Abstract: Multiple-image encryption scheme based on the Phase Retrieval Algorithm（PRA） in Fractional Fourier Transform（FrFT） domain is proposed. A set of parallel images as amplitude part of complex-value images are encrypted into a chaotic picture with different orders；the phase keys are achieved from nonlinear encryption process and determined by different plaintexts, the known-plaintext attacks, chosen-plaintext attacks and chosen-ciphertext attacks can be avoided in this method. All images can be extracted independently from the chaotic picture which is recovered from chaotic system with enough encryption capacity. Numerical simulation results demonstrate the feasibility, effectiveness and security of the proposed method.

Key words: fractional Fourier transform, multiple-image encryption, chaotic picture, phase retrieval

摘要： 基于相位恢复算法提出了分数傅里叶变换域的多图像加密算法。一组图像作为复值图像的振幅部分分别采用不同分数阶傅里叶变换加密到一个混沌图上；通过非线性加密过程产生的相位密钥与明文相关，所提的加密算法可以抵抗已知明文攻击，选择明文攻击和选择密文攻击。通过混沌系统还原的混沌图可以独立解密所有图像，加密容量较大。仿真结果验证了该方法的可行性、有效性和安全性。

关键词: 分数傅里叶变换, 多图像加密, 混沌图, 相位恢复