基于分数阶傅里叶变换域变换的信号加密策略
Signal Encryption Strategy based on Domain change of the Fractional Fourier Transform
摘要：
利用分数阶傅里叶变换（FRFT）在$L^{1}$上不可逆的特点，提出了一种双重加密算法。一个加密密钥是将"好”$L^{2}$信号映射到"坏”$L^{1}$信号的函数。描述在时间-频率平面上与该算子相关联的旋转的FRFT参数提供另一加密密钥。利用\cite{CFGW}中建立的FRFT的Abel平均和Gauss平均等近似恒等式，在FRFT域上恢复加密信号。这种加密算法的设计即使在使用经典傅立叶变换时也是新的。最后通过仿真和音频实例验证了新策略的可行性。
英文摘要：
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.
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