Lattice-Based Cryptosystems A Design Perspective

This book focuses on lattice-based cryptosystems, widely considered to be one of the most promising post-quantum cryptosystems and provides fundamental insights into how to construct provably secure cryptosystems from hard lattice problems. The concept of

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Lattice-Based Cryptosystems A Design Perspective

Lattice-Based Cryptosystems

Jiang Zhang Zhenfeng Zhang •

Lattice-Based Cryptosystems A Design Perspective

123

Jiang Zhang State Key Laboratory of Cryptology Beijing, China

Zhenfeng Zhang Institute of Software Chinese Academy of Sciences Beijing, China

ISBN 978-981-15-8426-8 ISBN 978-981-15-8427-5 https://doi.org/10.1007/978-981-15-8427-5

(eBook)

© Springer Nature Singapore Pte Ltd. 2020 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, expressed 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. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

As we enter into the post-quantum era, traditional public-key cryptosystems face great challenges and will fail to protect our private information over the Internet. Due to several potential benefits, e.g., worst-case hardness assumptions and security against quantum computers, cryptosystem based on the hardness of lattice problems is a very promising candidate for providing security against quantum adversaries, and a lot of effort has been devoted to constructing lattice-based cryptosystems. In the past years, we were asked many times for providing a list of books on lattice-based cryptography for graduated students and young researchers, but to the best of our knowledge, there is actual no book on the design of lattice-based cryptosystems. Thus, we think it is very necessary to write a book on lattice-based cryptography such that it is easier for more people to access and enter into this research area. The proposed book mainly focuses on the construction of lattice-based cryptosystems, which can serve as a textbook for graduate-level courses. The book will first cover some basic mathematics on lattices, and then show how to use those math tools in constructing lattic