报告题目：Algebraic Number Fields and the High Dimensional RSA Protocol

报告人及单位：郑志勇 教授，中国人民大学

报告时间：2024年7月26日14:15-15:15

报告地点：A7-302

报告摘要：

The most known of public key cryptosystem was introduced in 1978 by Rivest, Shamir and

Adleman and now called the RSA public key cryptosystem in their honor. Later, a few authors gave a simply extension of RSA over algebraic numbers field, but they require that the ring of algebraic integers is Euclidean ring, this requirement is much more stronger than the class number one condition. In this paper, we introduce a high dimensional form of RSA by making use of the ring of algebraic integers of an algebraic number field and the lattice theory. We give an attainable algorithm of which is significant both from the theoretical and practical point of view. Our main purpose is to show that the high dimensional RSA is a lattice based on public key cryptosystem indeed, of which would be considered as a new number in the family of post-quantum cryptography. On the other hand, we give a matrix expression for any algebraic number fields , which is a new result even in the sense of classical algebraic number theory.

国际基础科学大会，是由北京市人民政府、科学技术部、中国科学技术协会及世界华人数学家联盟主办的国际基础科学领域的顶级学术盛会，创办于2023年。2024国际基础科学大会（International Congress of Basic Science,简称 ICBS）将于7月中旬在北京开幕，主题为“聚焦基础科学，引领人类未来”，重点围绕数学、理论物理、理论计算机与信息科学三大基础科学领域展开学术交流和研讨。

菲尔兹奖得主丘成桐院士担任大会主席，众多享誉世界的科学家将齐聚一堂，包括5位菲尔兹奖得主、3位图灵奖得主、1位诺贝尔奖得主、2位沃尔夫奖得主、3位邵逸夫奖得主等国际大奖得主以及数十位各国院士。他们将带来高水平学术报告，与中国青少年面对面交流，分享各自在基础科学领域的研究成果和见解。

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