Title : Investigation on information security techniques using chaotic maps
Supervisor : Dr. Aloka Sinha, Dept. of Physics, Indian Institute of Technology Delhi, India
Some new information security techniques using chaotic maps have been investigated by using optical techniques and digital electronic techniques. Chaotic maps are related to the nonlinear dynamical systems and it generates the random and uncorrelated signal (Known as chaotic signal) which is very sensitive to the initial condition. Small change in the initial condition gives the drastic change in the chaotic signal. Random phase mask (RPM)has been generated by these chaotic maps which is known as chaotic random phase mask (CRPM). Double random phase encoding method has been used for encryption and decryption of the image. In this method, two CRPMs has been used for encryption. First CRPM is multiplied with input image at input plane and first LCT is performed over it. At the output plane of first LCT, the second CRPM has been introduced and then second LCT has been performed over it as a results encrypted image in obtained at the output plane of second LCT. Computer simulations and experiment results have been presented to verify the validity of the proposed research work.
Computer Simulation:
v RPM has been generated by using chaotic maps which is known as CRPM.
v 2-D single and multiple images have been encryption and decryption by using CRPM and linear canonical transforms (LCTs). These LCTs are fractional Fourier transform, extended fractional Fourier transform, Gyrator transform and Fresnel transform.
v Digital image watermarking has been performed at Gyrator plane.
v Problem of bare decryption (decryption without key) has been solved by using jigsaw transform along with Hartley transform.
v A new Hartley transform has been investigated known as improper Hartley transform. This transform is also solved the problem of bare decryption.
Simulation research work of Ph.D. has been performed on MATLAB platform.
v MATLAB program has been written to generate the 2-dimensional chaotic random phase mask by using 1- dimensional and 2- dimensional chaotic maps.
v MATLAB program has been written for linear canonical transforms such as fractional Fourier transform extended fractional Fourier transform, gyrator transform and Fresnel transform.
v MATLAB program has also been written for real transform Hartley transform and improper Hartley transform.
v MATLAB program has also been written for jigsaw transform.
v MATLAB program has also been written for double random phase encoding method using linear canonical transforms.
v MATLAB program has also been written to calculate the mean square error, signal to noise ratio and peak signal to noise ratio.
Experimental work
Experimental work has been performed by using experimental set of optical encryption and electronic hardware.
v Multiple image encryptions have been done by using digital holographic technique.
Ø He-Ne laser (Wavelength 633nm and power 10mW) has been used as light
source.
Ø Optical set of Mech-Zehender interferometer has been used of encryption and decryption.
Ø CCD camera has been used to capture the holograms.
Ø Spatial light modulator has been used to display the images.
Ø Polarizer and analyzer and quarter wave plate have been used for spatial
Light modulator.
Ø Reconstruction of the hologram has been performed on computer by
Using Fresnel Kirchhoff reconstruction method.
Ø Lenses has been used for performing Linear canonical transform.
Ø Cubic beam splitters have been used to split and combined the object
beam and reference beam.
v Optoelectronic secure communication system has been used to encoding the 1-D Signal by using the chaotic signal, hardware of pulse position modulator and hardware of voltage controlled oscillator. Noisy nature of the encoded signal has been detected by using eye pattern.
Ø Some modifications (technical and component replacement) have been done in the previous proposed electronic circuit of the logistic map. This Modified electronic circuit of the logistic map has been used to generate the chaotic signal and has been designed on PCB.
Ø Electronic circuit of the pulse position modulator and voltage controlled oscillator have been designed on PCB and used for modulation scheme.
Ø Optical fiber has been used as communication channel.
Ø Electronic circuit of eye pattern has been designed on PCB to detect the noisy nature of the encoded signal.
Ø Electronic circuit of DC shift has been designed on PCB to set the signal at zero level.
Ø Electronic circuit of amplifier of ¼ gain has been designed on PCB to set the signal between 0-1 Volt.
Ø Electronic circuit of multiplier has been designed on PCB to multiply the two signal.
Ø Electronic circuit of voltage follower has been designed on PCB to prevent from loading.