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Juan M. Vilardy
Grupo de Óptica e Informática, Department of Electronic Engineering, Universidad Popular del Cesar, Valledupar, Cesar, Colombia

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Journal article
Published: 15 May 2020 in Optik
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We present a new experimental system for optical encryption using a nonlinear joint transform correlator (JTC) to implement the optical security technique of the double random phase encoding (DRPE). The DRPE, which is usually performed in a 4f-processor, encodes an image into a noisy distribution (encrypted image) by using two random phase masks (RPMs). In our experimental setup, the input plane of the JTC is fully encoded in phase and this plane contains two non-overlapping data functions (images). In the encryption step, the phase-encoded image to be encrypted and the two RPMs are placed in the input plane of the JTC with the purpose of obtaining the needed intensity distributions at the output plane to compute the encrypted image. The optical and numerical transformations are performed in the Fourier domain. A nonlinear operation is introduced to modify the joint power spectrum (JPS) of the JTC in order to reproduce exactly the same results of the DRPE. The experimental optical encryption scheme based on a three-step JTC is implemented by using an optoelectronic setup. The input plane of the JTC is optically implemented by means of a phase-only spatial light modulator (SLM). The decryption process is performed using a virtual optical system. Experimental and numerical results of the optical encryption and simulated decryption systems are presented, in order to show the feasibility of the proposed security system.

ACS Style

Juan M. Vilardy; María S. Millán; Elisabet Pérez-Cabré. Experimental optical encryption scheme for the double random phase encoding using a nonlinear joint transform correlator. Optik 2020, 217, 164653 .

AMA Style

Juan M. Vilardy, María S. Millán, Elisabet Pérez-Cabré. Experimental optical encryption scheme for the double random phase encoding using a nonlinear joint transform correlator. Optik. 2020; 217 ():164653.

Chicago/Turabian Style

Juan M. Vilardy; María S. Millán; Elisabet Pérez-Cabré. 2020. "Experimental optical encryption scheme for the double random phase encoding using a nonlinear joint transform correlator." Optik 217, no. : 164653.

Journal article
Published: 14 December 2019 in Photonics
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We propose a new encryption system based on a nonlinear joint transform correlator (JTC) using the information of two biometrics (one digital fingerprint for each user) as security keys of the encryption system. In order to perform the decryption and authentication in a proper way, it is necessary to have the two digital fingerprints from the respective users whose simultaneous authentication is pursued. The proposed security system is developed in the Fourier domain. The nonlinearity of the JTC along with the five security keys given by the three random phase masks and the two digital fingerprints of the two users allow an increase of the system security against brute force and plaintext attacks. The feasibility and validity of this proposal is demonstrated using digital fingerprints as biometrics in numerical experiments.

ACS Style

Juan M. Vilardy O.; María S. Millán; Elisabet Pérez-Cabré. Image Encryption System Based on a Nonlinear Joint Transform Correlator for the Simultaneous Authentication of Two Users. Photonics 2019, 6, 128 .

AMA Style

Juan M. Vilardy O., María S. Millán, Elisabet Pérez-Cabré. Image Encryption System Based on a Nonlinear Joint Transform Correlator for the Simultaneous Authentication of Two Users. Photonics. 2019; 6 (4):128.

Chicago/Turabian Style

Juan M. Vilardy O.; María S. Millán; Elisabet Pérez-Cabré. 2019. "Image Encryption System Based on a Nonlinear Joint Transform Correlator for the Simultaneous Authentication of Two Users." Photonics 6, no. 4: 128.

Journal article
Published: 26 November 2019 in Photonics
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We propose the use of the Jigsaw transform (JT) and the iterative cosine transform over a finite field in order to encrypt and decrypt images. The JT is a nonlinear operation that allows one to increase the security over the encrypted images by adding new keys to the encryption and decryption systems. The finite field is a finite set of integer numbers where the basic mathematical operations are performed using modular arithmetic. The finite field used in the encryption and decryption systems has an order given by the Fermat prime number 257. The iterative finite field cosine transform (FFCT) was used in our work with the purpose of obtaining images that had an uniform random distribution. We used a security key given by an image randomly generated and uniformly distributed. The JT and iterative FFCT was utilized twice in the encryption and decryption systems. The encrypted images presented a uniformly distributed histogram and the decrypted images were the same original images used as inputs in the encryption system. The resulting decrypted images had a high level of image quality in comparison to the image quality of the decrypted images obtained by the actual optical decryption systems. The proposed encryption and decryption systems have three security keys represented by two random permutations used in the JTs and one random image. The key space of the proposed encryption and decryption systems is larger. The previous features of the security system allow a better protection of the encrypted image against brute force and statistical analysis attacks.

ACS Style

Juan M. Vilardy O.; Leiner Barba J.; Cesar O. Torres M.. Image Encryption and Decryption Systems Using the Jigsaw Transform and the Iterative Finite Field Cosine Transform. Photonics 2019, 6, 121 .

AMA Style

Juan M. Vilardy O., Leiner Barba J., Cesar O. Torres M.. Image Encryption and Decryption Systems Using the Jigsaw Transform and the Iterative Finite Field Cosine Transform. Photonics. 2019; 6 (4):121.

Chicago/Turabian Style

Juan M. Vilardy O.; Leiner Barba J.; Cesar O. Torres M.. 2019. "Image Encryption and Decryption Systems Using the Jigsaw Transform and the Iterative Finite Field Cosine Transform." Photonics 6, no. 4: 121.

Journal article
Published: 16 November 2019 in Photonics
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The gyrator transform (GT) is used for images processing in applications of light propagation. We propose new image processing operators based on the GT, these operators are: Generalized shift, convolution and correlation. The generalized shift is given by a simultaneous application of a spatial shift and a modulation by a pure linear phase term. The new operators of convolution and correlation are defined using the GT. All these image processing operators can be used in order to design and implement new optical image processing systems based on the GT. The sampling theorem for images whose resulting GT has finite support is developed and presented using the previously defined operators. Finally, we describe and show the results for an optical image encryption system using a nonlinear joint transform correlator and the proposed image processing operators based on the GT.

ACS Style

Ronal A. Perez; Juan M. Vilardy O.; Cesar O. Torres M.. Image Processing Operators Based on the Gyrator Transform: Generalized Shift, Convolution and Correlation. Photonics 2019, 6, 120 .

AMA Style

Ronal A. Perez, Juan M. Vilardy O., Cesar O. Torres M.. Image Processing Operators Based on the Gyrator Transform: Generalized Shift, Convolution and Correlation. Photonics. 2019; 6 (4):120.

Chicago/Turabian Style

Ronal A. Perez; Juan M. Vilardy O.; Cesar O. Torres M.. 2019. "Image Processing Operators Based on the Gyrator Transform: Generalized Shift, Convolution and Correlation." Photonics 6, no. 4: 120.

Journal article
Published: 07 November 2019 in Photonics
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A well-known technique for optical image encryption is the double random phase encoding (DRPE) technique, which uses two random phase masks (RPMs), one RPM at the input plane of the encryption system and the other RPM at the Fourier plane of the optical system, in order to obtain the encrypted image. In this work, we propose to use tilted planes for the Fourier and the output planes of the optical DRPE encryption system with the purpose of adding two new security keys, which are the angles of the tilted planes. The optical diffraction on a tilted plane is computed using the angular spectrum of plane waves and the coordinate rotation in the Fourier domain. The tilted distributions at the intermediate and output planes of the optical DRPE encryption system are the second RPM and the encrypted image, respectively. The angles of the tilted planes allow improvement to the security of the encrypted image. We perform several numerical simulations with the purpose of demonstrating the validity and feasibility of the proposed image encryption system.

ACS Style

Juan M. Vilardy O.; Carlos J. Jimenez; Cesar O. Torres M.. Optical Image Encryption System Using Several Tilted Planes. Photonics 2019, 6, 116 .

AMA Style

Juan M. Vilardy O., Carlos J. Jimenez, Cesar O. Torres M.. Optical Image Encryption System Using Several Tilted Planes. Photonics. 2019; 6 (4):116.

Chicago/Turabian Style

Juan M. Vilardy O.; Carlos J. Jimenez; Cesar O. Torres M.. 2019. "Optical Image Encryption System Using Several Tilted Planes." Photonics 6, no. 4: 116.

Journal article
Published: 07 November 2019 in Photonics
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The Collins diffraction transform (CDT) describes the optical wave diffraction from the generic paraxial optical system. The CDT has as special cases the diffraction domains given by the Fourier, Fresnel and fractional Fourier transforms. In this paper, we propose to describe the optical double random phase encoding (DRPE) using a nonlinear joint transform correlator (JTC) and the CDT. This new description of the nonlinear JTC-based encryption system using the CDT covers several optical processing domains, such as Fourier, Fresnel, fractional Fourier, extended fractional Fourier and Gyrator domains, among others. The maximum number of independent design parameters or new security keys of the proposed encryption system using the CDT increases three times in comparison with the same encryption system that uses the Fourier transform. The proposed encryption system using the CDT preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The viability of this encryption system is verified and analysed by numerical simulations.

ACS Style

Juan M. Vilardy O.; Ronal A. Perez; Cesar O. Torres M.. Optical Image Encryption Using a Nonlinear Joint Transform Correlator and the Collins Diffraction Transform. Photonics 2019, 6, 115 .

AMA Style

Juan M. Vilardy O., Ronal A. Perez, Cesar O. Torres M.. Optical Image Encryption Using a Nonlinear Joint Transform Correlator and the Collins Diffraction Transform. Photonics. 2019; 6 (4):115.

Chicago/Turabian Style

Juan M. Vilardy O.; Ronal A. Perez; Cesar O. Torres M.. 2019. "Optical Image Encryption Using a Nonlinear Joint Transform Correlator and the Collins Diffraction Transform." Photonics 6, no. 4: 115.

Conference paper
Published: 13 June 2019 in Journal of Physics: Conference Series
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We use the fractional convolution, nonlinear operations and random phase masks (RPMs) in order to encrypt images. The definition used in this paper of the fractional convolution is based on the fractional Fourier transform (FrFT). The amplitude and phase truncation are nonlinear operations that allow to select a specific information of a complex-valued image. The encryption and decryption systems are based on the double random phase encoding (DRPE). At the beginning of the encryption process, the image to encrypt is encoded in phase. The rest of the encryption and decryption process use two RPMs, the fractional convolution and the amplitude and phase truncation operations in a sequential way in order to get the encrypted and decrypted image. The amplitude and phase truncation and the phase encoding are nonlinear operations that improving the security of the encrypted image, because the obtained key space of the proposed encryption process is very larger. The fractional order of the FrFT introduces a new key for the security system and the encrypted image of the proposed encryption system is a real-valued image. The encryption-decryption system has five security keys. All these five keys with their correct values are necessary in the decryption process with the purpose of obtaining the original image that was encrypted in the encryption process.

ACS Style

Juan M. Vilardy; Cesar O. Torres; Carlos Jimenez. Fractional convolution and nonlinear operations applied to the image encryption. Journal of Physics: Conference Series 2019, 1221, 012058 .

AMA Style

Juan M. Vilardy, Cesar O. Torres, Carlos Jimenez. Fractional convolution and nonlinear operations applied to the image encryption. Journal of Physics: Conference Series. 2019; 1221 (1):012058.

Chicago/Turabian Style

Juan M. Vilardy; Cesar O. Torres; Carlos Jimenez. 2019. "Fractional convolution and nonlinear operations applied to the image encryption." Journal of Physics: Conference Series 1221, no. 1: 012058.

Conference paper
Published: 13 June 2019 in Journal of Physics: Conference Series
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In this work, the occlusion and noise test on the encrypted image produced by a joint transform correlator-based encryption system in the Fresnel domain (FrD) are computed and presented, in order to check the performance of this security system with respect to the image quality resulting in the decryption process for the retrieved image. The encryption system based on a joint transform correlator (JTC) in the FrD was proposed by us, with the purpose of using a lensless optical setup. We test the performance of this security system when the encrypted image is affected by common sources of degradation such as noise (additive and multiplicative) or partial occlusion. Finally, we evaluate the performance and robustness of the security system in the FrD by using the metric of the root mean square error (RMSE) between the image to encrypt and the decrypted image when the encrypted image is degraded by noise or modified by occlusion.

ACS Style

Juan M. Vilardy; Maria Millan; Elisabet Pérez–Cabré. Occlusion and noise tests on the encrypted image produced by a security system based on a joint transform correlator and the Fresnel transform. Journal of Physics: Conference Series 2019, 1221, 012046 .

AMA Style

Juan M. Vilardy, Maria Millan, Elisabet Pérez–Cabré. Occlusion and noise tests on the encrypted image produced by a security system based on a joint transform correlator and the Fresnel transform. Journal of Physics: Conference Series. 2019; 1221 (1):012046.

Chicago/Turabian Style

Juan M. Vilardy; Maria Millan; Elisabet Pérez–Cabré. 2019. "Occlusion and noise tests on the encrypted image produced by a security system based on a joint transform correlator and the Fresnel transform." Journal of Physics: Conference Series 1221, no. 1: 012046.

Conference paper
Published: 16 May 2019 in Journal of Physics: Conference Series
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The discrete cosine transform is a very important mathematical tool for image processing operations, such as filtering, recognition, segmentation, compression, etc. We present the design and implementation of the description and synthesis in VHDL code of the discrete cosine transform over the finite field with an order given by the Mersenne prime number 127, in order to perform the symmetric convolution operation. The development of the VHDL code for the discrete cosine transform and the symmetric convolution operations are performed using the HDL Coder in Simulink. The discrete cosine transform over finite field is defined using a new trigonometric transform proposed recently. The main aim for the development of the discrete cosine transform and the symmetric convolution hardware architectures over finite field is to integrate these architectures in applications of filtering, encryption and recognition of images.

ACS Style

J M Vilardy; L Barba; C O Torres. Design and implementation in VHDL code of the discrete cosine transform over finite fields for symmetric convolution operation. Journal of Physics: Conference Series 2019, 1219, 012020 .

AMA Style

J M Vilardy, L Barba, C O Torres. Design and implementation in VHDL code of the discrete cosine transform over finite fields for symmetric convolution operation. Journal of Physics: Conference Series. 2019; 1219 (1):012020.

Chicago/Turabian Style

J M Vilardy; L Barba; C O Torres. 2019. "Design and implementation in VHDL code of the discrete cosine transform over finite fields for symmetric convolution operation." Journal of Physics: Conference Series 1219, no. 1: 012020.

Conference paper
Published: 16 May 2019 in Journal of Physics: Conference Series
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In this paper, the fractional Fourier operators, the random phase masks and the nonlinear operations of amplitude and phase truncations are utilized to encrypt and decrypt images. We use the following fractional Fourier operators in the image encryption-decryption system: the fractional Fourier transform, the fractional traslation and the fractional correlation. The proposed encryption system uses nonlinear operations, such as phase encoding and truncation operations, in order to increase the security of the encrypted image. The encryption-decryption system has the following security keys: one fractional order of the fractional Fourier transform, two random phase masks and two pseudorandom code images. When all the proper security keys are used in the decryption system, the obtained decrypted image is a replica of the image to encrypt.

ACS Style

J M Vilardy; R Perez; C Jimenez. Nonlinear encryption system based on the fractional Fourier operators and truncation operations. Journal of Physics: Conference Series 2019, 1219, 012018 .

AMA Style

J M Vilardy, R Perez, C Jimenez. Nonlinear encryption system based on the fractional Fourier operators and truncation operations. Journal of Physics: Conference Series. 2019; 1219 (1):012018.

Chicago/Turabian Style

J M Vilardy; R Perez; C Jimenez. 2019. "Nonlinear encryption system based on the fractional Fourier operators and truncation operations." Journal of Physics: Conference Series 1219, no. 1: 012018.

Conference paper
Published: 13 June 2017 in Journal of Physics: Conference Series
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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.

ACS Style

Juan M. Vilardy; Carlos J. Jimenez; Ronal Perez. Image encryption using the Gyrator transform and random phase masks generated by using chaos. Journal of Physics: Conference Series 2017, 850, 12012 .

AMA Style

Juan M. Vilardy, Carlos J. Jimenez, Ronal Perez. Image encryption using the Gyrator transform and random phase masks generated by using chaos. Journal of Physics: Conference Series. 2017; 850 ():12012.

Chicago/Turabian Style

Juan M. Vilardy; Carlos J. Jimenez; Ronal Perez. 2017. "Image encryption using the Gyrator transform and random phase masks generated by using chaos." Journal of Physics: Conference Series 850, no. : 12012.

Conference paper
Published: 01 January 2017 in Journal of Physics: Conference Series
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ACS Style

Ronal Perez; Juan M. Vilardy; Carlos J. Jimenez. Nonlinear image encryption system using the Gyrator transform and truncation operations. Journal of Physics: Conference Series 2017, 792, 12046 .

AMA Style

Ronal Perez, Juan M. Vilardy, Carlos J. Jimenez. Nonlinear image encryption system using the Gyrator transform and truncation operations. Journal of Physics: Conference Series. 2017; 792 ():12046.

Chicago/Turabian Style

Ronal Perez; Juan M. Vilardy; Carlos J. Jimenez. 2017. "Nonlinear image encryption system using the Gyrator transform and truncation operations." Journal of Physics: Conference Series 792, no. : 12046.

Conference paper
Published: 01 January 2017 in Journal of Physics: Conference Series
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ACS Style

Carlos J. Jimenez; Juan M. Vilardy; Ronal Perez. A simplification of the fractional Hartley transform applied to image security system in phase. Journal of Physics: Conference Series 2017, 792, 12043 .

AMA Style

Carlos J. Jimenez, Juan M. Vilardy, Ronal Perez. A simplification of the fractional Hartley transform applied to image security system in phase. Journal of Physics: Conference Series. 2017; 792 ():12043.

Chicago/Turabian Style

Carlos J. Jimenez; Juan M. Vilardy; Ronal Perez. 2017. "A simplification of the fractional Hartley transform applied to image security system in phase." Journal of Physics: Conference Series 792, no. : 12043.

Conference paper
Published: 01 January 2017 in Journal of Physics: Conference Series
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ACS Style

Ronal Perez; Juan M. Vilardy; Cesar O. Torres. Mathematical description of the two-dimensional Gabor transform. Application to image encryption. Journal of Physics: Conference Series 2017, 792, 12047 .

AMA Style

Ronal Perez, Juan M. Vilardy, Cesar O. Torres. Mathematical description of the two-dimensional Gabor transform. Application to image encryption. Journal of Physics: Conference Series. 2017; 792 ():12047.

Chicago/Turabian Style

Ronal Perez; Juan M. Vilardy; Cesar O. Torres. 2017. "Mathematical description of the two-dimensional Gabor transform. Application to image encryption." Journal of Physics: Conference Series 792, no. : 12047.