Fast algorithm of discrete gyrator transform based on convolution operation

Optics and Lasers in Engineering

Millán

Pérez‐Cabré

2017

Abstract.A novel nonlinear image encryption scheme based on a fully phase nonzeroorder joint transform correlator architecture (JTC) in the Gyrator domain (GD) is proposed. In this encryption scheme, the two non-overlapping data distributions of the input plane of the JTC are fully encoded in phase and this input plane is transformed using the Gyrator transform (GT); the intensity distribution captured in the GD represents a new definition of the joint Gyrator power distribution (JGPD). The JGPD is modified by two nonlinear operations with the purpose of retrieving the encrypted image, with enhancement of the decrypted signal quality and improvement of the overall security. There are three keys used in the encryption scheme, two random phase masks and the rotation angle of the GT, which are all necessary for a proper decryption. Decryption is highly sensitivity to changes of the rotation angle of the GT as well as to little changes in other parameters or keys. The proposed encryption scheme in the GD still preserves the shift-invariance properties originated in the JTC-based encryption in the Fourier domain. The proposed encryption scheme is more resistant to brute force attacks, chosen-plaintext attacks, known-plaintext attacks, and ciphertext-only attacks, as they have been introduced in the cryptanalysis of the JTC-based encryption system. Numerical results are presented and discussed in order to verify and analyze the feasibility and validity of the novel encryption-decryption scheme.

Section: Decryption Schemementioning

confidence: 99%

Section: Decryption Schemementioning

confidence: 99%

Nonlinear image encryption using a fully phase nonzero-order joint transform correlator in the Gyrator domain

Optics and Lasers in Engineering

Millán

Pérez‐Cabré

2017

“…[22]. The digital GT will be computed using the fast algorithm of discrete GT based on convolution operation [24] for the nonlinear image encryption-decryption system that it will be described in section 5.…”

Section: The Gyrator Transformmentioning

confidence: 99%

Image encryption using the Gyrator transform and random phase masks generated by using chaos

Jimenez

Perez

2017

J. Phys.: Conf. Ser.

Abstract. The Gyrator transform (GT), chaotic random phase masks (CRPMs) and a random permutation of the Jigsaw transform (JT) are utilized to design an images encryption-decryption system. The encryption-decryption system is based on the double random phase encoding (DRPE) in the Gyrator domain (GD), this technique uses two random phase masks (RPMs) to encode the image to encrypt (original image) into a random noise. The RPMs are generated by using chaos, these masks are CRPMs. The parameters of the chaotic function have the control of the generation of the CRPMs. We apply a random permutation to the resulting image of the DRPE technique, with the purpose of obtaining an encrypted image with a higher randomness. In order to successfully retrieve the original image (without errors or noise-free) at the output of the decryption system is necessary to have all the proper keys, which are: the rotation angles of the GTs, the parameters of the chaotic function utilized to generate the two CRPMs and the random permutation of the JT. We check and analyze the validity of the image encryption and decryption systems by means of computing simulations. IntroductionThe image encryption is different from traditional cryptology because the spatial, frequency and redundancy features of the image to encrypt are analysed and processed by the image encryption system [1]. The double random phase encoding (DRPE) is a successful method for optical image encryption [1][2][3], the DRPE uses two random phase masks (RPMs) with the purpose of encoding the image to encrypt (original image) into a stationary white noise pattern (encrypted image). One of the main drawbacks of the image encryption systems based on the initial DRPE is that the security of the system is vulnerable to attacks, this weakness is due to the linear property of the DRPE scheme [1][2][3]. The DRPE has been further extended from the Fourier domain to the Fresnel domain [4][5][6], the fractional Fourier domain [7][8][9][10][11][12], the Gyrator domain (GD) [13][14][15][16] and other domains [17][18][19][20], with the purpose of adding more keys and increasing the security of the DRPE system.The Gyrator transform (GT) is a mathematical tool for analysis and processing of twodimensional signals [21]. The GT has been used in optics [22], signal processing [13] and image encryption [13][14][15][16].In this paper, we propose a nonlinear image encryption-decryption system based on the DRPE, the GT, the chaotic random phase masks (CRPMs) and the Jigsaw transform (JT), in order to overcome the security vulnerabilities of the initial DRPE proposed in Ref. [2]. We use the GT to improve the security of the original DRPE by adding a new key for the encryption system (the

“…When the PhCT is applied to the complex-valued image d(x), a photon-limited amplitude information |d(x)|, is generated from the normalized amplitude image g(x) = |d(x)|/ M j=1 |d(x j )| using the equation (4). The pixels that receive at least one photon count are considered in the photon-limited encrypted function d ph (x).…”

Section: Photon Counting Technique (Phct)mentioning

confidence: 99%

“…Figure 1(e) shows the amplitude of the photon-limited encrypted image |e ph (x, y)|, corresponding to figure 1(c) figure 1(f). The digital GT was implemented using the fast algorithm of the discrete GT based on convolution operation [4].…”

Section: Integration Of the Phct With The Drpe In The Gd For Secure Imentioning

confidence: 99%

Secure image encryption and authentication using the photon counting technique in the Gyrator domain

2015 20th Symposium on Signal Processing, Images and Computer Vision (STSIVA)

Millán

Pérez‐Cabré

2015

In this work, we present the integration of the photon counting technique (PhCT) with an encryption system in the Gyrator domain (GD) for secure image authentication. The encryption system uses two random phase masks (RPMs), one RPM is defined at the spatial domain and the other RPM is defined at the GD, in order to encode the image to encrypt (original image) into random noise. The rotation angle of the Gyrator transform adds a new key that increases the security of the encryption system. The decryption system is an inverse system with respect to the encryption system. The PhCT limits the information content of an image in a nonlinear, random and controlled way; the photon-limited image only has a few pixels of information, this type of image is usually known as sparse image. We apply the PhCT over the encrypted image. The resulting image in the decryption system is not a copy of the original image, this decrypted image is a random code that should contain the sufficient information for the authentication of the original image using a nonlinear correlation technique. Finally, we evaluate the peak-to-correlation energy metric for different values of the parameters involved in the encryption and authentication systems, in order to test the verification capability of the authentication system.