A. B. Orue

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.

High-speed free-space quantum key distribution system for urban daylight applications

We report a free-space quantum key distribution system designed for high-speed key transmission in urban areas. Clocking the system at gigahertz frequencies and efficiently filtering background enables higher secure key rates than those previously achieved by similar systems. The transmitter and receiver are located in two separate buildings 300 m apart in downtown Madrid and they exchange secure keys at rates up to 1 Mbps. The system operates in full bright daylight conditions with an average secure key rate of 0.5 Mbps and 24 h stability without human intervention.

Breaking Points in Quartic Maps

Dynamical systems, whether continuous or discrete, are used by physicists in order to study nonlinear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some phenomena can depend alternatively on two values of the same parameter. We use the quadratic map

A general view of pseudoharmonics and pseudoantiharmonics to calculate external arguments of Douady and Hubbard

x_{n+1} = 1 - ax_{n}^{2}

Chaos and Graphics: Drawing and computing external rays in the multiple-spiral medallions of the Mandelbrot set

when the parameter alternates between two values during the iteration process. In this case, the orbit of the alternate system is the sum of the orbits of two quartic maps. The bifurcation diagrams of these maps present breaking points at which there is an abrupt change in their evolution.

Coupling Patterns of External Arguments in the Multiple-Spiral Medallions of the Mandelbrot Set

Harmonics give us a compact formula and a powerful tool in order to calculate the external arguments of the last appearance hyperbolic components and Misiurewicz points of the Mandelbrot set in some particular cases. Antiharmonics seem however to have no application. In this paper, we give a general view of pseudoharmonics and pseudoantiharmonics, as a generalization of harmonics and antiharmonics. Pseudoharmonics turn out to be a more powerful tool than harmonics since they allow the calculation of external arguments of the Mandelbrot set in many more cases. Likewise, unlike antiharmonics, pseudoantiharmonics turn out to be a powerful tool to calculate external arguments of the Mandelbrot set in some cases.

A Review of Cryptographically Secure PRNGs in Constrained Devices for the IoT

The multiple-spiral medallions are beautiful decorations of the Mandelbrot set. Computer graphics provide an invaluable tool to study the structure of these decorations with point symmetry (i.e., the medallions can be rotated 180^o about a central point to form an identical structure). The multiple-spiral medallions are formed by an infinity of baby Mandelbrot sets. Until now, the external arguments of the external rays landing at the cusps of the cardioids of these baby Mandelbrot sets could not be calculated. Recently, a new algorithm has been proposed in order to calculate the external arguments in the Mandelbrot set. In this paper, we use an extension of this algorithm for the calculation of the binary expansions of the external arguments of the baby Mandelbrot sets in the multiple-spiral medallions.

A Method to Solve the Limitations in Drawing External Rays of the Mandelbrot Set

The multiple-spiral medallions are beautiful decorations situated in the proximity of the small copies of the Mandelbrot set. They are composed by an infinity of babies Mandelbrot sets that have external arguments with known structure. In this paper we study the coupling patterns of the external arguments of the baby Mandelbrot sets in multiple-spiral medallions, that is, how these external arguments are grouped in pairs. Based on our experimental data, we obtain that the canonical nonspiral medallions have a nested pairs pattern, the canonical single-spiral medallions have an adjacent pairs pattern, and we conjecture that the canonical double, triple, quadruple-spiral medallions have a 1-nested/adjacent pairs pattern.

Calculation of the Structure of a Shrub in the Mandelbrot Set

In this work we show a deep review of lightweight random and pseudorandom number generators designed for constrained devices such as wireless sensor networks and RFID tags along with a study of Trifork pseudorandom number generator for constrained devices.

A new parameter determination method for some double-scroll chaotic systems and its applications to chaotic cryptanalysis

The external rays of the Mandelbrot set are a valuable graphic tool in order to study this set. They are drawn using computer programs starting from the Bottcher coordinate. However, the drawing of an external ray cannot be completed because it reaches a point from which the drawing tool cannot continue drawing. This point is influenced by the resolution of the standard for floating-point computation used by the drawing program. The IEEE 754 Standard for Floating-Point Arithmetic is the most widely used standard for floating-point computation, and we analyze the possibilities of the quadruple 128 bits format of the current IEEE 754-2008 Standard in order to draw external rays. When the drawing is not possible, due to a lack of resolution of this standard, we introduce a method to draw external rays based on the escape lines and Bezier curves.