Cryptography using Latin squares

Reference No.	2023a016
Type/Category	Grant for Supporting the Advancement of Female Researchers- Short-term Visiting Researcher
Title of Research Project	Cryptography using Latin squares
Principal Investigator	Tomoko Adachi（Department of Computer Science, Shizuoka Institute of Science and Technology・Professor）
Research Period	September 4,2023. ～ September 12,2023.
Keyword(s) of Research Fields	Latin squares, Quasigroup, Secret Sharing Scheme
Abstract for Research Report	A Latin square of order $q$ is a $q \times q$ array in which $q$ distinct symbols are arranged so that each symbol occurs in each row and column. A quasigroup is equivalent to a Latin square. A secret sharing scheme in cryptography is developed for a set of participants to share secrets. The first and the most famous scheme is a threshold scheme which was proposed by Shamir in 1979. Secret sharing schemes using Latin squares have been investigated, for instance, Cooper’s scheme (1994) and Stones’ scheme (2016). Both schemes use a Latin square as a secret, and need to prepare a new Latin square each time the secret is changed. On the other hand, our scheme (submitted paper) use a Latin square in public, and can use an old Latin square so even if the secret is changed. Hence, in terms of cost, our scheme is better than Cooper’s scheme and Stones’ scheme. In terms of security, our scheme is better than Cooper’s scheme, and is as good as Stones’ scheme and Shamir’s scheme. In terms of computational complexity, our scheme is better than Stones’ scheme. Our challenge is to ensure that the computational complexity of our scheme is comparable to or less than that of Shamir's scheme.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Tomoko Adachi（Shizuoka Institute of Science and Technology・Professor） Koji Nuida（Kyushu University・Professor） Yujie Gu（Kyushu University・Assistant professor）