Unnikrishnan Gopinathan

A known-plaintext heuristic attack on the Fourier plane encryption algorithm

The Fourier plane encryption algorithm is subjected to a known-plaintext attack. The simulated annealing heuristic algorithm is used to estimate the key, using a known plaintext-ciphertext pair, which decrypts the ciphertext with arbitrarily low error. The strength of the algorithm is tested by using this estimated key to decrypt a different ciphertext which was also encrypted using the same original key. We assume that the plaintext is amplitude-encoded real-valued image, and analyze only the mathematical algorithm rather than a real optical system that can be more secure. The Fourier plane encryption algorithm is found to be susceptible to a known-plaintext heuristic attack.

Cryptanalysis of optical security systems with significant output images

The security of the encryption and verification techniques with significant output images is examined by a known-plaintext attack. We introduce an iterative phase-retrieval algorithm based on multiple intensity measurements to heuristically estimate the phase key in the Fourier domain by several plaintext-cyphertext pairs. We obtain correlation output images with very low error by correlating the estimated key with corresponding random phase masks. Our studies show that the convergence behavior of this algorithm sensitively depends on the starting point. We also demonstrate that this algorithm can be used to attack the double random phase encoding technique.

Key-space analysis of double random phase encryption technique.

We perform a numerical analysis on the double random phase encryption/decryption technique. The key-space of an encryption technique is the set of possible keys that can be used to encode data using that technique. In the case of a strong encryption scheme, many keys must be tried in any brute-force attack on that technique. Traditionally, designers of optical image encryption systems demonstrate only how a small number of arbitrary keys cannot decrypt a chosen encrypted image in their system. However, this type of demonstration does not discuss the properties of the key-space nor refute the feasibility of an efficient brute-force attack. To clarify these issues we present a key-space analysis of the technique. For a range of problem instances we plot the distribution of decryption errors in the key-space indicating the lack of feasibility of a simple brute-force attack.

Generalized in-line digital holographic technique based on intensity measurements at two different planes

In-line digital holography based on two-intensity measurements [Zhang Opt. Lett. 29, 1787 (2004)], is modified by introducing a pi shifting in the reference phase. Such an improvement avoids the assumption that the object beam must be much weaker than the reference beam in strength and results in a simplified experimental implementation. Computer simulations and optical experiments are carried out to validate the method, which we refer to as position-phase-shifting digital holography.

Coherence effects in digital in-line holographic microscopy

We analyze the effects of partial coherence in the image formation of a digital in-line holographic microscope (DIHM). The impulse response is described as a function of cross-spectral density of the light used in the space-frequency domain. Numerical simulation based on the applied model shows that a reduction in coherence of light leads to broadening of the impulse response. This is also validated by results from experiments wherein a DIHM is used to image latex beads using light with different spatial and temporal coherence.

Polarization encoding and multiplexing of two-dimensional signals: application to image encryption

We discuss an optical system that encodes an input signal to a polarization state, using a spatial light modulator (SLM). Using two SLMs the optical system multiplexes two 2D signals in the polarization domain, and we demonstrate the multiplexing of two binary images. The encryption and decryption of two binary images using an XOR operation is also presented.

Role of phase key in the double random phase encoding technique: an error analysis

We perform a numerical analysis of the double random phase encryption-decryption technique to determine how, in the case of both amplitude and phase encoding, the two decryption keys (the image- and Fourier-plane keys) affect the output gray-scale image when they are in error. We perform perfect encryption and imperfect decryption. We introduce errors into the decrypting keys that correspond to the use of random distributions of incorrect pixel values. We quantify the effects that increasing amounts of error in the image-plane key, the Fourier-plane key, and both keys simultaneously have on the decrypted image. Quantization effects are also examined.

A Projection System for Real World Three-Dimensional Objects Using Spatial Light Modulators

We discuss a projection system for real world three-dimensional objects using spatial light modulators (SLM). An algorithm to encode the digital holograms of real world objects on to an SLM is presented. We present results from experiments to project holograms of real world holograms using a nematic liquid crystal SLM. We discuss the case when the pixel sizes of the charge-coupled device (CCD) and SLM used for recording the hologram and projection are different.

Controlling speckle using lenses and free space

The correlation properties of speckle fields are studied for general paraxial systems. The previous studies on lateral and longitudinal speckle size for the case of free-space propagation (Fresnel transform) are generalized to the case of the linear canonical transform. These results have implications for the control of speckle size, through appropriate design of optical systems, with particular relevance for speckle interferometry.

Metrology and the linear canonical transform

It is shown experimentally that both surface tilt and in-plane translation motion can be independently estimated using the speckle photographic correlation technique by capturing consecutive images in two linear canonical transform domains (using two different quadratic phase systems). A geometric interpretation, based on use of the Wigner distribution function is presented to describe the method and a simple matrix approach, based on the ABCD matrix, is used to quantify it. It is shown that the sensitivity and dynamic range of measurement of both tilt and translation are both variable and depend on the parameters of the ABCD matrix.