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 randohinets of the encryption and the decryption function is so large that attackers cannot break this cryptosystem by statistic characteristics. In addition t o the security of the statistical point, even if the cryptosystern 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.
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. Namely, one of 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 networks are also studied, and such systems are confirmed to produce more complicated spatio-temporal phenomena.
In this study, a chaotic circuit suitable for an integrated circuit is proposed. The circuit consists of two CMOS ring oscillators and a pair of diodes. By using a simplified model of the circuit, the mechanism of generating chaos is explained and the exact solutions are derived. The exact expressions of the Poincaré map and its Jacobian matrix make those possible to confirm the generation of chaos using the Lyapunov exponents and to investigate the related bifurcation phenomena.
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