Optical Cryptosystems. Naveen K. Nishchal

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СКАЧАТЬ of including biometrics (face, fingerprint, iris, etc), and suitability for 2D data/images. Using the concept of holography, a three-dimensional (3D) object/scene can also be secured.

      For encoding data securely, optics offers several degrees of freedom such as amplitude, phase, wavelength, polarization, spatial frequency, and optical angular momentum to encode data securely. An intensity sensing device, such as a charge-coupled device (CCD) camera cannot record any phase information. It is possible to tuck away an optically based message in only one small section of a 2D array, a trick that forces unauthorized users to find the message’s position before they can begin to decode it. Therefore, it is believed that optical encryption techniques would provide a more complex environment and would be more resistant to attacks than purely electronic systems are.

      With the pioneering work on double random phase encoding (DRPE), optical techniques for information security have triggered much interest [1–3]. In the DRPE scheme, an input image to be encrypted is bonded with a random phase mask (RPM) and the product function is Fourier transformed. In the Fourier plane, another RPM is placed. Thus, the spectrum is again multiplied with the second RPM and its Fourier transformation is carried out, which gives a noisy image. This noisy image is called the encrypted image, which is a stationary white noise. Both the RPMs used in input and the Fourier plane are statistically independent and their values lie in the range [0,2π]. For decryption, the process is reversed and the conjugate of the RPMs at respective locations are used.

      An optical information system consists of light source, lenses, mirrors, beam splitters, detectors, display devices such as a spatial light modulator (SLM), and a CCD camera. These components can be arranged in various configurations to suit the type of desired optical information processing setup.

      Information in the form of a light wave passes through a converging lens that introduces delay or phase shift to the incident wavefront by an amount proportional to the thickness of lens, refractive index of the lens, and the wavelength of light. The light is distributed at the back focal plane of the lens, according to the spatial frequencies that are present in the original information. This spatial distribution in the back focal plane can be described mathematically as the Fourier transform of the input information. The Fourier transform capability of the converging lens is a crucial property of the optical information processors because it allows further manipulation of the optical information in the spatial frequency domain [4].

      Holograms have been used in credit cards, identity cards, monetary bills, and many other important documents for security purposes. With the rapid technological advancement in the computers, CCD technology, image processing hardware and software, printers, scanners and copiers, it is increasingly becoming possible to reproduce complex pictures, symbols, logos, etc. Therefore, it has now become possible to duplicate a holographic pattern. The publication of pioneering work on DRPE has broadened the research area of information security like encryption, authentication, watermarking, and hiding. The optical encryption techniques have been realized and have stimulated research in the information security areas [5–8].

      Pattern recognition is a science that concerns the description or classification of measurements. Pattern recognition techniques are often important components of intelligent systems and are used for both data processing and in decision-making. Opto-electronic techniques of pattern recognition for secure verification purposes are growing rapidly because of unique advantages offered by optical technologies [9]. Of late, the idea of authentication of credit cards, passports, driving license, and other personal identities has attracted much attention. The schemes use complex phase patterns that cannot be seen/copied by an intensity sensing device. Some security-enhanced optical security verification schemes have also been reported.

      Amongst the optical security techniques, encryption is an effective approach to ensure the protection of information (text, image, and video) from unauthorized use or access. To secure the stored information, it is required to encrypt the data. An unauthorized user cannot reveal the original data without knowledge of the exact random key code. Original information/data is encoded optically by using various encryption techniques including DRPE, polarization encryption, joint transform correlator (JTC)-based encryption, digital-optical image encryption, digital holography (DH)-based encryption, encryption using diffractive imaging, interference-based encryption, interference of polarized light-based encryption, chaos-based encryption, and quick response (QR) code-based encryption. Out of these, DRPE and its derivative techniques have been studied extensively. Figure 2.1 shows the growth in literature in the field of optical security over the years. There has been a constant increase in the number of articles published globally on the topic, which confirms the growing interest in the subject. No commercial device has been reported employing optical technology, but it is believed that such a product would be available in the coming future [8].

      Figure 2.1. Literature growth on optical information security techniques.

2.2 Encryption using linear canonical transforms

      During the last few decades, many signal processing operations have been brought into the realm of Fourier optics. Some of them belong to the class of the linear canonical transforms (LCTs). LCT is a four parameter class of linear integral transforms, which is a flexible transform and possesses extra degrees of freedom without increasing the computational complexity [10]. It has received considerable attention over the period in optical information processing in general and information security applications in particular. Fractional Fourier transform (FRT), Fresnel transform (FrT), and gyrator transform (GT) belong to such a class while wavelet transformation, fractional convolution, and Wigner distribution belong to the category of linear combinations of LCTs or as cascades of such transformations. After the implementation of basic DRPE, subsequent optical encryption methods based on such transformations have been focused on encoding information. There are clear benefits (additional keys without extra computational cost) of these optical transforms in image encryption, watermarking, and steganography applications. The brief introduction of such systems has been discussed in the following subsections.

2.2.1 Double random phase encoding

      In the DRPE technique, a primary image is encrypted using two RPMs, one bonded with the primary image and another placed in the Fourier domain, respectively. The schematic diagram of double random Fourier plane encoding is shown in figures 2.2(a) and (b). In DRPE, two statistically independent RPMs; exp{i2πR₁(x,y)} and exp{i2πR₂(u,v)} are employed at the image (input) and Fourier plane to encode an input image f(x,y) into a ciphertext E(x,y) as a complex-valued and stationary white noise. R₁(x,y) and R₂(u,v) are two independent white sequences uniformly distributed in [0,1].

      Figure 2.2. (a) Schematic diagram of the DRPE-based encryption scheme. (b) Schematic diagram of the DRPE-based decryption scheme.

      The first step is to bond an input image f(x,y) with an RPM, exp{i2πR₁(x,y)} СКАЧАТЬ