报告题目：2-to-1 Functions, Involutions, and Implicit Functions
报告时间：2025年3月24日14:00-15:00
报告地点：西南交通大学犀浦校区7教7510
报告人：李康荃
摘要：This talk focuses on the construction and applications of 2-to-1 functions, as well as the emerging concept of discrete implicit functions. It begins with the characterization of 2-to-1 functions, including a complete classification of low-degree (degree ≤5) 2-to-1 functions, analyses of 2-to-1 trinomials and quadrinomials, and practical examples in cryptography and coding theory. Next, the implicit relationship between 2-to-1 functions and fixed-point-free involutions is established, with proofs demonstrating how 2-to-1 functions can construct such involutions. On this basis, we introduce the novel concept of implicit functions over finite fields, detailing their properties and providing a complete characterization of low-degree implicit functions. Finally, some applications in cryptographic functions are discussed.
报告人简介：李康荃，国防科技大学副教授。2021年在国防科技大学获理学博士学位。研究方向为编码密码理论及其应用，以第一作者在中国密码学会A类期刊IEEE TIT、B类期刊DCC和FFA上发表论文17篇，1篇进入ESI引用前1%。主持国家自然科学基金青年科学基金项目1项，参与国家自然科学基金面上项目2项，获全军和中国密码学会优秀博士学位论文奖。
