R. Vázquez-Medina

Chaotic noise MOS generator based on logistic map

The Birkhoffs ergodic theorem (BET), bifurcation diagram (BD) and Lyapunovs exponent (LE) are used in order to design a chaotic noise generator that is governed by the logistic map (LM). For this, a MOS analog circuit that operates in the current-mode, which is based on translinear principle (TLP), is used. To iterate the transference function of this circuit and also to maintain the parameter control of the LM, a current amplifier has been used. The specifications of the design are obtained from the analysis of the model. The results demonstrate the correct operation of the circuit, even when a mismatching of 2% is considered between the devices that control the operation region. The statistical distribution of the output signal on the circuit is similar to uniform distribution and it is related with the parameter value that rules the transfer function of the circuit.

Numerical calculation of the lyapunov exponent for the logistic MAP

Chaotic maps can be used to describe the behavior of dynamical systems and they are characterized by a parameter. The logistic map (LM) is a chaotic map very used in different areas. In the analysis of the dynamical system an important feature is the system stability, which can be determined using the Lyapunov Exponent (LE). In this paper two ways to compute numerically the LE for the LM are shown. In the first alternative, the Birkhoffpsilas Ergodic Theorem (BET) and the orbit produced by the LM are used. In the second alternative, the stationary distribution rhoest of the LM is estimated using the first derived of the logistic function and the central values of each interval in the partition used in the estimation.

Steganographic communication channel using audio signals

Using MP3 and WAV audio digital signals an algorithm to build a steganographic communication channel is presented. This algorithm is conformed by the insertion and extraction procedures and it use direct sequence spread spectrum (DSSS) to insert confidential (subliminal) information in MP3 and WAV audio digital signals. Evaluation tests were applied to the different steganographic communications channels. According with the obtained results this algorithm can be used to property or exploitation right protection of the audio digital signals.

A steganographic method using Bernoulli's chaotic maps

A steganographic method for hiding information is proposed using four Bernoullis chaotic maps.It is applied a two-step scheme: Pixel selection and masking of sensitive information.A module function is applied to the chaotic maps considering an iterated process.There is no evidence of periodicity in the sequences produced by the modified Bernoullis maps.It is assumed that each map uses two 64-bits variables, and the key space has been estimated in 2508. Display Omitted This paper proposes an alternative for building a data hiding algorithm into digital images. The method is based on chaos theory and the least significant bit technique for embedding a secret message in a image. Specifically the Bernoullis chaotic maps are used, to perform the following processes: (i) encrypt the bits of the message before embedding them into the cover image, (ii) a random selection of the images compositions (R,G or B) must be performed and the insertion of the secret message in a random way to (iii) rows and (iv) columns of the image. Several experimental results are shown under different evaluation criteria, such as entropy, autocorrelation, homogeneity, contrast, energy, peak signal-to-noise ratio, mean squared error and maximum absolute squared deviation. Experimental results show a good improvement in the peak-signal-to-noise-ratio and Image Fidelity value of the proposed algorithm in comparison to the results obtained from similar algorithms.

A digitally programmable active resistor in CMOS technology

A technique for the implementation of a programmable grounded and floating resistors is presented. The grounded version of the resistor has been implemented in a standard CMOS technology, where a set of digital inputs allows the programming of the circuit. The performance of the circuit is shown by means of DC, AC, Transient and Monte Carlo simulations. Measurements on a 0.35 μm CMOS physical implementation are presented. Additionally, an application of the proposed circuit in programmable filters is described.

Cryptosystem with one dimensional chaotic maps

This paper presents a 64-bits chaotic block cryptosystem, which uses as noise generator one-dimensional chaotic maps with 8 bits sub-blocks data. These chaotic maps use a control parameter that allows them to operate in the chaotic region, which guarantees that each sub-block of data is mixed with unpredictable random noise. Statistical mechanic tools such as: bifurcation diagram, Lyapunov exponent, and invariant distribution have been used to analyze and evaluate the behavior of the noise generator. The cryptosystem has been evaluated using concepts of information theory, such as: entropy, as a diffusion measure in the encryption process, and mutual information as a measure of relationship between plaintext and its respective cryptogram. The noise generator has been used on the non-balanced and dynamic network proposed by L. Kocarev. The randomness of the cryptograms has been evaluated using the NIST random tests. The proposed cryptosystem can be a component in software applications that provides security to stored or communicated information. The proposed cryptosystem has a similar behavior to the one of currently used cryptosystems and it has been designed with chaotic sequence generators, which are aperiodic by definition.

Digital Noise Generator Based on Bernoulli Chaotic Map

This paper describes the noise emulation in materials through the digital implementation of a chaotic noise generator based on the Bernoulli map. The bifurcation diagram, Lyapunov exponent and the Ergodic Theorem were used in order to determine the operation conditions under which the Bernoulli map is able to generate noise with different statistical distributions. A 32-bits digital circuit was designed and implemented in a FPGA, and it can be used to emulate and analyze the noise in different materials. The obtained results are consistent with the generalized Bernoulli map behavior.

Analog current-mode implementation of a logistic-map based chaos generator

In this paper a cmos current-mode analog circuit for the generation of chaotic signals is presented. This circuit is an electronic realization of the Discrete Verhulsts Logistic Equation (Logistic Map). This circuit was implemented in a 0.35µm standard cmos technology. Monte Carlo simulations and experimental measurements of the fabricated integrated circuit are presented.

Symmetric cryptosystem based on skew tent map

This paper presents an efficient symmetric cryptosystem based on a non–scaled nor discretized skew tent map (STM); this system is implemented in a USB device interacting with a software module in a personal computer. The USB device uses a dedicated processor that contains a pseudorandom numbers generator (PRNG) to generate uniformly distributed chaotic sequences that satisfy the randomness tests defined in the NIST 800–22SP guide. The software module uses these sequences with substitution and rotation functions to produce cryptograms with confusion and diffusion properties, high level of security, high avalanche effect and high encryption and decryption speed. A variety of analysis and tests has been carried out to prove the security and the validity of the algorithm. Some of the evaluated characteristics are the statistical behavior, correlation, strength against differential attack, entropy, key space, key sensitivity, mutual information, encryption and decryption speed, and randomness test. Additionally, we analyze the structure of the proposed cryptosystem to find some security vulnerabilities; in this part, the analysis are based on known plaintext attack used in the literature on chaotic cryptosystems. In this way, the realized analysis shows that the performance of the proposed algorithm offers a high security level. Mutual information is calculated as evidence of this level of security.

Digital noise generator based in a one-dimensional tent chaotic map on FPGA

This paper presents a method to design and implement a digital noise generator module based on FPGA using the one-dimensional tent map (1-D tent map). In this proposal, the scaling and discretization processes are not necessary as other authors have done. When a one-dimensional chaotic map (1-D chaotic map) is scaled and discretized the resultant function is only an approximation to the 1-D chaotic map, whose output has evidence of periodicity within chaotic region. The design that we present in this paper is based on a floating point numerical representation in 64 bits double precision format of the IEEE-754: binary floating point arithmetic standard that provides a better representation of real numbers.