We propose a technique to protect and preserve a private key or a passcode in an encrypted two-dimensional graphical image. The plaintext private key or the passcode is converted into an encrypted QR code and embedded into a real-life color image with a steganographic scheme. The private key or the passcode is recovered from the stego color image by first extracting the encrypted QR code from the color image, followed by decryption of the QR code. The cryptographic key for encryption of the QR code is generated from the output of a Linear Feedback Shift Register (LFSR), initialized by a seed image chosen by the user. The user can store the seed image securely, without the knowledge of an attacker. Even if an active attacker modifies the seed image (without knowledge of the fact that it is the seed image), the user can easily restore it if he/she keeps multiple copies of it, so that the encryption key can be regenerated easily. Our experiments prove the feasibility of the technique using sample private key data and real-life color images.
KEYWORDS: Convolution, Fourier transforms, Digital signal processing, Optical signal processing, Optics education, Image processing, Digital image processing, Analog electronics, Optical simulations, Correlation function
Convolution operation is indispensable in studying analog optical and digital signal processing. Equally important is the correlation operation. The time domain community often teaches convolution and correlation only with one dimensional time signals. That does not clearly demonstrate the effect of convolution and correlation between two signals. Instead if we consider two dimensional spatial signals, the convolution and correlation operations can be very clearly explained. In this paper, we propose a lecture demonstration of convolution and correlation between two spatial signals using the Fourier transform tool. Both simulation and optical experiments are possible using a variety of object transparencies. The demonstration experiments help to clearly explain the similarity and the difference between convolution and correlation operations. This method of teaching using simulation and hands-on experiments can stimulate the curiosity of the students. The feedback of the students, in my class teaching, has been quite encouraging.
We propose a Fourier domain asymmetric cryptosystem for multimodal biometric security. One modality of biometrics (such as face) is used as the plaintext, which is encrypted by another modality of biometrics (such as fingerprint). A private key is synthesized from the encrypted biometric signature by complex spatial Fourier processing. The encrypted biometric signature is further encrypted by other biometric modalities, and the corresponding private keys are synthesized. The resulting biometric signature is privacy protected since the encryption keys are provided by the human, and hence those are private keys. Moreover, the decryption keys are synthesized using those private encryption keys. The encrypted signatures are decrypted using the synthesized private keys and inverse complex spatial Fourier processing. Computer simulations demonstrate the feasibility of the technique proposed.
Inspired by recent results of artificial color due to Caulfield, we carry out intuitive experimental investigations on color sensing under microwave illumination. Experiments have been carried out using a Gunn diode as the microwave source and a microwave diode as a detector. More precise experimental studies have also been carried out utilizing a vector network analyzer. Preliminary results of the experiments validate the feasibility of sensing and discriminating otherwise visual colors under microwave illumination. Caulfield's presumption possibly paves the way for artificial color perception using microwaves.
We propose a new technique for three-dimensional (3D) target recognition using the phase information from a Fourier transform profilometer (FTP). Instead of cross-correlating the 3D target/nontargets-induced distorted grating patterns or the associated phase differences directly, the phase information are rather utilized to synthesize two complex harmonic functions, spatial frequency distributions of which are proportional to the computed profilometric phase maps of the target and the nontargets and hence to respective shape information. These complex harmonic functions due to the target and the nontargets are cross-correlated to produce highest correlation peak at the target location and almost no correlation peak for others. The feasibility of the technique is
demonstrated by detailed simulations and experiments showing an excellent discrimination capability for 3D target recognition.
The kernel associated with Fresnel diffraction, which is an exponential chirp function, has recently been shown to possess the shifting and scaling properties of wavelet functions. However, these scaling chirp functions do not satisfy the commonly used admissibility conditions. We propose to synthesize a class of quasi-wavelet filter functions by taking difference of two such chirp functions with two different scaling depths and term these filters as difference-of-chirps (DOC). The Fourier transform of DOC functions have zero values at the origin, and can be used for edge feature extraction. Computer simulations as well as some experimental results have been presented.
A simple hybrid diffractive-refractive optical element is developed for simultaneous display of the image and the spectrum of an object in a single plane. An optically recorded holographic lens followed by a conventional Fourier lens constitutes the building block for the double channel image processor. Preliminary results are presented.
It is well known that a coherently illuminated conventional lens-based optical system can be used to display either the spatial frequency spectrum or the image of an object which are located in different planes. But, to get both of them in a single plane is difficult. We have suggested a simple method of achieving this. Two holographic optical elements (lens) of two different focal lengths are multiplexed on the same hologram, one focal length being double of the other. The multiplexed holographic lens is utilized to display the image and the spectrum of an object in a single plane in two spatially separated positions. Preliminary experimental results are presented.
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