Prabhakar G. Vaidya

Arithmetic coding as a non-linear dynamical system

Abstract In order to perform source coding (data compression), we treat messages emitted by independent and identically distributed sources as imprecise measurements (symbolic sequence) of a chaotic, ergodic, Lebesgue measure preserving, non-linear dynamical system known as Generalized Luroth Series (GLS). GLS achieves Shannon’s entropy bound and turns out to be a generalization of arithmetic coding, a popular source coding algorithm, used in international compression standards such as JPEG2000 and H.264. We further generalize GLS to piecewise non-linear maps (Skewed-nGLS). We motivate the use of Skewed-nGLS as a framework for joint source coding and encryption.

Re-visiting the One-Time Pad

In 1949, Shannon proved the perfect secrecy of the Vernam cryptographic system (One-Time Pad or OTP). It has generally been believed that the perfectly random and uncompressible OTP which is transmitted needs to have a length equal to the message length for this result to be true. In this paper, we prove that the length of the transmitted OTP actually contains useful information and could be exploited to compress the transmitted-OTP while retaining perfect secrecy. The message bits can be interpreted as True/False statements about the OTP, a private object, leading to the notion of private-object cryptography.

Multiplexing of discrete chaotic signals in presence of noise

Multiplexing of discrete chaotic signals in presence of noise is investigated. The existing methods are based on chaotic synchronization, which is susceptible to noise, precision limitations, and requires more iterates. Furthermore, most of these methods fail for multiplexing more than two discrete chaotic signals. We propose novel methods to multiplex multiple discrete chaotic signals based on the principle of symbolic sequence invariance in presence of noise and finite precision implementation of finding the initial condition of an arbitrarily long symbolic sequence of a chaotic map. Our methods work for single precision and as less as 35 iterates. For two signals, our method is robust up to 50% noise level.