Security Analysis Method Of Image Cryptosystem With Double Random Phase In Fractional Fourier Domain

Image encryption is an important part of information security. Transformencryption especially fractional Fourier transform encryption is a typical means toensure security of image information. Combining fractional Fourier transform withrandom phase encoding improve the security of image cryptosystem also is aneffective way, such as the image cryptosystem with double random phase infractional Fourier domain is the most representative.In this paper, we have established a security analysis method of the imagecryptosystem. Its security has been analyzed and demonstrated from three aspects.First of all, the encryption system has been analyzed and proved that it has fourstochastic natures as follows. First, the plaintext image is encrypted by the imagecryptosystem which gets ciphertext image and gray levels of any two pixels on it arestatistically irrelevant stochastic variables. Second，any plaintext image is encryptedcountless times which gets ciphertexts are statistically irrelevant. Third, the differentof plaintext images are encrypted which get ciphertext images are statisticallyirrelevant. Fourth，any plaintext and ciphertext image is statistically irrelevant. Itshows that this image cryptosystem is stochastic, and the ciphertext image isunpredictable. That is to say, before encrypt the plaintext image, it may correspondto countless ciphertexts. And on the contrary, countless ciphertext images maycorrespond to a plaintext image, which has laid a solid theoretical foundation foranalysis the security of this image cryptosystem.Then, it has been analyzed and proved from the perspective of cryptanalysisthat the image cryptosystem has immunity to five typical cryptography attacksincluding known-plaintext attack, chosen-plaintext attack, known-ciphertext attack,chosen-ciphertext attack and ciphertext-only attack, it also analyzed the security ofthis encryption system to other attacks.Finally, this paper has adopted digital simulation to study the immunity of thisimage cryptosystem when the phase retrieval algorithm attacks it, and the statisticalproperties of the key. The simulation results show that the image cryptosystem caneffectively resist the attack from the phase retrieval algorithm.In short, this paper has demonstrated image cryptosystem with double randomphase in fractional Fourier domain is a safe and stochastic image cryptosystem.