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  • Conference proceedings
  • Open Access
  • © 2021

International Symposium on Mathematics, Quantum Theory, and Cryptography

Proceedings of MQC 2019

  • Includes selected papers by leading researchers

  • Presents the latest research on post-quantum cryptography

  • Enhances understanding of the mathematical background

Part of the book series: Mathematics for Industry (MFI, volume 33)

Conference series link(s): MQC: International Symposium on Mathematics, Quantum Theory, and Cryptography

Conference proceedings info: MQC 2019.

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Table of contents (19 papers)

  1. Front Matter

    Pages i-xii
  2. Keynote

    1. Front Matter

      Pages 1-1
    2. Sustainable Cryptography

      • Johannes Buchmann
      Pages 3-3Open Access
  3. Summary

    1. Front Matter

      Pages 9-9
    2. Verified Numerical Computations and Related Applications

      • Shin’ichi Oishi
      Pages 11-12Open Access
  4. Quantum Computing and Information Theory

    1. Front Matter

      Pages 15-15
    2. Quantum Random Numbers Generated by a Cloud Superconducting Quantum Computer

      • Kentaro Tamura, Yutaka Shikano
      Pages 17-37Open Access
    3. From the Bloch Sphere to Phase-Space Representations with the Gottesman–Kitaev–Preskill Encoding

      • L. García-Álvarez, A. Ferraro, G. Ferrini
      Pages 79-92Open Access
  5. Quantum Interactions

    1. Front Matter

      Pages 93-93
    2. Number Theoretic Study in Quantum Interactions

      • Masato Wakayama
      Pages 95-101Open Access
    3. Quantum Optics with Giant Atoms—the First Five Years

      • Anton Frisk Kockum
      Pages 125-146Open Access
  6. Topics in Mathematics

    1. Front Matter

      Pages 147-147
    2. Generalized Group–Subgroup Pair Graphs

      • Kazufumi Kimoto
      Pages 169-185Open Access

About this book

This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing.


The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. 


This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography.

Editors and Affiliations

  • Department of Mathematical Informatics, University of Tokyo, Tokyo, Japan

    Tsuyoshi Takagi

  • Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan

    Masato Wakayama, Yasuhiko Ikematsu

  • Department of Mathematical and Computing Science, Tokyo Institute of Technology, Tokyo, Japan

    Keisuke Tanaka

  • Department of Computer Science, University of Tsukuba, Ibaraki, Japan

    Noboru Kunihiro

  • University of the Ryukyus, Okinawa, Japan

    Kazufumi Kimoto

About the editors

Prof. Wakayama is a Professor of Mathematics, Vice President at Tokyo University of Science (TUS) and Principal Fellow at Center for Research and Development Strategy, Japan Science and Technology Agency (CRDS/JST). He is also Professor Emeritus at Kyushu University. He obtained Ph.D. from Hiroshima University in 1985. His research interests include Representation Theory, Number Theory and Mathematical Physics, and has published over 100 referred research papers. He has contributed his experience and expertise to both academic works and university administration. His current appointments include Chair of Asia Pacific Consortium of Mathematics for Industry (2014-). He is the Editor-in-Chief of the Springer series “Mathematics for Industry”.

Prof. Takagi received his B.Sc. and M.Sc. degrees in mathematics from Nagoya University in 1993 and 1995, respectively. He was engaged in research on network security at NTT Laboratories from 1995 to 2001. He received his Ph.D. from Technical University of Darmstadt in 2001. He is currently a Professor in the Graduate School of Information Science and Technology at University of Tokyo. His current research interests are information security and cryptography. He received DOCOMO Mobile Science Award in 2013, IEICE Achievement Award in 2013, and JSPS Prize in 2014. Dr. Takagi was a Program Chair of the 7th International Conference on Post-Quantum Cryptography, PQCrypto 2016.

Prof. Tanaka is a Professor in the School of Computing at Tokyo Institute of Technology. He received his B.S. from Yamanashi University in 1992, and his M.S. and Ph.D. in Computer Science from Japan Advanced Institute of Science and Technology in 1994 and 1997, respectively. Before joining Tokyo Institute of Technology, he was Research Engineer at NTT Information Platform Laboratories. His research interests include theory of cryptography, cryptocurrency and blockchain technology, and cybersecurity.

Prof. Kunihiro received his B. E., M. E. and Ph.D. in Mathematical Engineering and Information Physics from the University of Tokyo in 1994, 1996 and 2001, respectively. He has been a professor of University of Tsukuba since 2019. He was a researcher of NTT Communication Science Laboratories from 1996 to 2002. He was an associate professor of the University of Electro-Communications from 2002 to 2008. He was an associate professor of the University of Tokyo from 2008 to 2019. His research interest includes cryptography, information security.

 Prof. Kimoto received his Ph.D in Mathematics from Kyushu University in 2003. He was an assistant professor of the University of the Ryukyus from October 2003 to December 2010. He was an associate professor of the University of the Ryukyus from January 2011 to March 2015. He has been a professor of the University of the Ryukyus since April 2015. His research interest includes representation theory, number theory, and combinatorics.

Prof. Ikematsu received his Ph.D. in Mathematics in 2016 from Kyushu University. He was a research fellow at the Institute of Mathematics for Industry, Kyushu University from 2016 to 2018 and in Department of Mathematical Informatics, University of Tokyo from April to December in 2018. He is currently an assistant professor in Institute of Mathematics for Industry, Kyushu University. His research interests include number theory and multivariate cryptography.

Bibliographic Information

Buy it now

Buying options

Softcover Book USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 59.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access