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Cryptography

Modern cryptography has become one of the most important research fields in information technology. We aim at development and security evaluation of the next-generation cryptographic systems. In particular, we study post-quantum
cryptography based on the mathematical problems (such as coding theory, lattice theory, multivariate polynomials,
graph theory, etc), which are computationally intractable even in the era of quantum computing.

Information Security

With cryptography it is possible to construct many security protocols that become the basic infrastructure for secure
communications such as SSL/TLS. These security protocols provide us with various security applications, for example,
copyright protection, electronic voting, cryptocurrency, and so on. This research group is engaged in the development
of new efficient cryptographic algorithms and implementation secure against physical attacks.

Optimal Modeling

Modeling is the first step for solving real-world problems and understanding complex phenomena via a mathematical approach. However, there could be enormous different models to the same phenomenon. Furthermore, even in essentially equivalent models, the difficulty of the numerical computation varies due to variable choices and freedom in mathematical expressions in these models. Exploiting techniques from discrete mathematics, optimization, and statistics, we aim to establish a systematic methodology for selecting an optimal model from enormous possible models.

Discrete Computational Geometry

Computational geometry studies algorithms for solving geometric problems. Our particular interest is to understand the discrete structures behind geometric graphs and networks in engineering topics such as robotics, structural mechanics, and bioinformatics, and establish mathematical foundations for efficient algorithms.

Sensor Fusion

Research on Sensor Fusion theory, construction of system architectures, and applications to high-speed intelligent robots aimed at the engineered re-formation of the five senses

Vision Architecture

Research on Vision Architecture for designing high-speed image processing technology (theory, algorithms, and devices) and the realization of application systems

Dynamic Image Control

Research on Dynamic Image Control for realizing high-speed imaging control using high-speed image processing and new active optical devices and systems

Active Perception

Research on Active Perception for creating a new style of interaction by using sensation-enhancing technology and its applications

Research Topics

Mathematical Analysis of Complex Systems
In order to comprehend diverse complex systems ranging over biology, brain science, and socio-economics, we are developing new mathematical techniques based on, e.g., bifurcation theory, time-series analysis, and statistics, and trying to construct universal theoretical frameworks for complex systems.

Understanding Information processing of biological systems
In order to unveil the design principle of biological systems and their information processing, we are working on theoretical biology and bioinformatics for different types of biological phenomena and data, which cover neuroscience, cell biology, developmental biology, immunology, physiology, epidemics, bioimaging, and next-generation sequencing. Additionally, we are employing our mathematical models of brain and neural networks for engineering new neuromorphic hardware.

Chaos engineering
We are developing new information processing systems taking full advantage of the diverse dynamical behaviors that chaos and complex systems generate. Those systems are applied to the implementation of nonlinear analog circuits, constructing an artificial brain, and other engineering problems.

Numerical Analysis

Many problems in science and engineering cannot be solved without computers. Numerical analysis is a field of study that deals with such problems based on various mathematical facts and a deep insight about the original background of the problems. Study in numerical analysis is concerned with a wide spectrum of topics from fundamental mathematics of computation to various application of numerical methods to problems in science and engineering.

Large Scale Simulation

Numerical simulation is said to be “third science” following theory and experiments. We study mathematical foundations of large scale simulations such as the method for solving linear equations by parallel computers. In the study, we take account of various aspects of a simulation such as physics, modeling, computer hardware, etc.

Numerical Simulation for Problems in Science and Engineering

Based on the theoretical and computational foundations stated above, we study state-of-the-art methods for computer-aided analysis of scientific phenomena such as nonlinear waves, and large data with matrix or tensor form.