Dual paths cryptosystem based on tilt Fresnel diffraction using non-spherical mirror and phase modulation in expanded fractional Fourier transform domain
Hang Chen, Zhengjun Liu, Camel Tanougast, Feifei Liu, Walter Blondel
In this paper, a dual optics paths optical image cryptosystem based on tilt Fresnel diffraction and a phase modulation in extend fractional Fourier transform (eFrFT) domain is presented. The tilt Fresnel is designed by using a non-spherical mirror. A part of data from the original image is modulated by the mirror, while the other part is encoded by an expanded fractional Fourier transform. Besides, the random data of the dual channels is combined for forming the encrypted image. The structure parameters in designing the optical hardware system and the random phase can be regarded as decryption keys. Various potential attack experiments are implemented to check the validity of the proposed cryptographic system.
In this paper, a dual optics paths optical image cryptosystem based on tilt Fresnel diffraction and a phase modulation in extend fractional Fourier transform (eFrFT) domain is presented. The tilt Fresnel is designed by using a non-spherical mirror. A part of data from the original image is modulated by the mirror, while the other part is encoded by an expanded fractional Fourier transform. Besides, the random data of the dual channels is combined for forming the encrypted image. The structure parameters in designing the optical hardware system and the random phase can be regarded as decryption keys. Various potential attack experiments are implemented to check the validity of the proposed cryptographic system.
Abstract We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks.
We present a nonlinear optical cryptosystem with multi-dimensional keys including phase, polarization and diffraction distance. To make full use of the degrees of freedom that optical processing offers, an elaborately designed vector wave with both a space-variant phase and locally linear polarization is generated with a common-path interferometer for illumination. The joint transform correlator in the Fresnel domain, implemented with a double optical wedge, is utilized as the encryption framework which provides an additional key known as the Fresnel diffraction distance. Two nonlinear operations imposed on the recorded joint Fresnel power distribution (JFPD) by a charge coupled device (CCD) are adopted. The first one is the division of power distribution of the reference window random function which is previously proposed by researchers and can improve the quality of the decrypted image. The second one is the recording of a hybrid JFPD using a micro-polarizers array with orthogonal and random transmissive axes attached to the CCD. Then the hybrid JFPD is further scrambled by substituting random noise for partial power distribution. The two nonlinear operations break the linearity of this cryptosystem and provide ultra security. We verify our proposal using a quick response code for noise-free recovery.
Most of the existing selective encryption schemes are based on image processing and cannot be realized by optical structures, so their practicality is limited. Combining the optical design, a local hybrid optical encryption system based on double random phase encoding is proposed. The system proposed in this paper possesses a common aperture and dual optical path structure, which is widely used in optical design and can effectively improve the practicality of optical encryption system. First, important information and non-important information in the original image are separated by a selective beam splitter. Then light waves carrying important information enter into the 4f system for encryption, and light waves carrying non-important information enter into the diffraction system for encryption. Finally, part of the diffraction system ciphertext is replaced with 4f system ciphertext to obtain the final encrypted image. Decryption is the reverse process of encryption. First, the 4f system ciphertext is cut out from the final ciphertext. Then the 4f system ciphertext is used to restore the information replaced in the diffraction system ciphertext, thereby obtaining the complete diffraction system ciphertext. Finally, the two ciphertexts go through the reverse process of their respective systems to complete the decryption. By comparing the statistical characteristics and mean square error of the original image and the encrypted image, the effectiveness of the proposed system's encryption process is proved. By analyzing the peak signal-to-noise ratio of the original image and the decrypted image, the effectiveness of the proposed system's decryption process is proved. The sensitivity of each key of the system is analyzed to prove the security of the system. Especially the system is highly sensitive to selective encryption key, which proves the effectiveness and security of the proposed system for selective encryption. Through simulation, it is verified that the proposed system is very resistant to diffraction attacks. Even if he can obtain all the diffraction keys, the attacker still cannot obtain the selectively encrypted information. Finally, through simulation, it is verified that the proposed system has good noise resistance and crop resistance, and high robustness as well. The proposed system can realize the selective encryption through optical structure, which is safe, effective and highly robust, and thus improving the practicality of selective optical encryption system.
A number of methods have recently been proposed in the literature for the encryption of two-dimensional information by use of optical systems based on the fractional Fourier transform. Typically, these methods require random phase screen keys for decrypting the data, which must be stored at the receiver and must be carefully aligned with the received encrypted data. A new technique based on a random shifting, or jigsaw, algorithm is proposed. This method does not require the use of phase keys. The image is encrypted by juxtaposition of sections of the image in fractional Fourier domains. The new method has been compared with existing methods and shows comparable or superior robustness to blind decryption. Optical implementation is discussed, and the sensitivity of the various encryption keys to blind decryption is examined.
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.
Abstract The similarity between in-plane directions of spatial optics and overlapped time ranges of temporal optics is introduced as a new rule of the space–time duality. Applying this rule, an optical dual random phase encoding (DRPE) cryptosystem in the temporal anamorphic fractional Fourier transform (TAFrFT) domain is proposed for physical-level protection of time-varying signals. The structure of a TAFrFT system is an anamorphic time lens (ATL) sandwiched by two identical dispersion elements. The additional key provided by a TAFrFT system is only related to phase profile of the involved ATL, leading to a dispersion-independent manner of key updating as well as an enlarged key space (KS) in comparison with the conventional temporal FrFT and Fresnel transform system. This manner of key updating has potential as a one-time key strategy to evade the intrinsic linearity and symmetry weakness of DRPE-like temporal cryptosystems, due to the updating speed being comparable to the frame rate of plaintext signals. As the temporal counterpart of a spatial optical device composed of cylindrical lenses along different directions, an ATL is designed as an equal-spaced array of time lenses with unipolar phase, constant extension, and varying phase height. Implemented by an arbitrary waveform generator (AWG)-driven electro-optic phase modulator (EOPM), the time interval of adjacent time lenses, extension of each time lens, and the standard phase height are optimally designed as functions of the AWG bandwidth B M and the EOPM damage phase threshold Γ 0 . By numerical simulations, a 16-slot input optical Gaussian pulse sequence with half pulse width of 10 ps and frame length of 2000 ps is encrypted with a KS near 2 698 provided by ATLs at parameters B M = 100 GHz and Γ 0 = 5 π radians under the state of the art, enough for resistance to brute-force attacks.