Towards improving security reductions in isogeny-based cryptosystems

Reference No.	2024a026
Type/Category	Grant for Young Researchers and Students- Short-term Visiting Researcher
Title of Research Project	Towards improving security reductions in isogeny-based cryptosystems
Principal Investigator	Yuji Hashimoto（Division of Information Systems and Design, School of Science and Engineering, Tokyo Denki University・Assistant professor）
Research Period	August 22,2024. ～ August 30,2024.
Keyword(s) of Research Fields	Cryptography, Category Theory, Isogeny-based Cryptosystems
Abstract for Research Report	In modern society, cryptosystems are an important tool for secure communications. Security of most of the cryptosystems currently proposed is based on computationally hard problems. That is, in the security proof, the problem of breaking the cryptosystem is reduced to a computationally hard problem. Thus, if the problem can be efficiently reduced to a computationally hard problem, it guarantees higher security for the cryptosystem, and also leads to its efficiency improvement. Therefore, in the field of cryptography, numerous security proof techniques have been proposed, but it is difficult to apply such existing methods to cryptosystems based on advanced mathematical structures such as isogeny-based cryptography. In our research, we aim to develop new security proof techniques with broader applicability. Specifically, we aim to develop new security proof techniques by formulating concepts such as 'oracles' and 'attackers', which appear in the security proofs, by using Resource Theory proposed as an application of category theory. As an application of these techniques, we aim to enhance the efficiency of individual isogeny-based cryptosystems by improving their security proofs.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Yuji Hashimoto（Tokyo Denki University・Assistant professor） Koji Nuida（Kyushu University・Professor）