Centre International De Mathématiques Pures Et Appliquées (CIMPA) School, with the theme “Application of Number Theory,” was successfully held in Ho Chi Minh City, Vietnam, from June 3 to June 14, 2024. The aim of this school was to introduce participants to various aspects of number theory (algorithmic) and arithmetic geometry, as well as the highly productive interactions between these subjects and the applied disciplines of cryptography and coding theory. The program consisted of four main topics: algorithmic number theory, elliptic curves, algebraic coding theory, and isogeny-based cryptography.
These topics provided in-depth knowledge of various tools in number theory and arithmetic geometry and their applications in cryptography and coding theory. Topics covered include class groups of number fields and Buchmann’s subexponential algorithm for computing them, the Mordell-Weil theorem for elliptic curves over number fields, Reed-Muller and Goppa codes, and algorithms for computing and evaluating isogenies of elliptic curves. Each course combined theoretical and practical aspects through exercises and programming sessions, so students learn proactively.
On this occasion, two UGM mathematics students, Saifullah Ali (M.Sc. in Mathematics) and Annisa Dini Handayani (Ph.D. in Mathematics), had the opportunity to participate in this event. Annisa Dini Handayani stated, “Meeting algebra enthusiasts from around the world, exchanging ideas on algebra research, and starting collaborations. I never imagined that I could enjoy algebra and cryptography even more. An incredible experience with CIMPA School 2024.”
The participation of these two students is expected to bring benefits to the development of science and research in the field of mathematics, especially in number theory and cryptography. Furthermore, they will convey what they have learned to other activities so that they will support SDGs point 4 related to quality education. In addition, the application of number theory to cryptography will also support SDGs point 11 Sustainable Cities and Communities because it will realize secure communication for the community.
Keywords: Number Theory, Cryptography, CIMPA School
Author: Uha Isnaini
Editor: Endang Sulastri
Foto: Annisa Dini Handayani