2019 Fiscal Year Annual Research Report
Discrete Mathematics and its Applications
| Project/Area Number |
18J23484
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| Research Institution | Kyoto University |
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Principal Investigator |
AZAM NAVEED AHMED 京都大学, 情報学研究科, 特別研究員(DC1)
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| Project Period (FY) |
2018-04-25 – 2021-03-31
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| Keywords | Substitution box / Elliptic curve / Image encryption / PCG / Chemical graphs / Linear programming / Neural networks / Graph enumeration |
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| Outline of Annual Research Achievements |
Our research project mainly focuses on the enumeration of graphs and cryptography. We have developed efficient methods to enumerate all pairwise compatibility graphs with a given number of vertices by using Linear programming and branch and bound algorithms. From this part of our research, we produced three papers. We have developed a method to efficiently count all trees with a given number of vertices and self-loops based on dynamic programming and published a paper. We developed a system to infer acyclic and monocyclic chemical graphs with given chemical properties by using linear programming, neural networks, and branch and bound algorithm and produced two papers. We have developed an efficient algorithm to generate substitution boxes over elliptic curves for secure data transfer. Furthermore, we have developed a fast and secure image encryption scheme based on elliptic curves and produced three papers.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
We have produced nine (9) papers related to substitution box, image encryption, graph enumeration. Due to the current situation because of coronavirus pandemic, the review process of some of our papers is delayed and some conferences have been canceled. However, even with this state, we can say that the research is progressing according to the research plan.
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| Strategy for Future Research Activity |
Our future aim is to further (1) improve our graph enumeration method so that it can work for a large number of vertices; (2) extend our method to enumerate all trees with vertices and self-loops; (3) extend our system to infer any chemical graph with a given property; (4) improve our cryptosystem and extend it for biomedical images.
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