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... both pre determine to choose the corresponding numerical values at t = 200, 201, 202 respectively. To convert the keys into integer, the sender and receiver both pre determine to [1000x] (Mod 38) and [1000 x 1 ] (Mod 38) respectively.Therefore the first key k 1 =12 (see Table 1) is the value of x at t = 200 with the transformation [1000x] Mod(38) and so on. ...Citations
... So, the information about the source has an important role in preventive maintenance. Apart from this application domain, the presence of noise impacts the performance of chaosbased communications, [36][37][38][39][40][41] chaos-based robotic navigation, [42][43][44] and chaotic time series prediction [45][46][47] since it hinders the capture of useful information. Therefore, it is vital to devise methods that can distinguish noise from deterministic chaos and its noise-corrupted version. ...
The problem of distinguishing deterministic chaos from non-chaotic dynamics has been an area of active research in time series analysis. Since noise contamination is unavoidable, it renders deterministic chaotic dynamics corrupted by noise to appear in close resemblance to stochastic dynamics. As a result, the problem of distinguishing noise-corrupted chaotic dynamics from randomness based on observations without access to the measurements of the state variables is difficult. We propose a new angle to tackle this problem by formulating it as a multi-class classification task. The task of classification involves allocating the observations/measurements to the unknown state variables in order to find the nature of these unobserved internal state variables. We employ signal and image processing based methods to characterize the different system dynamics. A deep learning technique using a state-of-the-art image classifier known as the Convolutional Neural Network (CNN) is designed to learn the dynamics. The time series are transformed into textured images of spectrogram and unthresholded recurrence plot (UTRP) for learning stochastic and deterministic chaotic dynamical systems in noise. We have designed a CNN that learns the dynamics of systems from the joint representation of the textured patterns from these images, thereby solving the problem as a pattern recognition task. The robustness and scalability of our approach is evaluated at different noise levels. Our approach demonstrates the advantage of applying the dynamical properties of chaotic systems in the form of joint representation of UTRP images along with spectrogram to improve learning dynamical systems in colored noise.
... In this scenario, the block ciphers can utilize chaos based cryptosystems along with cycles of chaotic maps [31] and chaotic round functions [32]. Additionally, stream ciphers use the chaos based pseudo-arbitrary bit generators [33]. ...
With the inclusion of mobile devices and ubiquitous connectivity of smart devices in Internet of Things (IoT), secure key management is mandatory to ensure privacy for information exchange. In this regard, the multiparty key establishment schemes achieve better security strength by taking shared parameters from neighboring member nodes to calculate the key. The similar multiparty mechanism can be adopted among other hierarchical nodes including head node, server and gateway node. Moreover, session keys can also be set up in a similar manner. The main problem in multiparty password-based authentication schemes is the computation of extensively hard problem that limits it to three parties and N-party is quite more complex or infeasible. This paper presents a novel Distributed Multiparty Keying (DMK) scheme where chaotic maps are used to provide one-way hashing and Chebyshev polynomial (CP) are used for establishing a common multiparty key. In our work, Phase-I covers keying among trusted server and group heads and Phase-II elaborates the key establishment among smart devices and their group heads. The scheme is verified through the formal specification and security analysis using Rubin Logic for inter-group key establishment scenario. We have validated the intra-group and inter-group key establishment by doing extensive simulations in NS 2.35. Moreover, a testbed is setup for GH to server level authentication and key establishment. Results prove the supremacy of our scheme as compared to preliminaries in terms of computation cost, communication cost and resilience.
... The former is based on the techniques of control [32] and synchronization [21,26] of chaos. Whereas digital chaos based cryptosystems can be realized by: block ciphers based on forward and/or reverse iterations of chaotic maps [37], block ciphers based on chaotic round functions [22], stream ciphers implementing chaos based pseudo random bit generators (PRBG) [29]. There are several ways through which analog chaos based cryptosystems can be realized such as: chaotic masking [15], chaotic modulation [18] chaotic switching [38] inverse system approach. ...
Robustness of cellular networks in case of handling faults still remains a daunting task. Mobile computing technology has rapidly become can indispensable mode in various e-commerce transactions along with voice and video communication. With these facilities comes the threat of security and integrity of information which are equally important to be tackled as the seamless transfer of data from remote locations to other remote or fixed locations and has currently drawn significant attention in the research community. The traditional ways of cryptography have been exhaustively explored during the past few decades. This chapter seeks ways to explore the implementation of a complex dynamic system in cryptographic application for another dynamic system. Mobile communications deals with a dynamic system characterized with intermittent disconnections. In the light of these facts, this work introduces fault tolerance technique with secure checkpointing and message logging while handling of mobile disconnections.We propose a secure communication technique and an efficient key management methodology for mobile computing environment based on the chaotic sequences generated by an optical chaos system with high fluctuating chaotic orbits. To the best of our knowledge, very little work has been done based on chaos cryptography in mobile computing. We propose a) A hybrid message logging and asynchronous checkpointing scheme at receiver’s end with an improved performance where messages exchanged by Mobile Hosts (MH) are logged at the stable base station b) The proposed message logging is made secure by introducing cryptography devised from a two-way coupled chaotic laser system derived from Maxwell Bloch’s equations. The entire process serves a dual purpose. Firstly, chaos synchronization would form a secure channel through which physical transfer of the private keys would be completely eliminated. Thereby, reducing the computational overhead incurred during the complex way of exchanging keys in Diffie Hellman Key Exchange (DHKE) protocol. Secondly,the inherent randomness and deterministic properties of chaotic system renders the scheme immune to major attacks. The entire scheme has been labeled as Chaos Key Exchange (CKE) method which uses the chaotic sequences generated by a synchronized chaotic laser system as the private keys to be used in cryptographic purpose. As a consequence, CKE forms as an efficient key management system used during encrypting messages involving voluminous data such as multimedia and images. The proposed logging process as well as the communication of messages has been made secure by applying CKE method.CKE has been demonstrated by encoding an image which is transmitted over a secure channel.The ergodicity of the chaotic system adds the necessary confusion and diffusion properties required for efficient cryptography.Simulation result highlight the merit of the scheme which precisely recovers the messages at the receiver section thereby proving the robustness of the scheme which is efficiently extended to achieve secure logging of the messages.
... This method of chaos cryptography is the outcome of the phenomenal work of chaos synchronization demonstrated by Pecora and Carroll [1]. This bifurcation from the traditional methods of encryption realized with the synchronization of two coupled chaotic trajectories opened a whole new dimension for cryptographic applications [2][3][4][5][6][7]. Its principle of operation relies primarily on the fact that the chaotic nonlinear oscillator plays the role of a broadband signal generator and the chaotic waveform can mask the information. ...
... Through the modulo operation, the length is restricted to the range [0, M ] or [1, M +1]. These processed keys are of the same length as that of the message and are used exactly once and therefore this organization is theoretically unbroken [4]. So, the advantage of the Vignere cipher is reaped by our scheme.Then in order to encode an image of length M × N , we convert the set Y 1 and Y 2 into a chaotic sequence K 1 and K 2 respectively containing the M × N elements as that of the plain image P of dimension M × N . ...
Optical chaos is a topic of current research characterized by
high-dimensional nonlinearity which is attributed to the delay-induced
dynamics, high bandwidth and easy modular implementation of optical feedback.
In light of these facts, which adds enough confusion and diffusion properties
for secure communications, we explore the synchronization phenomena in
spatiotemporal semiconductor laser systems. The novel system is used in a
two-phase colored image encryption process. The high-dimensional chaotic
attractor generated by the system produces a completely randomized chaotic time
series, which is ideal in the secure encoding of messages. The scheme thus
illustrated is a two-phase encryption method, which provides sufficiently high
confusion and diffusion properties of chaotic cryptosystem employed with unique
data sets of processed chaotic sequences. In this novel method of cryptography,
the chaotic phase masks are represented as images using the chaotic sequences
as the elements of the image. The scheme drastically permutes the positions of
the picture elements. The next additional layer of security further alters the
statistical information of the original image to a great extent along the
three-color planes. The intermediate results during encryption demonstrate the
infeasibility for an unauthorized user to decipher the cipher image. Exhaustive
statistical tests conducted validate that the scheme is robust against noise
and resistant to common attacks due to the double shield of encryption and the
infinite dimensionality of the relevant system of partial differential
equations.
... achieved by using chaotic carriers obtained from semiconductor lasers to encode an information. Chaos Cryptography [3,4,5,6,7], an offshoot of traditional cryptography is realized with the synchronization of two coupled chaotic trajectories. The genesis of chaos based cryptography is attributed to the pioneering work of chaos synchronization by Pecora and Carroll [8]. ...
... Moreover, for absolute secrecy the keys space should not be reused. The scheme adheres to Kirchoff's principle and the arrangement of the key set forms a Vignere cipher which is theoretically unbroken [7]. At synchronization, say at t=t max =20 (dimensionless unit), the system will remain the same for any t i > t max at which the error between E ±1 and E ±2 will approach zero. ...
The Optical chaotic systems, with infinite dimensionality, have gained a lot of attention for communication and cryptographic purposes. The semiconductor devices act as a cryptosystem with high bandwidth. We explore the synchronization phenomenon between two spatio-temporal chaotic semi conductor lasers with bi-directional coupling. The coupling facilitates two way simultaneous communication. The ease of modular implementation of optical feedback together with the randomness and ergodic properties of the infinite dimensional systems produces completely randomized chaotic time series. Such a system is an ideal candidate for cryptographic purposes of large streams of data such as a digital image. The system renders enough confusion and diffusion properties to the transmitted gray scaled image rendering the statistically disordered cipher image totally incoherent from the original message. Simulation result and statistical tests demonstrate the merit of the system in achieving robust and secure cryptography with deterministic chaos aiding in the correct recovery of the encoded image.
In this work, we propose to enable security mechanisms on a chaotic
communication system based upon common noise induced synchronization
between two time-delayed semiconductor laser systems. The cryptosystem
subjected to the common additive Gaussian colored noise undergoes a
transition to follow identical trajectories. An investigation of the
system together with a novel scheme for authentication based message
encryption process are presented. The encrypted message is also sent
over a public channel, while the key is never transmitted at all. The
advantage of the scheme is its security, based on the authentication and
asymmetric encryption. Extended statistical tests with the proposed two
phase cryptography scheme demonstrate the efficiency of the system being
robust and tolerant to different types of statistical attacks.
This work aims to demonstrate the effect of synchronization phenomena in chaotic laser systems described by modified Lang–Kobayashi's (L–K) delay differential equations. The synchronized system considered for numerical simulations and for cryptography consists of identical semiconductor lasers operating in single longitudinal mode. The two lasers are bidirectionally coupled by linear optical feedback. As this is essential in simultaneous transmission of messages, we have applied the corresponding coupled chaotic dynamics to secure communications. An investigation of the system together with a novel scheme for digital cryptography and visual recurrence analysis (VRA) of the chaotic time series are presented. Extended statistical tests with the proposed two phase scheme demonstrate the efficiency of these infinite dimensional systems in being tolerant to different types of statistical attacks. The result emphasizes the merits of the uncertainty and high dimensionality of optical chaos system in duplex high speed secure communications.
