Discrete Multiple-parameter Fractional Fourier Research Articles

Double image encryption based on a hybrid phase-truncation scheme

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.

Optical multiple-image encryption in discrete multiple-parameter fractional Fourier transform scheme using complex encoding, theta modulation and spectral fusion

We present a novel encryption method for multiple images in a discrete multiple-parameter fractional Fourier transform scheme, using complex encoding, theta modulation and spectral fusion. All pairs of original images are encoded separately into a complex signal. The spectrum of each complex signal can then be scattered into various positions in the spectral plane and multiplexed into one spectral image with a combination of theta modulation and spectral fusion. After Fourier transforming back to the spatial domain, the multiplexed signal is encrypted in the discrete multiple-parameter fractional Fourier transform domain. Information about the original images can only be successfully decrypted given the possession of all correct keys. The parameters of chaotic pixel scrambling for the proposed method enlarge the key space. Moreover, the proposed method solves the crosstalk problem of multiple images and improves the multiplexing capacity. Numerical simulations demonstrate the effectiveness of the proposed method.

Optical encryption of hyperspectral images using improved binary tree structure and phase-truncated discrete multiple-parameter fractional Fourier transform

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.

Asymmetric multiple-image interference cryptosystem using discrete cosine transform and conditional decomposition

In this study, we propose an asymmetric multiple-image encryption technique based on optical interference that utilizes the discrete cosine transform (DCT) and conditional decomposition. First, the DCT spectrum of each original image is cropped by a low-pass filter and spatially multiplexed into a synthetized spectral signal with the same size as the original image. The synthetized spectral signal is then transformed by the DCT to the spatial domain. After undergoing pixel-scrambling, the synthetized signal is encrypted into three phase-only masks (POMs) based on the interference in the discrete multiple-parameter fractional Fourier transform domain and conditional decomposition. One of the POMs is a plaintext-independent cyphertext and the other two are plaintext-dependent private keys. The silhouette of the original image cannot be identified using only one or two of the POMs, all POMs are required. Finally, we demonstrate the performance of our technique through simulations.

Asymmetric image encryption using phase-truncated discrete multiple-parameter fractional Fourier transform

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.

Silhouette-free image encryption using interference in the multiple-parameter fractional Fourier transform domain.

A novel approach for silhouette-free image encryption based on interference is proposed using discrete multiple-parameter fractional Fourier transform (DMPFrFT), which generalizes from fractional Fourier transform. An original image is firstly applied by chaotic pixel scrambling (CPS) and then encoded into the real part of a complex signal. Using interference principle, the complex signal generates three phase-only masks in DMPFrFT domain. The silhouette of the original image cannot be extracted using one or two of the three phase-only masks. The parameters of both CPS and DMPFrFT can also serve as encryption keys to extend the key space, which further enhance the level of cryptosystem security. Numerical simulations are demonstrated to show the feasibility and validity of this approach.

Dual domain robust watermarking scheme using random DFRFT and least significant bit technique

This paper presents a novel image watermarking scheme that uses multiple-parameter discrete fractional Fourier transform (MPDFRFT) with random DFRFT and least significant bit (LSB) technique. The proposed scheme uses the LSB technique to embed watermark image in an original image, while RDFRFT and MPDFRFT are used to enhance the security of the watermarked image. The presented method aims to make the system more robust and secure at two different levels along with faster embedding and extraction process. The MPDFRFT is input data points of order DFRFT parameters. The MPDFRFT can be converted to the DFRFT when all of its order parameters have same values. On the other hand, RDFRFT is kernel matrix with random values of their DFT eigenvectors and Eigenvalues. Random magnitude and phase of its transformed output are unique features of RDFRFT that utilised to enhance security. LSB technique is preferred for watermark embedding because of its lesser effect on the image perceptibility. In proposed scheme, the cover image is converted into sub-images and MPDFRFT is applied to each sub-image. Then RDFRFT is applied in tandem to transformed sub-images in order to enhance robustness followed by watermark embedding using LSB technique. In watermark extraction process the inverse of MPDFRFT and RDFRFT is applied for reconstruction of original images along with LSB extraction mechanism. The performance of the proposed system is evaluated by using MATLAB software under various attacks and distortions. The simulation results validate that the embedding scheme presented in this work has better performance in terms of robustness along with perceptibility and security over contemporary existing schemes.

Multiple-image encryption using spectral cropping and spatial multiplexing

A multiple-image encryption scheme is proposed using spectral cropping and space multiplexing based on discrete multiple-parameter fractional Fourier transform (DMPFRFT). Spectrum of each original image is firstly cropped by a low-pass filter, and the image is then recovered with the same size of the filter. The recovered images are spatially shifted and multiplexed into a complex signal with the same size of original image. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted into one image by DMPFRFT. The multiplexing images can be retrieved with correct keys, and the original images can be then obtained by enlarging the demultiplexing images. Numerical simulations have been done to demonstrate the validity and the security of the proposed method.

A non-linear preprocessing for opto-digital image encryption using multiple-parameter discrete fractional Fourier transform

In this paper, a novel opto-digital image encryption technique is proposed by introducing a new non-linear preprocessing and using the multiple-parameter discrete fractional Fourier transform (MPDFrFT). The non-linear preprocessing is performed digitally on the input image in the spatial domain using a piecewise linear chaotic map (PLCM) coupled with the bitwise exclusive OR (XOR). The resulting image is multiplied by a random phase mask before applying the MPDFrFT to whiten the image. Then, a chaotic permutation is performed on the output of the MPDFrFT using another PLCM different from the one used in the spatial domain. Finally, another MPDFrFT is applied to obtain the encrypted image. The parameters of the PLCMs together with the multiple fractional orders of the MPDFrFTs constitute the secret key for the proposed cryptosystem. Computer simulation results and security analysis are presented to show the robustness of the proposed opto-digital image encryption technique and the great importance of the new non-linear preprocessing introduced to enhance the security of the cryptosystem and overcome the problem of linearity encountered in the existing permutation-based opto-digital image encryption schemes.

Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method.

Robust Watermarking against Geometric Attacks using Multiple Parameter Discrete Fractional Fourier Transform and Least Significant Bit Technique

Watermarking is an important technique used for copyright protection, authentication, tamper detection and hiding secret information in multimedia contents. In this article a new digital watermarking scheme is proposed based on multiple parameter discrete fractional Fourier transform and using least significant bit (LSB) technique. The multiple parameter discrete fractional Fourier transform (MPDFRFT) is the generalization of the discrete fractional Fourier transform (DFRFT) in terms of its different nature of its fractional orders. The MPDFRFT can converge to DFRFT when all of its fractional order parameters having a similar value. The multiple parameter discrete fractional transforms shows it’s superiority over DFRFT because of that it benefitted us with an extra degree of freedom that is provided by its multiple fractional orders. The LSB technique is more preferable because of its lesser effect on the image characteristics. During the implementation of proposed scheme cover image is subdivided and MPDFRFT is applied to each subdivided image to transformed coefficients and watermark images are embedded by using LSB technique. Similarly during watermark extraction process the reverse order of MPDFRFT is applied for reconstruction of original images along with LSB extraction mechanism. The MPDFRFT fractional order parameters are used as secret key to improve the robustness of the system. The robustness of the watermark image is tested under different attacks such as additive noise, cropping, rotation and Gaussian low-pass filtering is analyzed and the results demonstrate that the embedding scheme has good performance of robustness. The imperceptibility of the proposed scheme against the hostile person is also verified by simulations results.

Hybrid Encryption-Compression Scheme Based on Multiple Parameter Discrete Fractional Fourier Transform with Eigen Vector Decomposition Algorithm

Encryption along with compression is the process used to secure any multimedia content processing with minimum data storage and transmission. The transforms plays vital role for optimizing any encryptioncompression systems. Earlier the original information in the existing security system based on the fractional Fourier transform (FRFT) is protected by only a certain order of FRFT. In this article, a novel method for encryption-compression scheme based on multiple parameters of discrete fractional Fourier transform (DFRFT) with random phase matrices is proposed. The multiple-parameter discrete fractional Fourier transform (MPDFRFT) possesses all the desired properties of discrete fractional Fourier transform. The MPDFRFT converts to the DFRFT when all of its order parameters are the same. We exploit the properties of multipleparameter DFRFT and propose a novel encryptioncompression scheme using the double random phase in the MPDFRFT domain for encryption and compression data. The proposed scheme with MPDFRFT significantly enhances the data security along with image quality of decompressed image compared to DFRFT and FRFT and it shows consistent performance with different images. The numerical simulations demonstrate the validity and efficiency of this scheme based on Peak signal to noise ratio (PSNR), Compression ratio (CR) and the robustness of the schemes against bruit force attack is examined.

Image Compression Based On Multiple Parameter Discrete Fractional Fourier Transform for Satellite and Medical Images

Image Compression Based On Multiple Parameter Discrete Fractional Fourier Transform for Satellite and Medical Images

A Novel Image Encryption Scheme based on Multiple Parameter Discrete Fractional Fourier Transform

is one of the most challenging aspects in internet and Multimedia applications. Encryption is a process which is used to secure data. The Encryption algorithms and suitable transforms play a crucial role to form efficient security systems. In this regard the original information in the existing security system based on the fractional Fourier transform (FRFT) is protected by only a certain order of FRFT. In this paper, we propose a novel method to encrypt an image by using multiple parameters discrete fractional Fourier transform (DFRFT) with random phase matrices. The multiple-parameter discrete fractional Fourier transform (MPDFRFT) possesses all the desired properties of discrete fractional Fourier transform. The MPDFRFT converts to the DFRFT when all of its order parameters are the same. We exploit the properties of multiple-parameter DFRFT and propose a novel encryption scheme using the double random phase in the MPDFRFT domain for encrypting digital data. The proposed encoding scheme with MPDFRFT significantly enhances the data security compared to DFRFT and FRFT and it shows consistent performance with different images. The scheme offers a high degree of resistance towards bruteforce attack.

Double image encryption based on discrete multiple-parameter fractional Fourier transform and chaotic maps

A double image encryption method is proposed by utilizing discrete multiple-parameter fractional Fourier transform and chaotic maps. One of the two original images scrambled by one chaotic map is encoded into the amplitude of a complex signal with the other original image as its phase. The complex signal multiplied by another chaotic random phase mask is then encrypted by discrete multiple-parameter fractional Fourier transform. The parameters in chaotic map and discrete multiple-parameter fractional Fourier transform serve as the keys of this encryption scheme. Numerical simulations have been done to demonstrate the performance of this algorithm.

The discrete multiple-parameter fractional Fourier transform

As a generalization of the Fourier transform (FT), the fractional Fourier transform (FRFT) has many applications in the areas of optics, signal processing, information security, etc. Therefore, the efficient discrete computational method is the vital fundament for the application of the fractional Fourier transform. The multiple-parameter fractional Fourier transform (MPFRFT) is a generalized fractional Fourier transform, which not only includes FRFT as special cases, but also provides a unified framework for the study of FRFT. In this paper, we present in detail the discretization method of the MPFRFT and define the discrete multiple-parameter fractional Fourier transform (DMPFRFT). Then, we utilize the tensor product to define two-dimensional multiple-parameter fractional Fourier transform (2D-MPFRFT) and the corresponding two-dimensional discrete multiple-parameter fractional Fourier transform (2D-DMPFRFT). Finally, as an application, a novel image encryption method based on 2D-DMPFRFT is proposed. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.

Image encryption based on the multiple-parameter discrete fractional Fourier transform and chaos function

In recent years, the chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. In this paper, we propose a new approach for image encryption based on the multiple-parameter discrete fractional Fourier transform and chaotic logistic maps in order to meet the requirements of the secure image transmission. In the proposed image encryption scheme, the image is encrypted by juxtaposition of sections of the image in the multiple-parameter discrete fractional Fourier domains and the alignment of sections is determined by chaotic logistic maps. This method does not require the use of phase keys. The new method has been compared with several existing methods and shows comparable or superior robustness to blind decryption.

On the Security of a Cryptosystem Based on Multiple-Parameters Discrete Fractional Fourier Transform

Pei and Hsue (IEEE Signal Processing Letters, Vol. 13, No. 6, pp. 329-332, June 2006) proposed an encryption scheme based on multiple-parameter discrete fractional Fourier transform. We show that all the building blocks of this scheme are linear, and hence, breaking this scheme, using a known plaintext attack, is equivalent to solving a set of linear equations.

The multiple-parameter discrete fractional Fourier transform

The discrete fractional Fourier transform (DFRFT) is a generalization of the discrete Fourier transform (DFT) with one additional order parameter. In this letter, we extend the DFRFT to have N order parameters, where N is the number of the input data points. The proposed multiple-parameter discrete fractional Fourier transform (MPDFRFT) is shown to have all of the desired properties for fractional transforms. In fact, the MPDFRFT reduces to the DFRFT when all of its order parameters are the same. To show an application example of the MPDFRFT, we exploit its multiple-parameter feature and propose the double random phase encoding in the MPDFRFT domain for encrypting digital data. The proposed encoding scheme in the MPDFRFT domain significantly enhances data security.