We demonstrate in this communication the suppression of chaos in a chaotic oscillator by establis... more We demonstrate in this communication the suppression of chaos in a chaotic oscillator by establishing mutual coupling with an another weak periodic oscillator of the same kind. We have chosen specific locations of the state variable for the mutual coupling and the suppression of chaos is observed via period halving route as a result of increase in mutual coupling strength between the oscillators. The technique developed does not require any prior knowledge of the system dynamics and the system parameters are not changed explicitly. The method is expected to be useful for those physical chaotic systems in which direct accessibility of its parameters is either difficult or not possible.
Recently, Pareek et al. (Phys. Lett. A 309 (2003) 75) have developed a symmetric key block cipher... more Recently, Pareek et al. (Phys. Lett. A 309 (2003) 75) have developed a symmetric key block cipher algorithm using a one-dimensional chaotic map. In this paper, we propose a symmetric key block cipher algorithm in which multiple one-dimensional chaotic maps are used instead of a one-dimensional chaotic map. However, we also use an external secret key of variable length (maximum 128-bits) as used by Pareek et al. In the present cryptosystem, plaintext is divided into groups of variable length (i.e. number of blocks in each group is different) and these are encrypted sequentially by using randomly chosen chaotic map from a set of chaotic maps. For block-by-block encryption of variable length group, number of iterations and initial condition for the chaotic maps depend on the randomly chosen session key and encryption of previous block of plaintext, respectively. The whole process of encryption/decryption is governed by two dynamic tables, which are updated time to time during the encryption/decryption process. Simulation re- sults show that the proposed cryptosystem requires less time to encrypt the plaintext as compared to the existing chaotic cryptosystems and further produces the ciphertext having flat distribution of same size as the plaintext.
In recent years, it is observed that the third-order explicit autonomous differential equation, n... more In recent years, it is observed that the third-order explicit autonomous differential equation, named as jerk equation, represents an interesting sub-class of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we investigate the global dynamics of a special family of jerk systems ...
Communications in Nonlinear Science and Numerical Simulation, 2009
In a recent study Jaganathan and Sinha [Jaganathan R, Sinha S. A q-deformed nonlinear map. Phys L... more In a recent study Jaganathan and Sinha [Jaganathan R, Sinha S. A q-deformed nonlinear map. Phys Lett A 2005;338:277-87] have introduced a scheme for the q-deformation of nonlinear maps using the logistic map as an example and shown that the q-logistic map exhibits a wide spectrum of dynamical behaviours including the co-existence of attractors (which is a rare phenomenon in one-dimensional maps). In this paper, we aim to analyze another famous one-dimensional map -the Gaussian map (a known one-dimensional map exhibiting co-existing attractors) subject to the same qdeformation scheme. We compare the dynamical behaviour of the Gaussian map and q-deformed Gaussian map with a special attention on the regions of the parameter space, where these maps exhibit co-existing attractors. An important conclusion of the present study is that the appearance of co-existing attractors for a particular choice of system parameters can be understood as a consequence of the presence of multiple fixed points in one-dimensional nonlinear maps; however the converse is not always true.
Journal of Electron Spectroscopy and Related Phenomena, 2009
We report the results of our calculations of triple differential cross section (TDCS) for electro... more We report the results of our calculations of triple differential cross section (TDCS) for electron impact single ionization (i.e. (e, 2e) processes) from the 3s shell of argon using a modified distorted wave Born approximation formalism by including correlation-polarization potential, which accounts for both correlation and polarization effects. We observe that DWBA formalism including polarization potential is able to reproduce most of the trends of experimental data and hence provide a fututre direction for further investigation of ionization process from the 3s shell of argon. We also compare our results with the available theoretical and experimental results. The present calculations significantly improve the agreement with the experimental results but still there are certain discrepancies, which is a matter of further investigation.
A novel and robust chaos-based pseudorandom permutation–substitution scheme for image encryption ... more A novel and robust chaos-based pseudorandom permutation–substitution scheme for image encryption is proposed. It is a loss-less symmetric block cipher and specifically designed for the color images but may also be used for the gray scale images. A secret key of 161-bit, comprising of the initial conditions and system parameter of the chaotic map (the standard map), number of iterations and number of rounds, is used in the algorithm. The whole encryption process is the sequential execution of a preliminary permutation and a fix number of rounds (as specified in the secret key) of substitution and main permutation of the 2D matrix obtained from the 3D image matrix. To increase the speed of encryption all three processes: preliminary permutation, substitution and main permutation are done row-by-row and column-by-column instead of pixel-by-pixel. All the permutation processes are made dependent on the input image matrix and controlled through the pseudo random number sequences (PRNS) generated from the discretization of chaotic standard map which result in both key sensitivity and plaintext sensitivity. However each substitution process is initiated with the initial vectors (different for rows and columns) generated using the secret key and chaotic standard map and then the properties of rows and column pixels of input matrix are mixed with the PRNS generated from the standard map. The security and performance analysis of the proposed image encryption has been performed using the histograms, correlation coefficients, information entropy, key sensitivity analysis, differential analysis, key space analysis, encryption/decryption rate analysis etc. Results suggest that the proposed image encryption technique is robust and secure and can be used for the secure image and video communication applications.
A novel permutation-substitution scheme, which is based on chaotic standard map, for the image en... more A novel permutation-substitution scheme, which is based on chaotic standard map, for the image encryption is proposed. It is loss-less symmetric block cipher and specifically designed for the colour images. The initial condition & system parameter of the chaotic standard map, number of iterations and number of rounds constitute the secret key of the algorithm. Firstly we mix all three colour layers (3 D matrix) of the plain image and convert them into a 2D matrix. Each encryption round comprises of three stages: permutation rounds, substitution rounds and again permutation rounds. To increase the speed of encryption, the permutation and substitution are done row-by-row and column-by-column instead of pixel-by-pixel. The permutation process is controlled through the pseudo random number sequences (PRNS) generated from the discretization of chaotic standard map, however in the substitution, the properties of rows and column pixels of various layers are mixed with the PRNS generated from the standard map. The security of the proposed image encryption has been analyzed thoroughly using various statistical analysis, key sensitivity analysis, differential analysis, key space analysis, etc. Results suggest that the proposed image encryption technique can be used for the real time secure image and video communication applications.
Chaotic systems have many interesting features such as sensitivity on initial condition and syste... more Chaotic systems have many interesting features such as sensitivity on initial condition and system parameter, ergodicity and mixing properties. In this paper, we exploit these interesting properties of chaotic systems to design a random bit generator, called CCCBG, in which two chaotic systems are cross-coupled with each other. To evaluate the randomness of the bit streams generated by the CCCBG, the four basic tests: monobit test, serial test, auto-correlation, Poker test and the most stringent tests of randomness: the NIST suite tests have been performed. As a result no patterns have been observed in the bit streams generated by the proposed CCCBG. The proposed CCCBG can be used in many applications requiring random binary sequences and also in the design of secure cryptosystems.
Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms, 2011
We report the distorted wave Born approximation results of triple differential cross section of A... more We report the distorted wave Born approximation results of triple differential cross section of Ar (3p) by positron and electron impact. We compare the results of our calculations with the recent available experimental and theoretical results. We also provide a comparison of our positron impact ionization results with the electron impact ionization results to understand the effect of projectile charge on the projectile-target interaction.
We report the results of triple differential cross section of coplanar (e, 2e) processes on Mg (3... more We report the results of triple differential cross section of coplanar (e, 2e) processes on Mg (3s) atom in modified distorted wave Born approximation (DWBA). The standard DWBA formalism has been modified by including the correlation-polarization potential (which is function of electron density) and post collision interaction. We compare our computed results with the available experimental data and observe that the inclusion of polarization potential in the standard DWBA is able to improve the agreement with experimental results.
It has been recently investigated that the jerk dynamical systems are the simplest ever systems, ... more It has been recently investigated that the jerk dynamical systems are the simplest ever systems, which possess variety of dynamical behaviors including chaotic motion. Interestingly, the jerk dynamical systems also describe various phenomena in physics and engineering such as electrical circuits, mechanical oscillators, laser physics, solar wind driven magnetosphere ionosphere (WINDMI) model, damped harmonic oscillator driven by nonlinear memory term, biological systems etc. In many practical situations chaos is undesirable phenomenon, which may lead to irregular operations in physical systems. Thus from a practical point of view, one would like to convert chaotic solutions into periodic limit cycle or fixed point solutions. On the other hand, there has been growing interest to use chaos profitably by synchronizing chaotic systems due to its potential applications in secure communication. In this paper, we have made a thorough investigation of synchronization of identical chaotic jerk dynamical systems by implementing three well-known techniques: (i) Pecora-Carroll (PC) technique, (ii) Feedback (FB) technique and (iii) Active Passive decomposition (APD). We have given a detailed review of these techniques followed by the results of our investigations of identical synchronization of chaos in jerk dynamical systems. The stability of identical synchronization in all the aforesaid methods has also been discussed through the transversal stability analysis. Our extensive numerical calculation results reveal that in PC and FB techniques the x-drive configuration is able to produce the stable identical synchronization in all the chaotic jerk dynamical systems considered by us (except for a few cases), however y-drive and z-drive configurations do not lead to the stable identical synchronization. For the APD approach, we have suggested a generalized active passive decomposition, which leads to the stable identical synchronization without being bothered about the specific form of the jerk dynamical system. Several other active passive decompositions have also been listed with their corresponding conditional Lyapunov exponents to achieve the stable identical synchronization in various chaotic jerk dynamical systems.
In recent years, the chaos based cryptographic algorithms have suggested some new and efficient w... more In recent years, the chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. In this communication, we propose a new approach for image encryption based on chaotic logistic maps in order to meet the requirements of the secure image transfer. In the proposed image encryption scheme, an external secret key of 80-bit and two chaotic logistic maps are employed. The initial conditions for the both logistic maps are derived using the external secret key by providing different weightage to all its bits. Further, in the proposed encryption process, eight different types of operations are used to encrypt the pixels of an image and which one of them will be used for a particular pixel is decided by the outcome of the logistic map. To make the cipher more robust against any attack, the secret key is modified after encrypting each block of sixteen pixels of the image. The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission. q
Communications in Nonlinear Science and Numerical Simulation, 2009
... Cited By in Scopus (12). Permissions & Reprints. A new substitutiondiffusion bas... more ... Cited By in Scopus (12). Permissions & Reprints. A new substitutiondiffusion based image cipher using chaotic standard and logistic maps. Vinod Patidar a , Corresponding Author Contact Information , E-mail The Corresponding Author , NK Pareek b and KK Sud a. ...
During last one and half decade an interesting relationship between chaos and cryptography has be... more During last one and half decade an interesting relationship between chaos and cryptography has been developed, according to which many properties of chaotic systems such as: ergodicity, sensitivity to initial conditions/system parameters, mixing property, deterministic dynamics and structural complexity can be considered analogous to the confusion, diffusion with small change in plaintext/secret key, diffusion with a small change within one block of the plaintext, deterministic pseudo randomness and algorithmic complexity properties of traditional cryptosystems. As a result of this close relationship several chaos-based cryptosystems have been put forward since 1990. In one of the stages of the development of chaotic stream ciphers, the application of discrete chaotic dynamical systems in pseudo random bit generation has been widely studied recently. In this communication, we propose a novel pseudo random bit generator (PRBG) based on two chaotic logistic maps running side-by-side and starting from random independent initial conditions. The pseudo random bit sequence is generated by comparing the outputs of both the chaotic logistic maps. We discuss the suitability of the logistic map by highlighting some of its interesting statistical properties, which make it a perfect choice for such random bit generation. Finally, we present the detailed results of the statistical testing on generated bit sequences, done by the most stringent tests of randomness: the NIST suite tests, to detect the specific characteristics expected of truly random sequences.
International Journal of Information and Communication Technology, 2010
... Vinod Patidar and Krishan K. Sud ... Keywords: chaotic block cipher; permutation boxes; secre... more ... Vinod Patidar and Krishan K. Sud ... Keywords: chaotic block cipher; permutation boxes; secret key; cryptography. Reference to this paper should be made as follows: Pareek, NK, Patidar, V. and Sud, KK (2010) 'Block cipher using 1D and 2D chaotic maps', Int. ...
Communications in Nonlinear Science and Numerical Simulation, 2010
Recently Patidar et al. [Commun Nonlinear Sci Numer Simulat 14;2009:3056-75] proposed a new subst... more Recently Patidar et al. [Commun Nonlinear Sci Numer Simulat 14;2009:3056-75] proposed a new substitution-diffusion image cipher using chaotic standard and logistic maps, which is very fast and possess all the confusion and diffusion properties that any good cryptosystem should have. Soon after the proposal, Rhouma et al. [Commun Nonlinear Sci Numer Simulat 2010;15:1887-92.] proposed an equivalent description of the PPS09 cryptosystem which facilitated them in the cryptanalysis of the original cipher in terms of chosen plainext and known plaintext attacks. In this paper, we propose modifications in the Patidar et al.'s image cipher to make it robust against these two cryptanalytic attacks. The security analysis shows that the modified image cipher preserves all the good properties of the original cipher and is also capable to stand against the aforesaid attacks.
Communications in Nonlinear Science and Numerical Simulation, 2005
Recently, Pareek et al. [Phys. Lett. A 309 (2003) 75] have developed a symmetric key block cipher... more Recently, Pareek et al. [Phys. Lett. A 309 (2003) 75] have developed a symmetric key block cipher algorithm using a one-dimensional chaotic map. In this paper, we propose a symmetric key block cipher algorithm in which multiple one-dimensional chaotic maps are used instead of a one-dimensional chaotic map. However, we also use an external secret key of variable length (maximum 128-bits) as used by Pareek et al. In the present cryptosystem, plaintext is divided into groups of variable length (i.e. number of blocks in each group is different) and these are encrypted sequentially by using randomly chosen chaotic map from a set of chaotic maps. For block-by-block encryption of variable length group, number of iterations and initial condition for the chaotic maps depend on the randomly chosen session key and encryption of previous block of plaintext, respectively. The whole process of encryption/decryption is governed by two dynamic tables, which are updated time to time during the encryption/decryption process. Simulation results show that the proposed cryptosystem requires less time to encrypt the plaintext as compared to the existing chaotic cryptosystems and further produces the ciphertext having flat distribution of same size as the plaintext.
In this Letter, we propose a symmetric key block cipher algorithm utilizing the essence of chaos.... more In this Letter, we propose a symmetric key block cipher algorithm utilizing the essence of chaos. The proposed cryptosystem does not use explicitly the system parameter or initial condition of the chaotic map as a secret key. However, these parameters are generated by an external secret key of variable length (maximum 128-bits) and used in our algorithm. The encryption of each block of plaintext has been made dependent on the secret key and the cryptosystem is further made robust against any reasonable attack by using the feedback technique. Simulation results show that the proposed cryptosystem requires less time to encrypt the plaintext as compared to the existing chaotic cryptosystems and further produces the ciphertext having flat distribution of same size as the plaintext. available in the literature can be discussed with respect to the following aspects:
Recently, there have been several attempts to explain the features of triple differential cross s... more Recently, there have been several attempts to explain the features of triple differential cross section (TDCS) for the (e, 2e) processes on inert targets Ne, Ar and Xe but there are still certain discrepancies in theoretical results and measurements, which require more theoretical efforts to understand the collision dynamics of these targets. We present in this paper the results of our modified distorted wave Born approximation (DWBA) calculation of TDCS for the ionization of Ne (2p), Ar (3p) and Xe (5p) targets. We modify the standard DWBA formalism by including the correlation-polarization potential (which is function of electron density) and compare our computed results with the available experimental and theoretical data. We observe that the polarization potential is able to improve the agreement with experimental results.
We demonstrate in this communication the suppression of chaos in a chaotic oscillator by establis... more We demonstrate in this communication the suppression of chaos in a chaotic oscillator by establishing mutual coupling with an another weak periodic oscillator of the same kind. We have chosen specific locations of the state variable for the mutual coupling and the suppression of chaos is observed via period halving route as a result of increase in mutual coupling strength between the oscillators. The technique developed does not require any prior knowledge of the system dynamics and the system parameters are not changed explicitly. The method is expected to be useful for those physical chaotic systems in which direct accessibility of its parameters is either difficult or not possible.
Recently, Pareek et al. (Phys. Lett. A 309 (2003) 75) have developed a symmetric key block cipher... more Recently, Pareek et al. (Phys. Lett. A 309 (2003) 75) have developed a symmetric key block cipher algorithm using a one-dimensional chaotic map. In this paper, we propose a symmetric key block cipher algorithm in which multiple one-dimensional chaotic maps are used instead of a one-dimensional chaotic map. However, we also use an external secret key of variable length (maximum 128-bits) as used by Pareek et al. In the present cryptosystem, plaintext is divided into groups of variable length (i.e. number of blocks in each group is different) and these are encrypted sequentially by using randomly chosen chaotic map from a set of chaotic maps. For block-by-block encryption of variable length group, number of iterations and initial condition for the chaotic maps depend on the randomly chosen session key and encryption of previous block of plaintext, respectively. The whole process of encryption/decryption is governed by two dynamic tables, which are updated time to time during the encryption/decryption process. Simulation re- sults show that the proposed cryptosystem requires less time to encrypt the plaintext as compared to the existing chaotic cryptosystems and further produces the ciphertext having flat distribution of same size as the plaintext.
In recent years, it is observed that the third-order explicit autonomous differential equation, n... more In recent years, it is observed that the third-order explicit autonomous differential equation, named as jerk equation, represents an interesting sub-class of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we investigate the global dynamics of a special family of jerk systems ...
Communications in Nonlinear Science and Numerical Simulation, 2009
In a recent study Jaganathan and Sinha [Jaganathan R, Sinha S. A q-deformed nonlinear map. Phys L... more In a recent study Jaganathan and Sinha [Jaganathan R, Sinha S. A q-deformed nonlinear map. Phys Lett A 2005;338:277-87] have introduced a scheme for the q-deformation of nonlinear maps using the logistic map as an example and shown that the q-logistic map exhibits a wide spectrum of dynamical behaviours including the co-existence of attractors (which is a rare phenomenon in one-dimensional maps). In this paper, we aim to analyze another famous one-dimensional map -the Gaussian map (a known one-dimensional map exhibiting co-existing attractors) subject to the same qdeformation scheme. We compare the dynamical behaviour of the Gaussian map and q-deformed Gaussian map with a special attention on the regions of the parameter space, where these maps exhibit co-existing attractors. An important conclusion of the present study is that the appearance of co-existing attractors for a particular choice of system parameters can be understood as a consequence of the presence of multiple fixed points in one-dimensional nonlinear maps; however the converse is not always true.
Journal of Electron Spectroscopy and Related Phenomena, 2009
We report the results of our calculations of triple differential cross section (TDCS) for electro... more We report the results of our calculations of triple differential cross section (TDCS) for electron impact single ionization (i.e. (e, 2e) processes) from the 3s shell of argon using a modified distorted wave Born approximation formalism by including correlation-polarization potential, which accounts for both correlation and polarization effects. We observe that DWBA formalism including polarization potential is able to reproduce most of the trends of experimental data and hence provide a fututre direction for further investigation of ionization process from the 3s shell of argon. We also compare our results with the available theoretical and experimental results. The present calculations significantly improve the agreement with the experimental results but still there are certain discrepancies, which is a matter of further investigation.
A novel and robust chaos-based pseudorandom permutation–substitution scheme for image encryption ... more A novel and robust chaos-based pseudorandom permutation–substitution scheme for image encryption is proposed. It is a loss-less symmetric block cipher and specifically designed for the color images but may also be used for the gray scale images. A secret key of 161-bit, comprising of the initial conditions and system parameter of the chaotic map (the standard map), number of iterations and number of rounds, is used in the algorithm. The whole encryption process is the sequential execution of a preliminary permutation and a fix number of rounds (as specified in the secret key) of substitution and main permutation of the 2D matrix obtained from the 3D image matrix. To increase the speed of encryption all three processes: preliminary permutation, substitution and main permutation are done row-by-row and column-by-column instead of pixel-by-pixel. All the permutation processes are made dependent on the input image matrix and controlled through the pseudo random number sequences (PRNS) generated from the discretization of chaotic standard map which result in both key sensitivity and plaintext sensitivity. However each substitution process is initiated with the initial vectors (different for rows and columns) generated using the secret key and chaotic standard map and then the properties of rows and column pixels of input matrix are mixed with the PRNS generated from the standard map. The security and performance analysis of the proposed image encryption has been performed using the histograms, correlation coefficients, information entropy, key sensitivity analysis, differential analysis, key space analysis, encryption/decryption rate analysis etc. Results suggest that the proposed image encryption technique is robust and secure and can be used for the secure image and video communication applications.
A novel permutation-substitution scheme, which is based on chaotic standard map, for the image en... more A novel permutation-substitution scheme, which is based on chaotic standard map, for the image encryption is proposed. It is loss-less symmetric block cipher and specifically designed for the colour images. The initial condition & system parameter of the chaotic standard map, number of iterations and number of rounds constitute the secret key of the algorithm. Firstly we mix all three colour layers (3 D matrix) of the plain image and convert them into a 2D matrix. Each encryption round comprises of three stages: permutation rounds, substitution rounds and again permutation rounds. To increase the speed of encryption, the permutation and substitution are done row-by-row and column-by-column instead of pixel-by-pixel. The permutation process is controlled through the pseudo random number sequences (PRNS) generated from the discretization of chaotic standard map, however in the substitution, the properties of rows and column pixels of various layers are mixed with the PRNS generated from the standard map. The security of the proposed image encryption has been analyzed thoroughly using various statistical analysis, key sensitivity analysis, differential analysis, key space analysis, etc. Results suggest that the proposed image encryption technique can be used for the real time secure image and video communication applications.
Chaotic systems have many interesting features such as sensitivity on initial condition and syste... more Chaotic systems have many interesting features such as sensitivity on initial condition and system parameter, ergodicity and mixing properties. In this paper, we exploit these interesting properties of chaotic systems to design a random bit generator, called CCCBG, in which two chaotic systems are cross-coupled with each other. To evaluate the randomness of the bit streams generated by the CCCBG, the four basic tests: monobit test, serial test, auto-correlation, Poker test and the most stringent tests of randomness: the NIST suite tests have been performed. As a result no patterns have been observed in the bit streams generated by the proposed CCCBG. The proposed CCCBG can be used in many applications requiring random binary sequences and also in the design of secure cryptosystems.
Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms, 2011
We report the distorted wave Born approximation results of triple differential cross section of A... more We report the distorted wave Born approximation results of triple differential cross section of Ar (3p) by positron and electron impact. We compare the results of our calculations with the recent available experimental and theoretical results. We also provide a comparison of our positron impact ionization results with the electron impact ionization results to understand the effect of projectile charge on the projectile-target interaction.
We report the results of triple differential cross section of coplanar (e, 2e) processes on Mg (3... more We report the results of triple differential cross section of coplanar (e, 2e) processes on Mg (3s) atom in modified distorted wave Born approximation (DWBA). The standard DWBA formalism has been modified by including the correlation-polarization potential (which is function of electron density) and post collision interaction. We compare our computed results with the available experimental data and observe that the inclusion of polarization potential in the standard DWBA is able to improve the agreement with experimental results.
It has been recently investigated that the jerk dynamical systems are the simplest ever systems, ... more It has been recently investigated that the jerk dynamical systems are the simplest ever systems, which possess variety of dynamical behaviors including chaotic motion. Interestingly, the jerk dynamical systems also describe various phenomena in physics and engineering such as electrical circuits, mechanical oscillators, laser physics, solar wind driven magnetosphere ionosphere (WINDMI) model, damped harmonic oscillator driven by nonlinear memory term, biological systems etc. In many practical situations chaos is undesirable phenomenon, which may lead to irregular operations in physical systems. Thus from a practical point of view, one would like to convert chaotic solutions into periodic limit cycle or fixed point solutions. On the other hand, there has been growing interest to use chaos profitably by synchronizing chaotic systems due to its potential applications in secure communication. In this paper, we have made a thorough investigation of synchronization of identical chaotic jerk dynamical systems by implementing three well-known techniques: (i) Pecora-Carroll (PC) technique, (ii) Feedback (FB) technique and (iii) Active Passive decomposition (APD). We have given a detailed review of these techniques followed by the results of our investigations of identical synchronization of chaos in jerk dynamical systems. The stability of identical synchronization in all the aforesaid methods has also been discussed through the transversal stability analysis. Our extensive numerical calculation results reveal that in PC and FB techniques the x-drive configuration is able to produce the stable identical synchronization in all the chaotic jerk dynamical systems considered by us (except for a few cases), however y-drive and z-drive configurations do not lead to the stable identical synchronization. For the APD approach, we have suggested a generalized active passive decomposition, which leads to the stable identical synchronization without being bothered about the specific form of the jerk dynamical system. Several other active passive decompositions have also been listed with their corresponding conditional Lyapunov exponents to achieve the stable identical synchronization in various chaotic jerk dynamical systems.
In recent years, the chaos based cryptographic algorithms have suggested some new and efficient w... more In recent years, the chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. In this communication, we propose a new approach for image encryption based on chaotic logistic maps in order to meet the requirements of the secure image transfer. In the proposed image encryption scheme, an external secret key of 80-bit and two chaotic logistic maps are employed. The initial conditions for the both logistic maps are derived using the external secret key by providing different weightage to all its bits. Further, in the proposed encryption process, eight different types of operations are used to encrypt the pixels of an image and which one of them will be used for a particular pixel is decided by the outcome of the logistic map. To make the cipher more robust against any attack, the secret key is modified after encrypting each block of sixteen pixels of the image. The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission. q
Communications in Nonlinear Science and Numerical Simulation, 2009
... Cited By in Scopus (12). Permissions & Reprints. A new substitutiondiffusion bas... more ... Cited By in Scopus (12). Permissions & Reprints. A new substitutiondiffusion based image cipher using chaotic standard and logistic maps. Vinod Patidar a , Corresponding Author Contact Information , E-mail The Corresponding Author , NK Pareek b and KK Sud a. ...
During last one and half decade an interesting relationship between chaos and cryptography has be... more During last one and half decade an interesting relationship between chaos and cryptography has been developed, according to which many properties of chaotic systems such as: ergodicity, sensitivity to initial conditions/system parameters, mixing property, deterministic dynamics and structural complexity can be considered analogous to the confusion, diffusion with small change in plaintext/secret key, diffusion with a small change within one block of the plaintext, deterministic pseudo randomness and algorithmic complexity properties of traditional cryptosystems. As a result of this close relationship several chaos-based cryptosystems have been put forward since 1990. In one of the stages of the development of chaotic stream ciphers, the application of discrete chaotic dynamical systems in pseudo random bit generation has been widely studied recently. In this communication, we propose a novel pseudo random bit generator (PRBG) based on two chaotic logistic maps running side-by-side and starting from random independent initial conditions. The pseudo random bit sequence is generated by comparing the outputs of both the chaotic logistic maps. We discuss the suitability of the logistic map by highlighting some of its interesting statistical properties, which make it a perfect choice for such random bit generation. Finally, we present the detailed results of the statistical testing on generated bit sequences, done by the most stringent tests of randomness: the NIST suite tests, to detect the specific characteristics expected of truly random sequences.
International Journal of Information and Communication Technology, 2010
... Vinod Patidar and Krishan K. Sud ... Keywords: chaotic block cipher; permutation boxes; secre... more ... Vinod Patidar and Krishan K. Sud ... Keywords: chaotic block cipher; permutation boxes; secret key; cryptography. Reference to this paper should be made as follows: Pareek, NK, Patidar, V. and Sud, KK (2010) 'Block cipher using 1D and 2D chaotic maps', Int. ...
Communications in Nonlinear Science and Numerical Simulation, 2010
Recently Patidar et al. [Commun Nonlinear Sci Numer Simulat 14;2009:3056-75] proposed a new subst... more Recently Patidar et al. [Commun Nonlinear Sci Numer Simulat 14;2009:3056-75] proposed a new substitution-diffusion image cipher using chaotic standard and logistic maps, which is very fast and possess all the confusion and diffusion properties that any good cryptosystem should have. Soon after the proposal, Rhouma et al. [Commun Nonlinear Sci Numer Simulat 2010;15:1887-92.] proposed an equivalent description of the PPS09 cryptosystem which facilitated them in the cryptanalysis of the original cipher in terms of chosen plainext and known plaintext attacks. In this paper, we propose modifications in the Patidar et al.'s image cipher to make it robust against these two cryptanalytic attacks. The security analysis shows that the modified image cipher preserves all the good properties of the original cipher and is also capable to stand against the aforesaid attacks.
Communications in Nonlinear Science and Numerical Simulation, 2005
Recently, Pareek et al. [Phys. Lett. A 309 (2003) 75] have developed a symmetric key block cipher... more Recently, Pareek et al. [Phys. Lett. A 309 (2003) 75] have developed a symmetric key block cipher algorithm using a one-dimensional chaotic map. In this paper, we propose a symmetric key block cipher algorithm in which multiple one-dimensional chaotic maps are used instead of a one-dimensional chaotic map. However, we also use an external secret key of variable length (maximum 128-bits) as used by Pareek et al. In the present cryptosystem, plaintext is divided into groups of variable length (i.e. number of blocks in each group is different) and these are encrypted sequentially by using randomly chosen chaotic map from a set of chaotic maps. For block-by-block encryption of variable length group, number of iterations and initial condition for the chaotic maps depend on the randomly chosen session key and encryption of previous block of plaintext, respectively. The whole process of encryption/decryption is governed by two dynamic tables, which are updated time to time during the encryption/decryption process. Simulation results show that the proposed cryptosystem requires less time to encrypt the plaintext as compared to the existing chaotic cryptosystems and further produces the ciphertext having flat distribution of same size as the plaintext.
In this Letter, we propose a symmetric key block cipher algorithm utilizing the essence of chaos.... more In this Letter, we propose a symmetric key block cipher algorithm utilizing the essence of chaos. The proposed cryptosystem does not use explicitly the system parameter or initial condition of the chaotic map as a secret key. However, these parameters are generated by an external secret key of variable length (maximum 128-bits) and used in our algorithm. The encryption of each block of plaintext has been made dependent on the secret key and the cryptosystem is further made robust against any reasonable attack by using the feedback technique. Simulation results show that the proposed cryptosystem requires less time to encrypt the plaintext as compared to the existing chaotic cryptosystems and further produces the ciphertext having flat distribution of same size as the plaintext. available in the literature can be discussed with respect to the following aspects:
Recently, there have been several attempts to explain the features of triple differential cross s... more Recently, there have been several attempts to explain the features of triple differential cross section (TDCS) for the (e, 2e) processes on inert targets Ne, Ar and Xe but there are still certain discrepancies in theoretical results and measurements, which require more theoretical efforts to understand the collision dynamics of these targets. We present in this paper the results of our modified distorted wave Born approximation (DWBA) calculation of TDCS for the ionization of Ne (2p), Ar (3p) and Xe (5p) targets. We modify the standard DWBA formalism by including the correlation-polarization potential (which is function of electron density) and compare our computed results with the available experimental and theoretical data. We observe that the polarization potential is able to improve the agreement with experimental results.
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