報(bào)告題目：2-to-1 Functions, Involutions, and Implicit Functions

報(bào)告時(shí)間：2025年3月24日14:00-15:00

報(bào)告地點(diǎn)：kaiyun開云官方網(wǎng)站犀浦校區(qū)7教7510

報(bào)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(bào)告人簡(jiǎn)介：李康荃，國(guó)防科技大學(xué)副教授。2021年在國(guó)防科技大學(xué)獲理學(xué)博士學(xué)位。研究方向?yàn)榫幋a密碼理論及其應(yīng)用，以第一作者在中國(guó)密碼學(xué)會(huì)A類期刊IEEE TIT、B類期刊DCC和FFA上發(fā)表論文17篇，1篇進(jìn)入ESI引用前1%。主持國(guó)家自然科學(xué)基金青年科學(xué)基金項(xiàng)目1項(xiàng)，參與國(guó)家自然科學(xué)基金面上項(xiàng)目2項(xiàng)，獲全軍和中國(guó)密碼學(xué)會(huì)優(yōu)秀博士學(xué)位論文獎(jiǎng)。