Searcharxiv⌕ Search

arXiv subjects

Prabhakar G. Vaidya

Publications and source records attributed to Prabhakar G. Vaidya.

7 recordsLinked to original sources
arXiv2009

Separating a mixture of chaotic signals

Chaos is popularly associated with its property of sensitivity to initial conditions. In this paper we will show that there can be a flip side to this property which is quite fascinating and highly useful in many applications. As a result, we can mix a large number of chaotic signals and one completely arbitrary signal and later a recipient of this transformed and weighted mixture can separate each of the signals, one by one. The chaotic signals, could be generated by various maps which belong to the logistic family. The arbitrary signal, could be a message, some random noise, some periodic signal or a chaotic signal generated by a source, either belonging or not belonging to the family. The key behind this procedure is a family of maps which can dovetail into each other without altering each of their predecessor's symbolic sequence.

nlin.CD↗
arXiv2008

Increasing Average Period Lengths by Switching of Robust Chaos Maps in Finite Precision

Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits ($T$) of a dynamical system scales as a function of computer precision ($ε$) and the correlation dimension ($d$) of the chaotic attractor: $T \sim ε^{-d/2}$. In this work, we are concerned with increasing the average period length which is desirable for chaotic cryptography applications. Our experiments reveal that random and chaotic switching of deterministic chaotic dynamical systems yield higher average length of periodic orbits as compared to simple sequential switching or absence of switching. To illustrate the application of switching, a novel generalization of the Logistic map that exhibits Robust Chaos (absence of attracting periodic orbits) is first introduced. We then propose a pseudo-random number generator based on chaotic switching between Robust Chaos maps which is found to successfully pass stringent statistical tests of randomness.

nlin.CD↗
arXiv2008

Multiplexing of discrete chaotic signals in presence of noise

In this paper, multiplexing of discrete chaotic signals in the presence of noise is investigated. Existing methods are based on chaotic synchronization which is susceptible to noise and parameter mismatch. Furthermore, these methods fail for multiplexing more than two discrete chaotic signals. We propose two novel methods to multiplex multiple discrete chaotic signals based on the principle of symbolic sequence invariance in the presence of noise and finite precision implementation of finding the initial condition of an arbitrarily long symbolic sequence of a chaotic map.

nlin.CD↗
arXiv2008

One-Time Pad, Arithmetic Coding and Logic Gates: An unifying theme using Dynamical Systems

In this letter, we prove that the perfectly secure One-Time Pad (OTP) encryption can be seen as finding the initial condition on the binary map under a random switch based on the perfectly random pad. This turns out to be a special case of Grangetto's randomized arithmetic coding performed on the Binary Map. Furthermore, we derive the set of possible perfect secrecy systems using such an approach. Since OTP encryption is an XOR operation, we thus have a dynamical systems implementation of the XOR gate. We show similar implementations for other gates such as NOR, NAND, OR, XNOR, AND and NOT. The dynamical systems framework unifies the three areas to which Shannon made foundational contributions: lossless compression (Source Coding), perfect encryption (Cryptography), and design of logic gates (Computation)

nlin.CD↗
arXiv2007

A non-linear dynamical systems approach to source compression for constrained sources

We have recently established a strong connection between the Tent map (also known as Generalized Luroth Series or GLS which is a chaotic, ergodic and lebesgue measure preserving non-linear dynamical system) and Arithmetic coding which is a popular source compression algorithm used in international compression standards such as JPEG2000 and H.264. This was for independent and identically distributed binary sources. In this paper, we address the problem of compression of ergodic Markov binary sources with certain words forbidden from the message space. We shall show that GLS can be modified suitably to achieve Shannon's entropy rate for these sources.

nlin.CD↗