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 standardizepost-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.

Includes selected papers by leading researchers Presents the latest research on post-quantum cryptography Enhances understanding of the mathematical background

Autorentext

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.

Inhalt
Sustainable Cryptography.- What Kind of Insight Provide Analytical Solutions of Quantum Models?.- Emerging Ultrastrong Coupling between Light and Matter Observed in Circuit Quantum Electrodynamics.- Quantum Random Numbers Generated by a Cloud Superconducting Quantum Computer.- Quantum Factoring Algorithm: Resource Estimation and Survey of Experiments.- A Review of Secret Key Distribution Based on Bounded Observability.- Towards Constructing Fully Homomorphic Encryption without Ciphertext Noise from Group Theory.- Number Theoretic Study in Quantum Interactions.- From the Bloch Sphere to Phase Space Representations with the Gottesman-Kitaev-Preskill Encoding.- A Data Concealing Technique with Random Noise Disturbance and A Restoring Technique for the Concealed Data by Stochastic Process Estimation.