数学系 Seminar 第2035期
2020年建设高水平大学项目——研究生课程《近代分析》系列报告
报告主题：基于分数次傅里叶变换的信号加密策略
报 告 人：傅尊伟 教授 （临沂大学）
报告时间：2020年10月29日（周四） 14:00
参会方式：腾讯会议
会议ID：141 210 356
邀 请 人：赵发友
主办部门：理学院数学系
报告摘要：We provide a double encryption algorithm that uses the lack of invertibility of the fractional Fourier transform (FRFT) on $L^{1}$. One encryption key is a function, which maps a "good" $L^{2}(\mathbb{R})$ signal to a "bad" $L^{1}(\mathbb{R})$ signal. The FRFT parameter which describes the rotation associated with this operator on the time-frequency plane provides the other encryption key. With the help of approximate identities, such as of the Abel and Gauss means of the FRFT established, we recover the encrypted signal on the FRFT domain. This design of an encryption algorithm seems new even when using the classical Fourier transform. This is joint work with Dr. Wei Chen, Prof. L. Grafakos and Dr. Yue Wu.
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