Overview
- Contributes to a better understanding of current state of modern cryptography
- Develops new advanced mathematical techniques and their applications in the post-quantum cryptography
- Focuses on the areas that have not yet been fully exploited for the representation theory, and mathematical physics
- Is open access, which means that you have free and unlimited access
Part of the book series: Mathematics for Industry (MFI, volume 40)
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About this book
This open access book presents mathematical foundations for cryptography securely used in the era of quantum computers.
In particular, this book aims to deepen the basic mathematics of post-quantum cryptography, model the strongest possible attacks such as side-channel attacks, and construct cryptographic protocols that guarantee security against such attacks.
This book is a sequel of the successful book entitled by ``Mathematical Modeling for Next-Generation Cryptography - CREST Crypto-Math Project'' which was published in 2018.
The book is suitable for use in an advanced graduate course in mathematical cryptography and as a reference book for experts.
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Table of contents (24 chapters)
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Front Matter
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Mathematical Foundation and Quantum Theory
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Front Matter
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Quantum and Physical Cryptanalysis
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Front Matter
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Post-quantum Cryptography
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Front Matter
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Editors and Affiliations
About the editors
Tsuyoshi Takagi is a professor in the Department of Mathematical Informatics at the University of Tokyo. His current research interests are information security and cryptography. He received the Ph.D. from the Technical University of Darmstadt in 2001. He received IEICE Achievement Award in 2013 and JSPS Prize in 2014. He was a program chair of the 7th International Conference on Post-Quantum Cryptography, PQCrypto 2016.
Masato Wakayama is the Fundamental Mathematics Research principal of NTT Institute for Fundamental Mathematics in Nippon Telegraph and Telephone Corporation. He also serves as a principal fellow at Center for Research and Development Strategy of Japan Science and Technology Agency and a professor emeritus at Institute of Mathematics for Industry of Kyushu University. His current research interests are representation theory and its applications to number theory and quantum physics. He received the Ph.D. from Hiroshima University in 1985. He received Nice-Step-Researcher Award in 2007 by Ministry of Education, Culture, Sports, Science, and Technology (MEXT). He also managed various research projects on mathematics for industry such as Global COE Program “Education and Research Hub for Mathematics-for-Industry” by MEXT.
Noboru Kunihiro is a professor in the Department of Faculty of Engineering, Information, and Systems at the University of Tsukuba. His current research interests are information security and cryptography. He received the Ph.D. from the University of Tokyo in 2001. He has served as program committees of many international conferences on information security, for example, a program chair of the 5th International Workshop on Security, IWSEC2010.
Keisuke Tanaka is a professor in School of Computing at Tokyo Institute of Technology. His current research interests are cryptography and computational complexity theory. He received the Ph.D. from Japan Advanced Institute of Science and Technology in 1997. He received IEICE Distinguished Educational Practitioners Award in 2020.
Kazufumi Kimoto is a professor in the Department of Mathematical Sciences at the University of the Ryukyus. His current research interests are representation theory and its applications to cryptography. He received the Ph.D. from Kyushu University in 2003. He received Inoue Research Award for Young Scientists in 2003.
Momonari Kudo is an assistant professor in the Faculty of Information Engineering at Fukuoka Institute of Technology. His current research interests are computational algebraic geometry and its applications to cryptography. He received the Ph.D. from Kyushu University in 2017. He received JSIAM Best Presentation Award in 2017 and JSSAC Research Award for Young Scientists in 2020.
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Bibliographic Information
Book Title: Mathematical Foundations for Post-Quantum Cryptography
Book Subtitle: Crypto-Math CREST
Editors: Tsuyoshi Takagi, Masato Wakayama, Noboru Kunihiro, Keisuke Tanaka, Kazufumi Kimoto, Momonari Kudo
Series Title: Mathematics for Industry
DOI: https://doi.org/10.1007/978-981-96-1218-5
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s) 2026
Hardcover ISBN: 978-981-96-1217-8Published: 28 October 2025
Softcover ISBN: 978-981-96-1220-8Due: 11 November 2026
eBook ISBN: 978-981-96-1218-5Published: 27 October 2025
Series ISSN: 2198-350X
Series E-ISSN: 2198-3518
Edition Number: 1
Number of Pages: IX, 496
Number of Illustrations: 21 b/w illustrations, 25 illustrations in colour
Topics: Mathematical Physics, Algebraic Geometry, Number Theory