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.     

Optical image encryption based on compressive sensing and chaos in the fractional Fourier domain

We propose a novel image encryption algorithm based on compressive sensing (CS) and chaos in the fractional Fourier domain. The original image is dimensionality reduction measured using CS. The measured values are then encrypted using chaotic-based double-random-phase encoding technique in the fractional Fourier transform domain. The measurement matrix and the random-phase masks used in the encryption process are formed from pseudo-random sequences generated by the chaotic map. In this proposed algorithm, the final result is compressed and encrypted. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys for distribution simultaneously. Numerical experiments verify the validity and security of the proposed algorithm.     

Image encryption scheme based on random fractional discrete cosine transform and dependent scrambling and diffusion

An image encryption scheme is proposed by combining the random fractional discrete cosine transform (RFrDCT) with the dependent scrambling and diffusion (DSD). The application of the randomization, irrational choice and vectorization of fractional orders and the randomization of generating sequences improves the key-sensitivity and thus enlarges the key space greatly. Both the locations and the values of RFrDCT transformed coefficients are changed during the stage of DSD to further enhance the security of image encryption scheme. Numerical simulations demonstrate that the proposed image encryption scheme is feasible, secure and capable of resisting common classical attacks.     

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.     

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.     

Image encryption based on a reality-preserving fractional discrete cosine transform and a chaos-based generating sequence

A novel image encryption technique based on a reality-preserving fractional discrete cosine transform (FrDCT) and a chaos-based generating sequence is proposed. The FrDCT is a generalization of the discrete cosine transform (DCT). This reality-preserving FrDCT inherits the virtues of both the DCT and fractional transform, providing improved security and flexibility by employing the generating sequence as an extra key in addition to the fractional orders. The most fascinating advantage of the FrDCT is its reality-preserving property, which ensures real ciphertext for real plaintext, which is conducive to display, storage, and transmission. Performance and security analysis demonstrates that this algorithm is valid, secure, sensitive to keys, and robust to noise and occlusion attacks.     

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.     

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.     

Greyscale image encoding and watermarking based on optical asymmetric cryptography and variational image decomposition

In this paper, a novel greyscale image encoding and a watermarking scheme based on optical asymmetric cryptography and variational image decomposition (VID) are proposed. In this proposed scheme, the greyscale watermark is encoded into a noise-like pattern by the phase-truncated Fresnel transform (PT-FrT)-based optical asymmetric cryptography. The greyscale host image is decomposed into its cartoon part and texture part by the VID technique. After that, the encoded watermark is embedded into the host image’s texture part by a discrete wavelet transform (DWT) based fusion approach. The proposed scheme can achieve a better watermark invisibility and a higher robustness by embedding the watermark into the host image’s texture part. Additionally, the proposed scheme can achieve a high security, because the PT-FrT-based optical asymmetric cryptography can resist some common cryptographic attacks. The feasibility, robustness and security of the proposed scheme have been demonstrated by extensive experiments and comparison with other relevant image encoding and watermarking schemes.     

Flexible multiple-image encryption algorithm based on log-polar transform and double random phase encoding technique

We present a novel multiple-image encryption algorithm by combining log-polar transform with double random phase encoding in the fractional Fourier domain. In this algorithm, the original images are transformed to annular domains by inverse log-polar transform and then the annular domains are merged into one image. The composite image is encrypted by the classical double random phase encoding method. The proposed multiple-image encryption algorithm takes advantage of the data compression characteristic of log-polar transform to obtain high encryption efficiency and avoids cross-talk in the meantime. Optical implementation of the proposed algorithm is demonstrated and numerical simulation results verify the feasibility and the validity of the proposed algorithm.     

Joint image compression–encryption using discrete fractional transforms

Exchange of data in the form of text and image on internet is in fast progression and it is spawning new compression and encryption algorithms for bandwidth and security respectively. We have proposed a new kind of joint algorithm using discrete fractional transforms for compression–encryption of image. In this algorithm, the discrete fractional Fourier transform which is discrete version of fractional Fourier transform, is used to compress the images with variation of its parameter ‘α’ (order of transform). The compressed image is encrypted using discrete fractional cosine transform to provide security. The advantage of this method is its feasible implementation in practice, superior, robustness, security and sensitivity of keys, which has a good prospect and practicability in information security field. Results of computer simulations are presented to verify the validity of the proposed method such as mean square error (MSE) and peak signal to noise ratio between the original image and decrypted image. Sensitivity for right decryption key is proved with respect to MSE.     

Image encryption using the random FrDCT and the chaos-based game of life

A novel image encryption algorithm using the random fractional DCT (RFrDCT) and the chaos-based Game of Life (GoL) is presented here. Firstly the plaintext image is transformed by the reality-preserving RFrDCT into the RFrDCT domain, and a preliminary encryption output is obtained. And then a combination of the confusion and diffusion (C&D) processes is performed in the transform domain, where the confusion process is carried out by GoL, and the diffusion process is carried out by an XOR operation. Therefore a more random-like encryption result can be obtained after further encryption by the C&D. Both the GoL and XOR operation are based on chaos whose control parameters serve as cipher keys in order to enlarge cipher space and enhance key sensitivity. Theoretical analysis and simulation experiments for the proposed algorithm are described, the desirable encryption performance is obtained, and it is secure against various common attacks.     

A New Multi Chaos-Based Compression Sensing Image Encryption

The advancements in technology have substantially grown the size of image data. Traditional image encryption algorithms have limited capabilities to deal with the emerging challenges in big data, including compression and noise toleration. An image encryption method that is based on chaotic maps and orthogonal matrix is proposed in this study. The proposed scheme is built on the intriguing characteristics of an orthogonal matrix. Gram Schmidt disperses the values of pixels in a plaintext image by generating a random orthogonal matrix using logistic chaotic map. Following the diffusion process, a block-wise random permutation of the data is performed using multi-chaos. The proposed scheme provides sufficient security and resilience to JPEG compression and channel noise through a series of experiments and security evaluations. It enables Partial Encryption (PE) for faster processing as well as complete encryption for increased security. The higher values of the number of pixels change rates and unified average change intensity confirm the security of the encryption scheme. In contrast to other schemes, the proposed approach can perform full and partial encryption depending on security requirements.     

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。     

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。     

Affine cryptosystem of double-random-phase encryption based on the fractional Fourier transform

An affine mapping mathematical expression of the double-random-phase encryption technique has been deduced utilizing the matrix form of discrete fractional Fourier transforms. This expression clearly describes the encryption laws of the double-random-phase encoding techniques based on both the fractional Fourier transform and the ordinary Fourier transform. The encryption process may be regarded as a substantial optical realization of the affine cryptosystem. It has been illustrated that the encryption process converts the original image into a white Gaussian noise with a zero-mean value. Also, the decryption process converts the data deviations of the encrypted image into white Gaussian noises, regardless of the type of data deviations. These noises superimpose on the decrypted image and degrade the signal-to-noise ratio. Numerical simulations have been implemented for the different types of noises introduced into the encrypted image, such as the white noise with uniform distribution probability, the white noise with Gaussian distribution probability, colored noise, and the partial occlusion of the encrypted image.     

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.     

双光束叠加与差异模的光学图像加密算法

目的为了解决当前基于干涉原理的光学图像加密算法因存在轮廓显现导致其安全性不高的问题,提出双光束相干叠加与差异模矢量分解的图像加密算法。方法基于Gyrator变换,将明文变成一个Gyrator频域的复杂函数;随后引入矢量分解方法,将Gyrator频域复杂函数进行差异分解,输出幅度与相位不均等的2个矢量成分;利用2个相位掩码对矢量成分进行调制,将其从频域变为空域,将其相位部分视为私密,而幅度部分视为最终加密密文。结果实验显示,与当前基于模均等分解的图像加密技术相比,所提算法具有更高的保密性与敏感性,有效消除了轮廓显现问题。结论所提算法能够确保图像信息在网络中的安全传输,有效抵御外部攻击,在包装印刷与防伪二维码等领域具有一定的应用价值。     

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.