Veronica Fernandez

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.

Cryptanalysis of a new chaotic cryptosystem based on ergodicity

This paper analyzes the security of a recent cryptosystem based on the ergodicity property of chaotic maps. It is shown how to obtain the secret key using a chosen-ciphertext attack. Some other design weaknesses are also shown.

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.

Correction of beam wander for a free-space quantum key distribution system operating in urban environment

Free-space quantum key distribution links in urban environment have demanding operating needs, such as functioning in daylight and under atmospheric turbulence, which can dramatically impact their performance. Both effects are usually mitigated with a careful design of the field of view of the receiver. However, a trade-off is often required, since a narrow field of view improves background noise rejection but it is linked to an increase in turbulence-related losses. In this paper, we present a high-speed automatic tracking system to overcome these limitations. Both a reduction in the field-of-view to decrease the background noise and the mitigation of the losses caused by atmospheric turbulence are addressed. Two different designs are presented and discussed, along with technical considerations for the experimental implementation. Finally, preliminary experimental results of beam wander correction are used to estimate the potential improvement of both the quantum bit error rate and secret key rate of a free space quantum key distribution system.

A basic framework for the cryptanalysis of digital chaos-based cryptography

Chaotic cryptography is based on the properties of chaos as source of entropy. Many different schemes have been proposed to take advantage of those properties and to design new strategies to encrypt information. However, the right and efficient use of chaos in the context of cryptography requires a thorough knowledge about the dynamics of the selected chaotic system. Indeed, if the final encryption system reveals enough information about the underlying chaotic system it could be possible for a cryptanalyst to get the key, part of the key or some information somehow equivalent to the key just analyzing those dynamical properties leaked by the cryptosystem. This paper shows what those dynamical properties are and how a cryptanalyst can use them to prove the inadequacy of an encryption system for the secure exchange of information. This study is performed through the introduction of a series of mathematical tools which should be the basic framework of cryptanalysis in the context of digital chaos-based cryptography.

Breaking a SC-CNN-based Chaotic Masking Secure Communication System

This paper studies the security of a chaotic cryptosystem based on Chuas circuit and implemented with State Controlled Cellular Neural Networks (SC-CNN). Here, we prove that the plaintext can be retrieved by bandpass filtering of the ciphertext or by using an imperfect decoder with wrong receiver parameters. In addition, we find that the key space of the system can be reduced notably, and the required resolution of the parameter values to recover a meaningful plaintext is as coarse as 5%, easing a brute-force attack. The system parameters can be determined with high precision through the analysis of the decoding error produced by the mismatch between the parameters of receiver and transmitter.

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

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.

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

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.

Correction of Wavefront Tilt Caused by Atmospheric Turbulence Using Quadrant Detectors for Enabling Fast Free-Space Quantum Communications in Daylight

Low photon-level signals used in most free-space quantum communication systems require a narrow field of view in the receiver to minimize the amount of background noise coupled into the single photon detectors. This can be achieved through beam tracking techniques, which compensate atmospheric effects, such as beam wander, in the receiver, reducing the long-term beam area. However, reducing the diameter of this area below a few microns, typically necessary to achieve a low level of solar background noise and successful daylight quantum transmission, require fine tracking precision and diffraction-limited optics. We demonstrate that this can be done with standard voice-coil fast steering mirrors and cheap commercially-available quadrant detectors. Two correcting strategies (open and closed loop) are experimentally tested and analyzed for their applicability in metropolitan (~km range) free-space quantum communications. The area containing the random fluctuations of the beam centroid caused by atmospheric turbulence at the focal plane of the receiver was reduced by a factor of 4 with an open-loop configuration, and up to a factor of nine with a closed loop configuration. This is equivalent to a reduction in the quantum bit error rate caused by background solar noise of up to one order of magnitude, which, combined with spectral filtering techniques, enable the possibility of fast daylight quantum key distribution.

Free-Space Quantum Key Distribution

Based on the firm laws of physics rather than unproven foundations of mathematical complexity, quantum cryptography provides a radically different solution for encryption and promises unconditional security. Quantum cryptography systems are typically built between two nodes connected to each other through fiber optic. This chapter focuses on quantum cryptography systems operating over free-space optical channels as a cost-effective and license-free alternative to fiber optic counterparts. It provides an overview of the different parts of an experimental free-space quantum communication link developed in the Spanish National Research Council (Madrid, Spain).