论文标题
基于分数傅立叶变换的域变化的信号加密策略
Signal Encryption Strategy based on Domain change of the Fractional Fourier Transform
论文作者
论文摘要
本文提供了一种双加密算法，该算法使用$ l^{1} $上的分数傅立叶变换（FRFT）缺乏可逆性。一个加密密钥是一个函数，它映射``好的'$ l^{2} $ - 信号 - ``bad''$ l^{1} $ - 信号。描述与该操作员在时频平面上相关的旋转的FRFT参数提供了其他加密密钥。借助近似身份，例如在\ cite {cfgw}中建立的frft的ABEL和GAUSS手段，我们在FRFT域上恢复了加密信号。即使使用经典的傅立叶变换，加密算法的这种设计似乎是新的。最后，通过模拟和音频示例验证了新策略的可行性。
This paper provides 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" $L^{2}$-signal to a ``bad" $L^{1}$-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 in \cite{CFGW}, we recover the encrypted signal on the FRFT domain. This design of an encryption algorithm seems new even when using the classical Fourier transform. Finally, the feasibility of the new strategy is verified by simulation and audio examples.
