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In this paper, the security strength of a phase-only asymmetric cryptosystem based on interference and phase-truncated Fourier transforms (PTFTs) has been evaluated. Compared to the conventional PTFTs-based scheme where the plaintext is directly encoded into two phase masks (PMs) and the ciphertext, here the plaintext is firstly converted to the phase-only distribution by PTFTs-based encryption process I, and then modulated by the encryption process II with the aid of two masks generated by a carrier image. The security strength of this cryptosystem has been enhanced by an additional secure layer for the output of PTFTs-based structure. Moreover, the four masks generated in the encryption processes I and II are required for the decryption also, it enlarges the key space which further ensures the security strength of the improved cryptosystem. However, we noticed that the carrier image used to generate one of private keys is same as the ciphertext when the input of the encryption is the zero matrix. Thus, the amplitude mask (AM) as the private key could be recovered by the designed chosen-plaintext attack, and then it can be used as the known parameter in the iterative attacks. Employing the recovered mask, two specific attacks with different constraints are designed to break the cryptosystem based on interference and PTFTs successfully. Based on our cryptoanalysis, it is found that most information of the plaintexts were encoded into the AM and the PM in the encryption process I, and silhouette problem would be caused when one of these keys is known. Numerical simulations have been carried out to validate the feasibility and effectiveness of proposed hybrid attacks. [ABSTRACT FROM AUTHOR]

We propose a double image encryption approach based on a hybrid phase-truncation scheme. This approach is realized by spatial and Fresnel encoding, where two plaintexts are encrypted by a random amplitude mask into two private key masks and one ciphertext mask. The random amplitude mask is introduced to break the functional relation of the plaintexts to the ciphertext. Compared with other reported phase-truncation-based techniques, the proposed hybrid scheme is not only free from information leakage but also resistant to several different types of attacks. In addition, the parameters of the Fresnel transform and discrete multiple parameter fractional Fourier transform serve as additional keys to strengthen security significantly. Numerical simulations and a performance analysis are conducted to demonstrate the reliability and validity of the proposed approach. [ABSTRACT FROM AUTHOR]

We present an optical encryption scheme for hyperspectral images using an improved binary tree structure (IBTS) and phase-truncated discrete multiple-parameter fractional Fourier transform (PTdmpFrFT). In the IBTS, the encryption modules based on the phase-truncated fractional Fourier transform represented the branch nodes, while the hyperspectral bands of the plain images were considered as leaf nodes. All pairs of bands were encoded into intermediate data using the IBTS, with subsequent encryption into asymmetric ciphertexts using the PTdmpFrFT. The proposed approach generated different pairs of bands with different secret keys, and encryption and decryption paths. Compared with state-of-the-art optical hyperspectral encryption methods, our approach not only achieved superior encryption security but also reduced the computation and storage requirements of the encrypted data. The original hyperspectral image information could be successfully decrypted only when using all the correct keys. Numerical simulations were performed to verify the performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a double image encryption mechanism for iris template protection using 3D Lorenz chaotic system with modified equal modulus decomposition in the hybrid transform domain is proposed. The hybrid transform is produced by the combination of Walsh transform, Kekre transform and fractional Fourier transform of various orders. Here the fractional orders of the fractional Fourier transform enlarge the key-space of the proposed scheme and improve robustness against brute-force attack. The proposed scheme is asymmetric and non-linear in nature. To validate and authenticate the proposed cryptosystem, the numerical simulations have been performed on grayscale images. Results demonstrate that the proposed cryptosystem has higher robustness against noise and special attacks. [ABSTRACT FROM AUTHOR]

An asymmetric image encryption scheme is proposed using a phase-truncated discrete multiple-parameter fractional Fourier transform (DMPFRFT). After applying a pixel-scrambling operation and random-phase mask, an asymmetric ciphertext with stationary white noise can be obtained using phase truncation in the DMPFRFT domain. Using the phase key, an inverse pixel-scrambling operation, and the parameters of the DMPFRFT, the original image can be successfully retrieved. Numerical simulations were conducted to demonstrate the validity and the security of the proposed method, and electro-optical hybrid setups are suggested for encryption and decryption. [ABSTRACT FROM AUTHOR]

A novel asymmetric cryptosystem for optical image is proposed using fingerprint based on iterative fractional Fourier transform. To enhance the security, a hyperchaotic phase generated by a 4D Lorenz system is considered as the public key in the proposed encryption system, while the private key is emerged by the retrieved phase and fingerprint. In the encryption process, the secret information is hid into the hyperchaotic phase. Subsequently, the private key can be obtained by a reversible operation. To decrypt the original image, the ciphertext and private key are imported into the input plane of fractional Fourier system. This system is also applicable for information authentication because the fingerprint is used both in encryption and decryption approach. Some numerical simulations have been done to test the validity and capability of the encryption system. [ABSTRACT FROM AUTHOR]

In this paper an image authentication scheme is proposed based on double-image encryption and partial phase decryption in nonseparable Fractional Fourier transform domain. Two original images are combined and transformed into the nonseparable fractional Fourier domain. Only part of the phase information of the encrypted result is kept for decryption while the rest part of phase and all the amplitude information are discarded. The two recovered images are hardly recognized by visual inspection but can be authenticated by the nonlinear correlation algorithm. The numerical simulations demonstrate the viability and validity of the proposed image authentication scheme. [ABSTRACT FROM AUTHOR]

Known-plaintext attack is considered for decrypting the image generated by iterative random phase encoding in fractional Fourier transform domains. The double random phase encoding in Fourier domains is introduced to design the known-plaintext attack procedure. The decryption test is explored without both fractional order and these random phase masks. Some numerical simulations are made to demonstrate the validity of the known-plaintext attack. [ABSTRACT FROM AUTHOR]

Based on multi-beam interference and common vector decomposition, we propose a new method for optical image encryption. In encryption process, the information of an original image is encoded into n amplitude masks and n phase masks which are regarded as a ciphertext and many keys. In decryption process, parallel light irradiates the amplitude masks and phase masks, then passes through lens that takes place Fourier transform, and finally we obtain the original image at the output plane after interference. The security of the encryption system is also discussed in the paper, and we find that only when all the keys are correct, can the information of the original image be recovered. Computer simulation results are presented to verify the validity and the security of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a modified multiple-parameter fractional Fourier transform (MMPFRFT) is proposed which is another form of fractional Fourier transform in term of its degree of freedom. The defect has been found in encryption technique, illustrated in (R. Tao, J. Lang, Y. Wang, Opt. Lett. 33 (06) (2008) 581–583), dissolved and verification has been done on MATLAB ® . A novel technique for single channel, four-image encryption is also proposed based on MMPFRFT and pixel scrambling technique. The low frequency components which are extracted from four primitive images and placed in the center position, have utilized pixel scrambling technique and then encrypted based on MMPFRFT. Scrambling technology is utilized to enhance the security of the system. Numerical simulations are presented and it is claimed that this technique is superior to the existing techniques (Z. Liu et al., Optik 122 (11) (2011) 1010–1013, J. Wu, X. Luo, N. Zhou, Opt. Laser Technol. 45 (2013) 571–577). [ABSTRACT FROM AUTHOR]

A multiple-image cryptosystem is proposed based on the cascaded fractional Fourier transform. During an encryption procedure, each of the original images is directly separated into two phase masks. A portion of the masks is subsequently modulated into an interim mask, which is encrypted into the ciphertext image; the others are used as the encryption keys. Using phase truncation in the fractional Fourier domain, one can use an asymmetric cryptosystem to produce a real-valued noise-like ciphertext, while a legal user can reconstruct all of the original images using a different group of phase masks. The encryption key is an indivisible part of the corresponding original image and is still useful during decryption. The proposed system has high resistance to various potential attacks, including the chosen-plaintext attack. Numerical simulations also demonstrate the security and feasibility of the proposed scheme. [ABSTRACT FROM AUTHOR]

We propose a multichannel random discrete fractional Fourier transform (MRFrFT) with random weighting coefficients and partial transform kernel functions. First, the weighting coefficients of each channel are randomized. Then, the kernel functions, selected based on a choice scheme, are randomized using a group of random phase-only masks (RPOMs). The proposed MRFrFT can be carried out both electronically and optically, and its main features and properties have been given. Numerical simulation about one-dimensional signal demonstrates that the MRFrFT has an important feature that the magnitude and phase of its output are both random. Moreover, the MRFrFT of two-dimensional image can be viewed as a security enhanced image encryption scheme due to the large key space and the sensitivity to the private keys. [ABSTRACT FROM AUTHOR]

In this paper, a new method for optical image encryption based on multi-beams interference principle and vector composition is proposed. In this encryption, the original image is encoded into n −1 phase only masks which are regarded as the keys of the encryption system and a ciphertext according to multi-beams interference principle and vector composition. In decryption process, n beams of parallel incident light illuminate at the phase only masks and the ciphertext, and we can obtain the decrypted image at output plane after Fourier transforms. The security of the proposed method is discussed, finding that no decrypted image can be obtained only when all the keys used are right. Furthermore, the keys can be stored separately resulting in improving the security of encryption system. Computer simulation results are presented to verify the validity of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce fractional Fourier transforms over finite fields GF(p), where . Such a definition is based on the approach given in [1], which corresponds to a finite field extension of the commuting matrix method for defining discrete fractional Fourier transforms [2]. The transforms we have constructed are then used as the basis of a novel image encryption scheme. Security aspects of such a scheme are analyzed through computer simulations and specific metrics. [Copyright &y& Elsevier]

Based on the two-step phase-shifting interference (PSI) technique in fractional Fourier transform (FRT) domain and random mixed encoding, we present a new scheme for double image encryption. In the proposed scheme, information of each primitive image is recorded in two intensity interference patterns of FRT spectra by PSI technique, from which an encrypted image for each primitive image can be digitally derived. Random mixed encoding is then employed to divide and recombine both encrypted images into a single synthetic encrypted image. During the mixed encoding process, repositioning operations based on shift-variance of FRT are performed on the encrypted images to realize the spatial separation of decoded results in the output plane. By inverse FRT with correct fractional order, any of the primitive images can be easily retrieved directly from the synthetic encoded image with the corresponding phase encoding key. Crosstalk effect due to the overlapping of decoded images is alleviated for their spatial separation. Computer simulation and experimental results are presented to verify the validity and efficiency of our scheme. [ABSTRACT FROM AUTHOR]

Abstract: To enhance the security of double random phase encoding, a kind of amplitude scrambling operation is designed and introduced into an image encryption process. The random data of the second phase mask in double random phase encoding is also employed for scrambling amplitude distribution in order to save the space of storage and transmission of the key information. The scrambling operator is changeable for generating the key. Some numerical simulations have been provided for testing the validity of the image encryption scheme. [Copyright &y& Elsevier]

Abstract: Based on fractional Fourier transform, an image encryption algorithm is proposed and researched. A local random phase encoding is introduced into this algorithm. The data at the local area of complex function is converted by fractional Fourier transform. The local random phase encoding is performed many times. Moreover only one set of random phase data is used in image encryption process. Compare to double random phase encoding, the parameter defining local area can be regarded as the additional key to increase the security of the encryption scheme. Some numerical simulations are achieved to demonstrate the performance of the image encryption scheme. [Copyright &y& Elsevier]

Quantum image encryption offers major advantages over its classical counterpart in terms of key space, computational complexity, and so on. A novel double quantum image encryption approach based on quantum Arnold transform (QAT) and qubit random rotation is proposed in this paper, in which QAT is used to scramble pixel positions and the gray information is changed by utilizing random qubit rotation. Actually, the independent random qubit rotation operates once, respectively, in spatial and frequency domains with the help of quantum Fourier transform (QFT). The encryption process accomplishes pixel confusion and diffusion, and finally the noise-like cipher image is obtained. Numerical simulation and theoretical analysis verify that the method is valid and it shows superior performance in security and computational complexity. [ABSTRACT FROM AUTHOR]