Number-theoretic algorithms related to algebraic curves and abelian varieties

Reference No.	2025c001
Type/Category	Openings at any time-Workshop (II)
Title of Research Project	Number-theoretic algorithms related to algebraic curves and abelian varieties
Principal Investigator	Ryo Ohashi（Graduate School of Information Science and Technology, The University of Tokyo・Project Researcher）
Research Period	October 20,2025. - October 22,2025.
Keyword(s) of Research Fields	Algebraic curves / Abelian varieties / Number-theoretic algorithms / Isogeny-based cryptography / Superspecial curves
Abstract for Research Report	A standardization project for post-quantum cryptography is currently underway, led by the National Institute of Standards and Technology (NIST) in the United States. In particular, an additional call for proposals for digital signature schemes was conducted in 2023, and among the candidates, the isogeny-based cryptosystem SQIsign remains under consideration. Other isogeny-based cryptographic schemes have also attracted attention due to advantages such as small key and ciphertext sizes, and there is a growing industrial demand for these schemes. In this context, further improvements in the efficiency and security analysis of isogeny-based cryptography have become extremely important research challenges. Fundamental to addressing these challenges are number-theoretic algorithms related to algebraic curves and abelian varieties. In July 2022, a polynomial-time attack was reported against SIDH, which had previously been considered a promising isogeny-based cryptographic scheme. The theory of higher-dimensional abelian varieties played a central role in this attack. This event spurred the proposal of many new isogeny-based cryptographic schemes that utilize abelian varieties, and algorithms for efficiently computing isogenies between abelian varieties have been developed to improve the efficiency of these schemes. Moreover, such algorithms have been applied to problems in algebraic geometry, including the enumeration of superspecial curves and the structural analysis of isogeny graphs, thereby contributing to the security analysis of isogeny-based cryptography. As described above, algebraic geometry, number-theoretic algorithms, and isogeny-based cryptography are closely interconnected, and further advances in these areas will require the sharing of knowledge and collaboration across these fields. The purpose of this research workshop is to bring together a wide range of researchers working in these areas to share the latest research trends, achievements, future prospects, and challenges, and to engage in active discussions. Through these exchanges, it is expected that new research problems transcending individual fields will be identified, leading to outcomes such as the promotion of collaborative research among participants.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Yusuke Aikawa（The University of Tokyo・Assistant Professor） Yasuhiko Ikematsu（Kyushu University・Associate Professor） Yukihiro Uchida（Tokyo Metropolitan University・Associate Professor） Hiroshi Onuki（The University of Tokyo・Project Lecturer） Momonari Kudo（Fukuoka Institute of Technology・Associate Professor） Kohei Nakagawa（NTT Social Informatics Laboratories・Researcher） Ryo Yoshizumi（Kyushu University・Ph.D. student）