A Review of Analog Audio Scrambling Methods for Residual Intelligibility

In this paper, a review of the techniques available in different categories of audio scrambling schemes is done with respect to Residual Intelligibility. According to Shannon's secure communication theory, for the residual intelligibility to be zero the scrambled signal must represent a white signal. Thus the scrambling scheme that has zero residual intelligibility is said to be highly secure. Many analog audio scrambling algorithms that aim to achieve lower levels of residual intelligibility are available. In this paper a review of all the existing analog audio scrambling algorithms proposed so far and their properties and limitations has been presented. The aim of this paper is to provide an insight for evaluating various analog audio scrambling schemes available up-to-date. The review shows that the algorithms have their strengths and weaknesses and there is no algorithm that satisfies all the factors to the maximum extent. Keywords: residual Intelligibility, audio scrambling, speech scramblin

The quantum cat map on the modular discretization of extremal black hole horizons

Based on our recent work on the discretization of the radial AdS$_2$ geometry of extremal BH horizons,we present a toy model for the chaotic unitary evolution of infalling single particle wave packets. We construct explicitly the eigenstates and eigenvalues for the single particle dynamics for an observer falling into the BH horizon, with time evolution operator the quantum Arnol'd cat map (QACM). Using these results we investigate the validity of the eigenstate thermalization hypothesis (ETH), as well as that of the fast scrambling time bound (STB). We find that the QACM, while possessing a linear spectrum, has eigenstates, which are random and satisfy the assumptions of the ETH. We also find that the thermalization of infalling wave packets in this particular model is exponentially fast, thereby saturating the STB, under the constraint that the finite dimension of the single--particle Hilbert space takes values in the set of Fibonacci integers.Comment: 28 pages LaTeX2e, 8 jpeg figures. Clarified certain issues pertaining to the relation between mixing time and scrambling time; enhanced discussion of the Eigenstate Thermalization Hypothesis; revised figures and updated references. Typos correcte