G. Pastor

Cryptanalysis of an ergodic chaotic cipher

In recent years, a growing number of cryptosystems based on chaos have been proposed, many of them fundamentally flawed by a lack of robustness and security. In this Letter, we offer our results after having studied the security and possible attacks on a very interesting cipher algorithm based on the logistic maps ergodicity property. This algorithm has become very popular recently, as it has been taken as the development basis of new chaotic cryptosystems.

Breaking two secure communication systems based on chaotic masking

This paper describes the security weakness of two generalized nonlinear state-space observers-based approaches for both chaos synchronization and secure communication, using chaotic masking and chaotic modulation of a Lorenz system. We show that the security is compromised without any knowledge of the chaotic system parameter values and even without knowing the transmitter structure.

Keystream cryptanalysis of a chaotic cryptographic method

Recently a new chaotic encryption system has been proposed as a modified version of the chaotic cryptographic method based on iterating a logistic map. A fundamental weakness of this new cryptosystem is pointed out that allows for three successful cryptanalytic attacks.

Cryptanalysis of a chaotic secure communication system

Abstract Recently a chaotic encryption system has been proposed by P. Garcia et al. It represents an improvement over an algorithm previously presented by some of the same authors. In this Letter, several weaknesses of the new cryptosystem are pointed out and four successful cryptanalytic attacks are described.

Breaking a secure communication scheme based on the phase synchronization of chaotic systems.

A security analysis of a recently proposed secure communication scheme based on the phase synchronization of chaotic systems is presented. It is shown that the system parameters directly determine the cipher text waveform, hence it can be readily broken by system parameter estimation from the cipher text signal.

Misiurewicz points in one-dimensional quadratic maps

Misiurewicz points are constituted by the set of unstable or repellent points, sometimes called the set of exceptional points. These points, which are preperiodic and eventually periodic, play an important role in the ordering of hyperbolic components of one-dimensional quadratic maps. In this work we use graphic tools to analyse these points, by measuring their preperiods and periods, and by ordering and classifying them.

ON THE CALCULATION OF MISIUREWICZ PATTERNS IN ONE-DIMENSIONAL QUADRATIC MAPS

In this work we give for the first time a table with all Misiurewicz points Mn,p for low values of the preperiod and period (2⩽n⩽8, 1⩽p⩽5) in one-dimensional quadratic maps. In the particular case of Mn,1 (important Misiurewicz points which are all placed in the period-1 chaotic band) the preperiod values are (2⩽n⩽11). A brute-force algorithm to obtain all the symbolic sequences (patterns) of the Mn,p and a more efficient algorithm to obtain the patterns of Mn,1 are also shown.

ALTERNATED JULIA SETS AND CONNECTIVITY PROPERTIES

In this work we present the alternated Julia sets, obtained by alternated iteration of two maps of the quadratic family and prove analytically and computationally that these sets can be connected, disconnected or totally disconnected verifying the known Fatou–Julia theorem in the case of polynomials of degree greater than two. Some examples are presented.

Determination of the parameters for a Lorenz system and application to break the security of two-channel chaotic cryptosystems

This Letter describes how to determine the parameter of the chaotic Lorenz system used in a two-channel cryptosystem. First the geometrical properties of the Lorenz system are used to reduce the parameter search space. Second the parameters are exactly determined—directly from the ciphertext—through the minimization of the average jamming noise power created by the encryption process.

External arguments of Douady cauliflowers in the Mandelbrot set

Abstract Near to the cusp of a cardioid of the Mandelbrot set, except for the main cardioid, there is a sequence of baby Mandelbrot sets. Each baby Mandelbrot set is in the center of a Douady cauliflower, a decoration constituted by an infinity of minute Mandelbrot sets and Misiurewicz points linked by filaments. A Douady cauliflower appears to have a complicated structure, and how the external rays land without intersecting in its Misiurewicz points and minute Mandelbrot sets is not really well known. In this work we study the Douady cauliflowers, giving a binary tree model to calculate the binary expansions of the external arguments of both the main cardioid of each minute Mandelbrot set and Misiurewicz points, and creating a horsetail model that explains the arrangement of its corresponding external rays.