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duction to Security Reduction

Introduction to Security Reduction

Fuchun Guo • Willy Susilo • Yi Mu

Introduction to Security Reduction

Fuchun Guo School of Computing & Information Technology University of Wollongong Wollongong, New South Wales, Australia

Willy Susilo School of Computing & Information Technology University of Wollongong Wollongong, New South Wales, Australia

Yi Mu School of Computing & Information Technology University of Wollongong Wollongong, New South Wales, Australia

ISBN 978-3-319-93048-0 ISBN 978-3-319-93049-7 (eBook) https://doi.org/10.1007/978-3-319-93049-7 Library of Congress Control Number: 2018946564 © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To my lovely wife Yizhen, two adorable sons John and Kevin, and my kindly mother Suhua. To the memory of my father Yongming. –Fuchun Guo

To my wife Aurelia and our beloved son Jayden, without whom this work will never be accomplished. –Willy Susilo

To my family! –Yi Mu

Preface

Security reduction is a very popular approach for proving security in public-key cryptography. With security reduction, roughly speaking, we can show that breaking a proposed scheme is as difficult as solving a mathematical hard problem. However, how to program a correct security reduction using an adversary’s adaptive attack is rather complicated. The reason is that there is no universal security reduction for all proposed schemes. Security reductions given in cryptographic research papers are often hard for beginners to fully comprehend. To aid the beginners, some cryptography textbooks have illustrated how to c