 DOI 10.1007/978-0-387-88757-9 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009929845 © Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
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Preface
Algebraic Cryptanalysis is the process of breaking codes by solving polynomial systems of equations. In some ways this book began when the author began to explore cryptanalysis as a beginning graduate student, and realized with frustration that no book whatsoever existed on the topic. Since that time, some books have been written about Linear Cryptanalysis or Differential Cryptanalysis (e.g. [211] and [214] cover both), but none on Algebraic Cryptanalysis, which is a rich and growing field. The author had some difficulty entering the field of Algebraic Cryptanalysis. Of course step one is a solid background in Abstract Algebra, and a solid background in cryptography1 . But after these twin foundations, one is not quite ready to read research papers. This book is intended to be that stepping stone for graduate students wishing to do their dissertation in Algebraic Cryptanalysis, or any other part of cryptanalysis. Furthermore, researchers in other areas of Applied Abstract Algebra or cryptography might benefit from seeing what is going on in cryptanalysis. The nucleus for the book was my dissertation, under the title “Algorithms for the Solution of Linear and Polynomial Systems of Equations over Finite Fields, with Applications to Cryptanalysis”, submitted for the degree Doctor of Philosophy of Applied Mathematics and Scientific Computation, defended in the Summer of 2007, under the guidance of Professor Lawrence C. Washington. The author is extremely grateful for Prof. Washington’s time, help and assistance at all stages. In addition to being a text for graduate students, the author hopes the book will be also useful for those currently working in the field as well. The pressures of page counts often require that the internals or variants of algorithms cannot be published in exhaustive detail in the standard scientific literature. Here,
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