Mathematical Modelling for Next-Generation Cryptography

Outline

Mathematical Modelling for Prevention
of Future Security Compromises

Recent advances in cryptanalysis, brought in particular by the quantum computation and the physical attacks on the cryptographic devices (such as the side-channel analysis or the power analysis), introduced the growing security risks for the state-of-the-art cryptographic schemes. This project will focus on developing foundations for the mathematical modeling of the next-generation cryptographic systems, hereby addressing the above mentioned risks.

In order to achieve this goal, a new mathematical approach will be used that will draw ideas from beyond the number theory and the theory of computation, which historically proven to provide a good interchange with cryptography. Specifically, the focus will be made on the areas that have not yet been fully exploited for the cryptographic applications such as the representation theory, the mathematical physics and others. In particular, this project will create a platform for involving mathematicians into the research focused on promotion of the safe society, while at the same time stimulating a development of the respective branches of mathematics.

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What's New

 
2017/11/8 Prof. Tsuyoshi Takagi delivered a keynote talk on "Recent Developments in Post-Quantum Cryptography" at the 17th Brazilian Symposium in Information Security and Computational Systems (SBSeg 2017) held in Brasilia.
SBSeg 2017
2017/8/1 Prof. Masato Wakayama delivered a keynote talk on "Mathematics for Industry in Japan" at International Seminar on Mathematics in Industry 2017 held in Malaysia.
2017/7/28 A book on CryptoMathCREST was published by Springer.
Mathematical Modelling for Next-Generation Cryptography, Mathematics for Industry, Vol.29, Springer, 2017. http://www.springer.com/in/book/9789811050640
2017/7/12 Prof. Masato Wakayama delivered an invited talk on "Spectral degeneracies in asymmetric quantum Rabi models and representations" at Integrability in Low-Dimensional Quantum Systems held at University of Melbourne.
2017/6/1 Dr. Katsuyuki Takashima (Kunihiro group) received the IEICE Best Paper Award in 2016. pdf(in Japanese)
2017/4/1 Prof. Tsuyoshi Takagi moved to Graduate School of Information Science and Technology, the University of Tokyo.
He also has a cross appointment with Institute of Mathematics for Industry, Kyushu University.
2017/3/22-23 3rd Asian Post-Quantum Cryptography Forum was held at Tokyo Institute of Technology.
http://www.is.c.titech.ac.jp/3rd-asia-pqc-forum/
2017/3/16 Prof. Fumio Hiroshima (Wakayama group) delivered an invited talk on "Feynman-Kac formula and its application to quantum physics" at Journée Thématique EDP: Mathematical Analysis of Interacting Quantum Systems held at Université de Rennes.
2017/3/14 Prof. Noboru Kunihiro delivered an invited talk on "Recovering RSA Secret Keys from Noisy Keys" at UTokyo-IIT Madras Workshop on Theoretical Computer Science held in Madras.
2017/3/10 Dr. Katsuyuki Takashima (Kunihiro group) delivered an invited talk on "Elliptic Curve Cryptography in Industry and Society" at International Seminar for Applied and Industrial Mathematics held at Waseda University.
2017/3/10 Prof. Hideyuki Miura (Tanaka group) delivered an invited talk "On uniqueness for the harmonic map heat flow in supercritical dimensions" at Waseda University.
2017/2/28 Prof. Masato Wakayama delivered an invited talk on "Symmetry of asymmetric quantum Rabi models" at University of Bologna.
2017/2/20 Prof. Shinya Nishibata (Tanaka group) delivered an invited talk on "Asymptotic stability of rarefaction waves for symmetric hyperbolic-parabolic systems" at PDE Seminar held at University of Konstanz.
2017/2/16 Prof. Masato Wakayama delivered an invited talk on "Endeavors for Mathematics for Industry in Japan" at 9th Ludwig Boltzmann Symposium Tokyo 2017 held at Austrian Embassy in Tokyo.
2016/12/7 Prof. Tsuyoshi Takagi served as Program Co-Chairs at Asiacrypt 2016 held in Hanoi.
http://www.asiacrypt2016.org/
2016/11/29 Prof. Tsuyoshi Takagi delivered an invited talk on "Computational Problems in Post-Quantum Cryptography" at PQC Asia Forum in Seoul held at Seoul National University.
2016/11/22 Shinya Okumura, Koichiro Akiyama and Tsuyoshi Takagi received the Outstanding Paper Award in the Fourth International Symposium on Computing and Networking (CANDAR'16)
"An Estimate of the Complexity of the Section Finding Problem on Algebraic Surfaces"
The Fourth International Symposium on Computing and Networking (CANDAR'16) http://is-candar.org/
2016/10/29 Prof. Masato Wakayama delivered an invited talk on "Symmetry of asymmetric quantum Rabi models" at Zeta Functions in Okinawa 2016 held at Okinawa Convention Center.
2016/10/26 Prof. Sadayoshi Kojima (Tanaka group) delivered an invited talk on "Normalized entropy versus volume for pseudo-Anosovs" at Kyoto University.
2016/10/1 A new member joined CREST team: Masahiro Ishii in Tanaka group (Adjunct Assistant Professor, Graduate School of Information Science and Engineering, Tokyo Institute of Technology)
2016/9/22 Prof. Tsuyoshi Takagi delivered a Keynote lecture on "Security Evaluation of Post-Quantum Cryptography" at Chinacrypt 2016, the biggest conference in China. http://cacr2016.cacrnet.org.cn/
2016/9/19 Prof. Masato Wakayama delivered an invited talk on "Generalized quantum Rabi models and representations theory" at "International Workshop on Ultra-Strong Light-Matter Interactions: theory and applications to quantum information" held at University of the Basque Country.
2016/9/14 Atsushi Takayasu delivered an invited talk on "Parameter Selections for Approximate GCD Problems" at IWSEC 2016 held in Akihabara, Tokyo.
2016/9/13 Dr. Katsuyuki Takashima (Kunihiro group) received the Best Paper Award in 2016 of the Japan Society for Industrial and Applied Mathematics (JSIAM). http://www2.jsiam.org/ronbun-bestauthor2016
2016/9/10 Prof. Masato Wakayama delivered an invited talk on "Generalized Quantum Rabi models and Finite Dimensional Representations of sl_2" in Okinawa.
2016/7/5 Atsushi Takayasu (Kunihiro group) has received the Best Student Paper at 21st Australasian Conference on Information Security and Privacy, ACISP 2016.
Atsushi Takayasu, Noboru Kunihiro, "Partial Key Exposure Attacks on RSA with Multiple Exponent Pairs".
Homepage of ACISP 2016 http://nsclab.org/acisp2016/index.html
2016/7/1 A new member joined CREST team: Yasuhiko Ikematsu in Takagi group (Postdoctoral Research Fellow, IMI, Kyushu University)
2016/6/10 Prof. Tsuyoshi Takagi delivered an invited talk on "State of the Art of Lattice Reduction Algorithms" at First Post-Quantum Cryptography Asia Forum held in Chengdu, China.
2016/6/9-10 Prof. Tsuyoshi Takagi and Prof. Kirill Morozov delivered invited talks at the Workshop "First Post-Quantum Cryptography Asia Forum" ,held in Chengdu. http://cps.cqu.edu.cn/
2016/6/6 Prof. Masato Wakayama delivered an invited talk on "Representation theoretic approach to the spectrum of quantum Rabi or its generalized models" at "Mathematical quantum field theory and related topics" held at Kyushu University.
2016/6/2 Dr. Katsuyuki Takashima (Kunihiro group) received the IEICE Best Paper Award in 2015. pdf(in Japanese)
2016/5/29 Prof. Shinya Nishibata (Tanaka group) delivered an invited talk on "Microlocal Analysis and Related Topic" at Workshop on the Boltzmann Equation held at Kyoto University.
2016/5/1 Dr. Shinya Okumura, Postdoctoral Research Fellow, moved to Institute of Systems, Information Technologies and Nanotechnologies (ISIT) as a researcher
2016/4/27 CALL FOR PAPERS : CREST BOOK  "Mathematical Modelling for Next-Generation Cryptography", Mathematics for Industry, Springer.
Submission Deadline: December 2nd, 2016
2016/4/22 Prof. D.Braak delivered an invited talk on "Exact Methods in Theoretical Quantum Optics " , held at Kyushu University. http://www.imi.kyushu-u.ac.jp/eng/seminars/view/1058
2016/4/1 Prof. Ishikawa (Wakayama group) moved to Graduate School of Natural Science and Technology, Okayama University from University of the Ryukyus.
Prof. Morozov moved to School of Computing, Tokyo Institute of Technology from Kyushu University.
2016/3/23 Yao Lu (Kunihiro group) delivered an invited talk on "Solving Linear Equations Modulo Unknown Divisors: Revisited" at a workshop held at National Institute of Advanced Industrial Science and Technology.
2016/3/14 Prof. Tsyoshi Takagi delivered an invited talk on "Lattice Reduction and Lattice Cryptography" at Taft Research Center held at University of Cinccinati.
2016/3/9 Prof. Kazufumi Kimoto (Wakayama group) delivered an invited talk on "Alpha-determinants and the Alon-Tarsi conjecture" at Tutorials and Workshop on New Developments in Representation Theory held at National University of Singapore.
2016/2/24-26 Post-Quantum Cryptography 2016 was held at Nishijin Plaza, Kyushu University.

https://pqcrypto2016.jp

NIST’s Plan for the Future was introduced at the conference. (pdf)

2016/2/3 NIST published a draft of the report on post-quantum cryptography NISTIR 8105.

http://csrc.nist.gov/publications/drafts/nistir-8105/nistir_8105_draft.pdf

CREST Crypto-Math project was introduced in this report.

2016/1/14 Prof. Tsuyoshi Takagi delivered a keynote talk on "Recent Developments of Post-Quantum Cryptography" at Future Cryptographic Technology Symposium: Cryptographic Technologies in the Era of Quantum Computation held at Seoul National University.
2015/12/15 CryptoMathCREST Workshop was held at IMI, Kyushu University
2015/12/12 Prof. Tsuyoshi Takagi delivered an invited talk at CMMA joint seminar at Meiji University, Tokyo http://cmma.mims.meiji.ac.jp/events/another/4center20151212.html (in Japanese)
2015/12/10 Ye Yuan, Chen-Mou Cheng, Shinsaku Kiyomoto, Yutaka Miyake ane Tsuyoshi Takagi, "Portable Implementation of Lattice-based Cryptography using JavaScript," received the Outstanding Paper Award at The Third International Symposium on Computing and Networking, CANDAR 2015.
2015/11/25 Prof. Tsuyoshi Takagi delivered an invited talk at JST CREST Optimum Modeling seminar at the University of Tokyo.
2015/11/12 Prof. Masaaki Umehara (Tanaka group) delivered an invited talk on "Indices of isolated umbilics on surfaces" at Geometric Analysis in Geometery and Topology 2015 held at Tokyo University of Science.
2015/11/12 Prof. Tsuyoshi Takagi delivered an invited talk at Netherlands-Japan Collaborative Cyber Security Conference in Tokyo http://www.iperc.uec.ac.jp/staging/en/cyber-security-coference-and-reception-in-uec.html
2015/11/9 Prof. Yoshinori Yamasaki (Wakayama group) delivered an invited talk on "Ramanujan Cayley graphs and the Hardy-Littlewood conjecture" at Nagoya University.
2015/10/31 Prof. Shinya Nishibata (Tanaka group) delivered an invited talk on "Stationary waves to symmetric hyperbolic-parabolic systems in half line" at International Conference on Nonlinear Analysis held at Institute of Mathematics, Academia Sinica in Taiwan.
2015/10/26-30 Forum "Math-for-Industry" 2015 - The Role and Importance of Mathematics in Innovation was held at IMI, Kyushu University
2015/10/7 Prof. Tsuyoshi Takagi delivered an invited talk on "Security analysis of quantum safe cryptography" at ETSI 3rd Quantum-Safe Crypto Workshop held in Seoul, Korea.
ETSI 3rd Quantum-Safe Crypto Workshop
2015/9/25 Prof. Hideyuki Miura (Tanaka group) delivered an invited talk "On Ukai-type solution formula for the Stokes system in a domain with boundary" at 4th International Conference on Mathematical Theory of Turbulence via Harmonic Analysis and Computational Fluid Dynamics in 2015 held at Hotel Nikko Nara.
2015/9/8 Prof. Yoshinori Yamasaki (Wakayama group) delivered an invited talk on "格Ramanujan Cayley graphs and the Hardy-Littlewood conjecture" at "Group actions and metric embeddings" held at Kyoto University.
2015/9/6-11 Prof. Tsuyoshi Takagi and Prof. Kirill Morozov delivered invited talks at Dagstuhl Seminar "Quantum Cryptanalysis" held in Germany.
Prof. Tsuyoshi Takagi: "Improvement on BKZ Lattice Reduction Algorithm"
Prof. Kirill Morozov: "On security of the Courtois-Finiasz-Sendrier signature"
2015/8/6 Prof. Sadayoshi Kojima (Tanaka group) delivered an invited talk on "Normalized Entropy versus Volume for pseudo-Anosovs" at Nagoya Institute of Technology.
2015/8/4 Prof. Hideyuki Miura (Tanaka group) delivered an invited talk on "Growth of the vorticity gradient for the two dimensional Euler flows around a corne" at ISSAC 2015 held at University of Macau.
2015/7/24 Prof. Yuji Terashima (Tanaka group) delivered an invited talk on "Partition q-series" at Keio University.
2015/7/16 Prof. Shinya Nishibata (Tanaka group) delivered an invited talk on "Stationary waves to hyperbolic-parabolic systems in half line" at UNIST Workshop on Nonlinear Partial Differential Equations held at Ulsan National Institute of Science and Technology.
2015/6/25 Prof. Shinya Nishibata (Tanaka group) delivered an invited talk on "Stationary waves to symmetric hyperbolic-parabolic systems in half line" at Workshop on Hyperbolic Conservation Laws and Related Topics held at Seoul National University.
2015/6/5 Prof. Hideyuki Miura (Tanaka group) delivered an invited talk "On Ukai-type solution formula for the Stokes system in a domain with boundary" at Asymptotic Problems: Elliptic and Parabolic Issues held in Vilnius, Lithuania.
2015/4/30 Prof. Masato Wakayama delivered an invited talk on "Spectrum of the quantum Rabi model and representation theory" at Workshop on "Probabilistic models with determinantal structure" held at Kyushu University.
2015/4/1 New members joined CREST team:
Masaya Yasuda and Shinya Okumura in Takagi group
Shingo Sugiyama in Wakayama group
Yao Lu in Kunihiro group
2015/2/25 Prof. Masato Wakayama delivered an invited talk on "Quantum Rabi’s model and representation theory" at Universit of Bologna.
2015/1/21-22 The 4th international conference on Mathematical Analysis on Fluid Dynamics and Conservation Laws was held.
2015/1/13 Prof. Tsuyoshi Takagi delivered an invited talk on "MQ Challange:hardness evaluation of solving multivariate quadratic problems" at DIMACS Workshop on The Mathematics of Post-Quantum Cryptography held at Rutgers University.
DIMACS Workshop on The Mathematics of Post-Quantum Cryptography
2014/11/18 Prof. Hideyuki Miura (Tanaka group) delivered an invited talk "On isomorphism for the space of solenoidal vector fields and its application to the Stokes problem" at Kyoto University.
2014/11/6 Prof. Yuji Terashima (Tanaka group) delivered an invited talk on "Mutation loops and geometry" in Sugadaira, Nagao.
2014/10/23-24 Mathematics and Physics of Interacting Quantum Systems (MPIQS) was held.
2014/10/16 Prof. Shinya Nishibata (Tanaka group) delivered an invited talk on "Stability of stationary solutions to hyperbolic-parabolic systems in half space and the convergence rate" at Kyoto University.
2014/10/7 Prof. Masato Wakayama delivered an invited talk on "Quantum Rabi's model and non-commutative harmonic oscillators" at Kyoto University.