Abstract. A double-image encryption scheme is proposed based on an asymmetric technique, in which the encryption and decryption processes are different and the encryption keys are not identical to the decryption ones. First, a phase-only function (POF) of each plain image is retrieved by using an iterative process and then encoded into an interim matrix. Two interim matrices are directly modulated into a complex image by using the convolution operation in the fractional Fourier transform (FrFT) domain. Second, the complex image is encrypted into the gray scale ciphertext with stationary white-noise distribution by using the FrFT. In the encryption process, three random phase functions are used as encryption keys to retrieve the POFs of plain images. Simultaneously, two decryption keys are generated in the encryption process, which make the optical implementation of the decryption process convenient and efficient. The proposed encryption scheme has high robustness to various attacks, such as brute-force attack, known plaintext attack, cipher-only attack, and specific attack. Numerical simulations demonstrate the validity and security of the proposed method.
IntroductionWith the rapid popularity of computer networks, images as an effective carrier of information have been widely used in various fields of modern society and image encryption issues have become an important field for information security. Since Refregier and Javidi 1 proposed the classical optical double-random phase encoding (DRPE) technique, many optical encryption and authentication systems in Fourier transform (FT), Fresnel transform (FrT), fractional Fourier transform (FrFT), and gyrator transform (GT) domains have been proposed during the past decades.2-11 Moreover, Alfalou and Brosseau 12 pointed out that these techniques can be used for compression operations simultaneously. Though most reported optical encryption techniques based on DRPE have the excellent parallel and multidimensional capability of signal processing, it should be pointed out that these schemes belong to the category of symmetric cryptosystems, where the keys in the encryption process are used for decryption. Some research investigations indicate that these schemes are vulnerable to the conventional attacks because of the inherently linear property of mathematical or optical transformation. [13][14][15] In order to resist these attacks, Qin and Peng 16 proposed an asymmetric encryption based on the phase-truncated Fourier transform (PTFT), where the decryption keys are different from the encryption keys and the linearity of the cryptosystem is broken by using the nonlinear operation of phase truncation.