By Igor Izmailov, Boris Poizner, Ilia Romanov, Sergey Smolskiy
This e-book offers tips on how to increase details defense for safe communique. It combines and applies interdisciplinary medical engineering thoughts, together with cryptography, chaos thought, nonlinear and singular optics, radio-electronics and self-changing synthetic platforms. It additionally introduces extra how one can enhance details protection utilizing optical vortices as info providers and self-controlled nonlinearity, with nonlinearity enjoying a key "evolving" function. The proposed recommendations permit the common phenomenon of deterministic chaos to be mentioned within the context of knowledge safeguard difficulties at the foundation of examples of either digital and optical structures. extra, the booklet offers the vortex detector and communique structures and describes mathematical types of the chaos oscillator as a coder within the synchronous chaotic conversation and acceptable decoders, demonstrating their potency either analytically and experimentally. finally it discusses the cryptologic positive factors of analyzed platforms and indicates a chain of latest constructions for convinced communication.
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Extra resources for Cryptology Transmitted Message Protection: From Deterministic Chaos up to Optical Vortices
Classical generators are Teodorchik–Kaptsov system, its modiﬁcation in the Anishchenko–Astakhov system, Kiyashko–Pikovskiy–Rabinovich, Dmitriev– Kislov, Chua systems. Here we are not to go into the description of the chaotic oscillation of the Neimark pendulum , as well as the maser and laser (the Lorenz–Haken model (1975) [37–39]), and the chaotic oscillation based on the semiconductor lasers , and some other issues. 10 1 Deterministic Chaos Phenomenon from the Standpoint … Although it is sufﬁcient for the chaos generation that the system has one and a half degree of freedom, at the turn of the 21-st century, the diversiﬁcation of dynamic chaos sources is developing, which goes beyond the matters discussed in our study.
7 The map of dynamic modes on the parameter plane (T; M) and phase portraits of attractors for the Dmitriev–Kislov oscillator at Q ¼ 10  of the equilibrium condition at the origin. As a result, the pair of symmetrically pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ located stable states x ¼ Qy ¼ z ¼ Æ lnðMÞ, which move away from the origin at þ TQÞ Þ, both these positions lose stability and M increase. When M1 ¼ expððT þ QÞð1 2TQ2 become the instable focuses. The limit cycle arises in the vicinities of each equilibrium position.
Let us review in detail one of the typical representatives of chaotic generators with delayed feedback. The chaotic generator based on the self-oscillating system with delay. The structural diagram of the chaotic generator with delayed feedback is shown in Fig. 16 [60, 61]. The feedback network is formed by the serial RLC-tuned circuit with normalized resonant frequency x0 ¼ 1 and the damping factor . The line of the delay зa the signal by s time is the second element. The mathematical model of the generator under investigation with the delayed feedback is given by the system of differential equations ( x_ 1 ðtÞ ¼ x2 ðtÞ; h i x_ 2 ðtÞ ¼ À x1 ðtÞ þ e @ Fðx@0xðtÀsÞÞ x ðt À sÞ À x ðtÞ ; 2 2 0 ð1:6Þ where x1 corresponds to x in Fig.