Yoshifumi Nishio

A secret key cryptosystem by iterating a chaotic map

Chaos is introduced to cryptology. As an example of the applications, a secret key cryptosystem by iterating a one dimensional chaotic map is proposed. This system is based on the characteristics of chaos, which are sensitivity of parameters, sensitivity of initial points, and randomness of sequences obtained by iterating a chaotic map. A ciphertext is obtained by the iteration of a inverse chaotic map from an initial point, which denotes a plaintext. If the times of the iteration is large enough, the randomness of the encryption and the decryption function is so large that attackers cannot break this cryptosystem by statistic characteristics. In addition to the security of the statistical point, even if the cryptosystem is composed by a tent map, which is one of the simplest chaotic maps, setting a finite computation size avoids a ciphertext only attack. The most attractive point of the cryptosystem is that the cryptosystem is composed by only iterating a simple calculations though the information rate of the cryptosystem is about 0.5.

An efficient algorithm for finding multiple DC solutions based on the SPICE-oriented Newton homotopy method

It is a very important, but difficult, task to calculate the multiple dc solutions in circuit simulations. In this paper, we show a very simple SFICE-oriented Newton homotopy method which can efficiently find out the multiple de solutions. In the paper, we show our solution curve-tracing algorithm based on the arc-length method and the Newton homotopy method. We will also prove an important theorem about how many variables should be chosen to implement our algorithm. It verifies that our simulator can be efficiently applied even if the circuit scales are relatively large. In Section III, we show that our Newton homotopy method is implemented by the transient analysis of SPICE. Thus, we do not need to formulate a troublesome circuit equation or the Jacobian matrix. Finally, applying our method to solve many important benchmark problems, all the solutions for the transistor circuits could be found on each homotopy path. Thus, our simulator can be efficiently applied to calculate the multiple dc solutions and perhaps all the solutions.

Spatio-temporal chaos in simple coupled chaotic circuits

In this paper, simple autonomous chaotic circuits coupled by resistors are investigated. By carrying out computer calculations and circuit experiments, irregular self-switching phenomenon of three spatial patterns characterized by the phase states of quasi-synchronization of chaos can be observed from only four simple chaotic circuits. This is the same phenomenon as chaotic wandering of spatial patterns observed very often from systems with a large number of degrees of freedom. Spatial-temporal chaos observed from systems of large size can be also generated in the proposed system consisting of only four chaotic circuits. A six subcircuits case and a coupled chaotic circuits network are also studied, and such systems are confirmed to produce more complicated spatio-temporal phenomena. >

Chaos glial network connected to Multi-Layer Perceptron for Solving Two-Spiral Problem

Some methods using artificial neural network were proposed for solving to the Two-Spiral Problem (TSP). TSP is a problem which classifies two spirals drawn on the plane, and it is famous as the high nonlinear problem. In this paper, we propose a chaos glial network which connected to Multi-Layer Perceptron (MLP). The chaos glial network is inspired by astrocyte which is glial cell in the brain. By computer simulations for solving TSP, we confirmed that the proposed chaos glial network connected to MLP gains better performance than the conventional MLP.

Synchronization phenomena in RC oscillators coupled by one resistor

There have been many investigations of the mutual synchronization of oscillators. Especially, we have analyzed N van der Pol type LC oscillators coupled by one resistor, and confirmed that this system can take a huge number of steady states. In this study, we analyze N Wien-bridge oscillators with the same natural frequency mutually coupled by one resister by both of computer calculations and circuit experiments. Because there is no inductor in this system, it is suitable for VLSI implementation. Moreover, the system has many more phase states than that of the system with van der Pol type LC oscillators when N is not so large. So we can utilize this system as a structural element of cellular neural networks.<<ETX>>

Mutually coupled oscillators with an extremely large number of steady states

N oscillators with the same natural frequency mutually coupled by one resistor are analyzed. In this system various synchronization phenomena can be observed. Particular attention is given to N-phase oscillation. It is confirmed that the system can stably take (N-1) phase states by both computer calculations and circuit experiments. Therefore, the system may be utilized as an extremely large memory.<<ETX>>

Fuzzy Adaptive Resonance Theory Combining Overlapped Category in consideration of connections

Adaptive resonance theory (ART) is an unsupervised neural network. Fuzzy ART (FART) is a variation of ART, allows both binary and continuous input patterns. However, fuzzy ART has the category proliferation problem. In this study, to solve this problem, we propose a new fuzzy ART algorithm: fuzzy ART combining overlapped category in consideration of connections (C-FART). C-FART has two important features. One is to make connections between similar categories. The other is to combine overlapping categories into with connections one category. We investigate the behavior of C-FART, and compare C-FART with the conventional FART.

SYNCHRONIZATION PHENOMENA IN VAN DER POL OSCILLATORS COUPLED BY A TIME-VARYING RESISTOR

In this study, synchronization phenomena observed in van der Pol oscillators coupled by a time-varying resistor are investigated. We realize the time-varying resistor by switching a positive and a negative resistor periodically. By carrying out circuit experiments and computer calculations, interesting synchronization phenomena can be confirmed to be generated in this system. Namely, the synchronization states change according to the switching frequency of the time-varying resistor.

Frequency response of nonlinear networks using curve tracing algorithm

For designing of nonlinear circuits, it is very important to know the frequency response characteristics and the intermodulation. In this paper, we propose an efficient method for calculating the characteristic curves of nonlinear circuits, which is based on the harmonic balance method and a curve tracing algorithm for solving the determining equation. Firstly, applying the harmonic balance method to each element in the circuit, we obtain the determining equation which is realized by two coupled resistive circuits corresponding to the sine and cosine components. Then, the frequency response characteristic curve is calculated by solving the circuit with a STC (solution curve tracing circuit) of Spice.

An efficient algorithm for finding multiple DC solutions based on Spice oriented Newton homotopy method

For circuit designing, it is very important to calculate the DC operating points. It is known that if the circuit contains positive feedback loops such as flip-flop and negative resistance circuits, it may have many DC solutions. It is very difficult to find all of the solutions for these circuits. In this paper, we show a very simple Spice oriented Newton homotopy method which can efficiently find out the multiple DC solutions, and perhaps all of the solutions.