報告題目：2-to-1 Functions, Involutions, and Implicit Functions
報告時間：2025年3月24日14:00-15:00
報告地點：kaiyun開云官方網(wǎng)站犀浦校區(qū)7教7510
報告人：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.
報告人簡介：李康荃，國防科技大學副教授。2021年在國防科技大學獲理學博士學位。研究方向為編碼密碼理論及其應(yīng)用，以第一作者在中國密碼學會A類期刊IEEE TIT、B類期刊DCC和FFA上發(fā)表論文17篇，1篇進入ESI引用前1%。主持國家自然科學基金青年科學基金項目1項，參與國家自然科學基金面上項目2項，獲全軍和中國密碼學會優(yōu)秀博士學位論文獎。
