Optical image encryption using password key based on phase retrieval algorithm

A novel optical image encryption system is proposed using password key based on phase retrieval algorithm (PRA). In the encryption process, a shared image is taken as a symmetric key and the plaintext is encoded into the phase-only mask based on the iterative PRA. The linear relationship between the plaintext and ciphertext is broken using the password key, which can resist the known plaintext attack. The symmetric key and the retrieved phase are imported into the input plane and Fourier plane of 4f system during the decryption, respectively, so as to obtain the plaintext on the CCD. Finally, we analyse the key space of the password key, and the results show that the proposed scheme can resist a brute force attack due to the flexibility of the password key.     

Hybrid structured phase mask in frequency plane for optical double image encryption in gyrator transform domain

This paper proposes a method of double image encryption based on hybrid structured phase mask (HSPM) in the gyrator transform (GT) domain. The scheme becomes more secure by parameters used in the HSPM. These HSPMs are generated by using the combination of the optical vortex phase masks and secondary images after taking Fourier transform (FT). The input images are encrypted and recovered with correct values of HSPMs, rotation angles of GT and their keys used during the encryption. The use of an HSPM-based phase mask increases the security and key space for encryption. It can also be implemented opto-electronically. The mean square error calculated between the input and retrieved images shows the efficacy of scheme. The proposed method has also been investigated for its sensitivity to encryption parameters and its security against occlusion and noise attacks under a number of iterations. A set of numerical simulation results support the feasibility and security of the proposed scheme.     

Optical encryption system that uses phase conjugation in a photorefractive crystal

We implement an optical encryption system based on double-random phase encoding of the data at the input and the Fourier planes. In our method we decrypt the image by generating a conjugate of the encrypted image through phase conjugation in a photorefractive crystal. The use of phase conjugation results in near-diffraction-limited imaging. Also, the key that is used during encryption can also be used for decrypting the data, thereby alleviating the need for using a conjugate of the key. The effect of a finite space-bandwidth product of the random phase mask on the encryption system's performance is discussed. A theoretical analysis is given of the sensitivity of the system to misalignment errors of a Fourier plane random phase mask.     

Security enhancement of a phase-truncation based image encryption algorithm

The asymmetric cryptosystem, which is based on phase-truncated Fourier transforms (PTFTs), can break the linearity of conventional systems. However, it has been proven to be vulnerable to a specific attack based on iterative Fourier transforms when the two random phase masks are used as public keys to encrypt different plaintexts. An improvement from the asymmetric cryptosystem may be taken by relocating the amplitude values in the output plane. In this paper, two different methods are adopted to realize the amplitude modulation of the output image. The first one is to extend the PTFT-based asymmetrical cryptosystem into the anamorphic fractional Fourier transform domain directly, and the second is to add an amplitude mask in the Fourier plane of the encryption scheme. Some numerical simulations are presented to prove the good performance of the proposed cryptosystems.     

Image encryption based on interference that uses fractional Fourier domain asymmetric keys

We propose an image encryption technique based on the interference principle and phase-truncation approach in the fractional Fourier domain. The proposed scheme offers multiple levels of security with asymmetric keys and is free from the silhouette problem. Multiple input images bonded with random phase masks are independently fractional Fourier transformed. Amplitude truncation of obtained spectrum helps generate individual and universal keys while phase truncation generates two phase-only masks analytically. For decryption, these two phase-only masks optically interfere, and this results in the phase-truncated function in the output. After using the correct random phase mask, universal key, individual key, and fractional orders, the original image is retrieved successfully. Computer simulation results with four gray-scale images validate the proposed method. To measure the effectiveness of the proposed method, we calculated the mean square error between the original and the decrypted images. In this scheme, the encryption process and decryption keys formation are complicated and should be realized digitally. For decryption, an optoelectronic scheme has been suggested.     

QR code-based non-linear image encryption using Shearlet transform and spiral phase transform

In this paper, we propose a new quick response (QR) code-based non-linear technique for image encryption using Shearlet transform (ST) and spiral phase transform. The input image is first converted into a QR code and then scrambled using the Arnold transform. The scrambled image is then decomposed into five coefficients using the ST and the first Shearlet coefficient, C₁ is interchanged with a security key before performing the inverse ST. The output after inverse ST is then modulated with a random phase mask and further spiral phase transformed to get the final encrypted image. The first coefficient, C₁ is used as a private key for decryption. The sensitivity of the security keys is analysed in terms of correlation coefficient and peak signal-to noise ratio. The robustness of the scheme is also checked against various attacks such as noise, occlusion and special attacks. Numerical simulation results are shown in support of the proposed technique and an optoelectronic set-up for encryption is also proposed.     

Color image security system using double random-structured phase encoding in gyrator transform domain

A novel method for encoding color information based on a double random phase mask and a double structured phase mask in a gyrator transform domain is proposed. The amplitude transmittance of the Fresnel zone plate is used as structured phase-mask encoding. A color image is first segregated into red, green, and blue component images. Each of these component images are then independently encrypted using first a random phase mask placed at the image plane and transmitted through the first structured phase mask. They are then encoded by the first gyrator transform. The resulting information is again encrypted by a second random phase mask placed at the gyrator transform plane and transmitted through the second structured phase mask, and then encoded by the second gyrator transform. The system parameters of the structured phase mask and gyrator transform in each channel serve as additional encryption keys and enlarge the key space. The encryption process can be realized with an electro-optical hybrid system. The proposed system avoids problems arising from misalignment and benefits of a higher space-bandwidth product. Numerical simulations are presented to confirm the security, validity, and possibility of the proposed idea.     

Double-image encryption by iterative phase retrieval algorithm in fractional Fourier domain

A novel double-image encryption algorithm is proposed, which can simultaneously encrypt two images into a single one as the amplitude of a fractional Fourier transform with two different groups of fractional orders. The two original images can be retrieved independently by fractional Fourier transforms with two different groups of fractional orders, one public phase mask, and two different private phase masks. The proposed approach can enlarge the key space, achieve faster convergence in the iterative process, and avoid cross-talk between the two images in reconstruction. Numerical simulations are presented to verify its validity and efficiency.     

Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask

A single channel asymmetric color image encryption scheme is proposed that uses an amplitude- and phase- truncation approach with interference of polarized wavefronts. Instead of commonly used random phase masks, wavelength-dependent structured phase masks (SPM) are used in the fractional Fourier transform domain for image encoding. The primary color components bonded with different SPMs are combined into one grayscale image using convolution. We then apply the amplitude and phase truncation to the fractional spectrum, which helps generate unique decryption keys. The encrypted image bonded with a different SPM is then encoded into a polarization selective diffractive optical element. The proposed scheme alleviates the alignment problem of interference and does not need iterative encoding and offers multiple levels of security. The effect of a special attack to the proposed asymmetric cryptosystem has been studied. To measure the effectiveness of the proposed method, we calculated the mean square error between the original and the decrypted images. The computer simulation results support the proposed idea.     

基于圆柱衍射与离散余弦变换的图像光学加密算法

目的为了实现多幅图像的同步加密,并增强加密系统的抗破译能力,提出一种基于圆柱衍射域的相位截断与离散余弦变换的多图像光学加密算法。方法首先引入压缩感知(CS,Compress Transform)方法,对输入明文实施压缩;基于离散余弦变换DCT(Discrete Cosine Transform)对压缩明文完成分解,获取相应的DCT系数,形成系数矩阵;构建迭代复数,将每个压缩明文对应的系数矩阵融合为一个复矩阵,通过DCT逆变换,形成一幅组合图像。联合Hilbert变换与波带片相位模型,构建调制掩码;引入圆柱衍射域的相位截断机制,联合调制掩码,对组合图像实施光学加密,获取密文与私钥。结果实验数据表明,相对于已有的多图像同步加密方法而言,所提算法具备更高的加密安全性,密文熵值以及相邻像素间的相关系数分别达到了7.998,0.0012,且具有强烈的密钥敏感性。结论所提加密算法可以抵御网络中外来攻击,在图像信息防伪领域具有一定的参考价值。     

Optical colour image encryption using spiral phase transform and chaotic pixel scrambling

In this study, we propose a new optical colour image encryption technique using spiral phase transform and chaotic pixel scrambling. For encryption, three channels of the colour image i.e. red, green and blue are first separated and modulated with three different structured phase masks. Spiral phase transform (SPT) with a particular order of modified spiral phase function (MSPF) is utilized for further processing. Random modulus decomposition is applied to the complex output after SPT to generate the private key for decryption. The pixels of the image are scrambled by using the chaotic Tinkerbell map for enhanced security. The order of MSPF, three structured phase masks, parameters of Tinkerbell mapping, and the private key generated during the encryption process serve as the security keys. The robustness of the proposed method is checked against various potential attacks. A series of numerical simulation results are presented to validate the proposed colour image encryption method.     

Study on the influence of key errors on the deciphered image in the double random phase encryption system by applying affine cryptography

In this paper, an explanation of the double random phase encryption technique using affine cryptography is proposed. The principle of this technique to decipher an optical image may be regarded as an optical realization of the affine cryptography. During the deciphering process of double random phase encryption based on the 4-f optical system, if there are errors in the random phase, which plays as a decryption key, these errors will be added to the encrypted image in the form of noise. The signal-to-noise ratio of the decrypted image has been analysed under the situation that the errors had occurred, both in the position of lateral direction and the value of the pixel function from the random phase mask. Furthermore, the fault tolerance of orientation in the decipher system has been discussed when only a part of the random phase mask is used.     

Asymmetric hybrid encryption scheme based on modified equal modulus decomposition in hybrid multi-resolution wavelet domain

In this paper, an asymmetric hybrid encryption scheme, using coherent superposition and modified equal modulus decomposition in a hybrid multi-resolution wavelet, is proposed. The hybrid multi-resolution wavelet is generated using fractional Fourier transform of multiple orders and Walsh transform. The fractional orders of the fractional Fourier transform increase the key space and hence provide additional strength to the cryptosystem. The designed scheme has a large key space to avoid brute-force attack and is non-linear in nature. The scheme is validated on grey-scale images. Computer-based simulations have been performed to verify the validity and performance of the proposed scheme against various attacks. Scheme's robustness to the special attack is also checked. Results show that single equal modulus decomposition with fractional Fourier transform and hybrid transform are vulnerable to the special attack, whereas the proposed scheme endures the special attack.     

基于混合幅度-相位检索技术与二维耦合混沌映射的光学图像加密算法

目的为了解决当前光学图像加密算法主要将单色光束直接作用于明文,使其在解密过程中易出现丢失颜色信息等问题。方法文中设计基于混合幅度-相位检索技术与二维耦合混沌映射的光学图像加密算法。首先,提取彩色图像的R, G, B分量;随后,引入Logistic映射与Sine映射,通过对二者进行非线性耦合,形成二维复合混沌映射;利用彩色图像的像素信息来迭代复合映射,获取3个混沌序列,通过构建位置引擎混淆机制,对R,G,B分量进行置乱;基于Logistic映射,利用明文像素生成的初值条件对其进行迭代,输出一个混沌随机掩码;最后,基于幅度-相位截断方法和Gyrator变换,设计混合幅度-相位检索技术,利用单向二进制相位函数和随机掩码,对置乱后的R, G, B分量进行加密,获取相应的检测振幅,再将其进行组合,形成实值函数的加密密文。结果实验结果显示,与当前光学图像加密机制相比,所提算法具有更高的安全性与解密质量,具备较强的抗明文攻击能力。结论所提加密技术具有较高的抗攻击能力,能够安全保护图像在网络中传输,在信息防伪等领域具有较好的应用价值。     

Color image hiding based on the phase retrieval technique and Arnold transform

A new (to our knowledge) method is proposed in this paper for color image hiding and extracting using the phase retrieval algorithm in the fractional Fourier transform (FRFT) domain and Arnold transform (ART). Based on a cascaded phase iterative FRFT algorithm, the three channels (R, G, and B) of the secret color image permuted by ART are encrypted. Then the encoded information is embedded in the blue channel (B channel) of the enlarged color host image. Using the security enhanced encryption method, not only the random phase mask and the wavelength but also the transform parameters of ART and FRFT are provided as additional keys for decryption. It is shown that the security of information hiding will be enhanced. Computer simulations are performed to show the hiding capacity of the proposed system. Numerical results are presented to verify the validity and efficiency of the proposed method.     

基于双向相关扩散与非线性混沌S盒的图像加密算法

目的 当前混沌加密方案主要采用存在迭代周期性的序列与单向扩散机制来实现像素的混淆,设计一种加密算法以解决其抗破译性能较弱的问题。方法 设计了基于双向相关扩散与非线性S盒的图像加密算法。借助哈希方案,形成一个与初始图像内容相关的密钥;基于2D混合混沌函数,利用子密钥来设计位置交叉规则,实现明文的像素置乱;基于线性分阶变换,联合混沌随机数组,构建一个16×16的非线性S盒;定义S盒的循环向前移位机制和向前扩散机制,对置乱图像完成正向加密;再更新混合混沌系统的初始条件,构建逆向扩散机制,对正向密文完成反向加密。结果 测试数据显示,与已有混沌加密方案相比,在安全性和效率方面,所提方案的优势更大,其时耗时仅为0.59 s,且稳定的NPCR和UACI值分别达到了99.74%,33.69%。结论 所提加密方案可以抵御网络中外来攻击,可充分保证图像内容的真实性。     

Multiple images encryption method via spiral phase mask rotations under a JTC system

A method of multiple-image encryption via spiral phase mask rotations based on the joint transform correlator encryption system was proposed. Multiple images can be encrypted into one ciphertext through this approach. When decrypted the ciphertext, we have no need to produce too many key masks, only need rotate the key mask to the angle corresponding to the plaintext. The system also has good resistance to occlusion attack and differential attack. Computer simulations initially verified the correctness of this method, and the experimental results also confirmed its validity further.     

Image compression and encryption scheme with hyper-chaotic system and mean error control

Based on a hyper-chaotic system, an image compression and encryption scheme is presented by adopting mean error control to improve the quantization compression performance of the discrete cosine transform (DCT) coefficients. The transform coefficients of DCT forming a structure similar to the sub-band can be classified and encoded. Then the image is scanned with Zigzag operation in different directions to achieve sufficiently scrambled effects. The cyclic shift matrix for image encryption is generated by the hyper-chaotic system. The four initial inputs for generating the cyclic shift matrix serve as the key. Simulation results demonstrate the security and the effectiveness of the proposed image compression and encryption scheme.     

Shift-tolerance property of fully phase encryption that uses a joint transform correlator

We technically investigate the robustness of an image encryption technique that uses a virtual phase image and a joint transform correlator (JTC) in the frequency domain. An encrypted image is obtained by the Fourier transform of the product of a virtual phase image, which camouflages the original image, and a random phase image. The resulting image is then decrypted by use of a decrypting key made from the proposed phase assignment rule in order to enhance the level of security. We demonstrate that the encrypted image generated by the proposed JTC-based decryption technique is robust to data loss and image shift.     

Shift-tolerance property of an optical double-random phase-encoding encryption system

We investigate the shift-tolerance property of the decrypting phase mask in an optical double-random phase-encoding encryption system. A simple method for improving the shift tolerance of the phase mask is proposed. We demonstrate how the robustness to data loss of the encrypted image extends the shift tolerance of the decrypting phase mask. The signal-to-noise ratio is calculated. Both a computer simulation and an experiment are presented.