| Inversion theorem is ancient and mysterious mathematical theorems, theMobius function is the main object of study of the function of the numbertheory, as early as in1857, R. Dedekind given to the Mobius inversionformula, it has a variety of extended form, it also is very useful in numbertheory and combinations of mathematics. Especially in the1990s, a famousscholar, Chinese Academy of Sciences, Tsinghua University, Professor Chenmade the Mobius inversion formula extend to a continuous form to open a newchapter in the Mobius inversion formula applied. Mobius inversion formulasuccessfully solve the inverse problem in applied physics, for example, theinverse problem of the Fermi system. The world famous magazine "NATURE"published a full-page article of Professor Chen Nanxian, and spoke highly ofits effects. Huaqiao University, Professor Su Wuxun let Chen-Mobiuspromotion applied to the field of communication and information, and haveachieved a certain amount of research. Chen-Mobius was applied to the wayfrom the beginning of the change in analog form to digital form in the field ofcommunications and information processing applications.it also cover thevoice communication by adjustment of the spread spectrum demodulation andthe space encryption in the form of voice communication encryption now.This topic of this article is the use of the Chen-Mobius transform family offunctions to generate an encryption algorithm. The principle is the use ofoblique-orthogonality of function sets evaluated by Chen-Mobius transform.by using high-speed A/D converter a variety of signals are converted intodigital signals, then, the serial digital signal are connected into a set of N-bitparallel signals, each signal (1or0) be coded by a special waveform offunction sets evaluated by Chen-Mobius transform. When they beentransmitted through the line, this N-bit (or N) encoded waveform is directlymixed together, At the receiver, these output signals are simultaneously putinto N parallel discriminations of signal. When the N-bit (or N) encoded waveform was integrated with each function set which was generated by thediscriminations of signal,we can identify each of the digital signal.In the course of the study, in order to verify the effect of the application ofthe realization, this article applied voice encrypted at DE2experimental boardof ALTERA. The main work is as follows:Ⅰ. The study of Chen-Mobius communication system. Analysis of the natureof the Mobius inverse transform, calculate the common signal waveforminverse transform coefficient. The analysis and comparison of Chen-Mobiustransform in analog implementations, in digital implementations, in multiplecarrier method, and the differences and advantages of the traditional means ofcommunication.Ⅱ. Build a new model of the Chen-Mobius encryption algorithm. analysisthe New Chen-Mobius encryption algorithm, build a functional model of thenew Chen-Mobius confidential system, the design parameters of variousfunctional modules, especially for the Chen-Mobius transform waveformmodule frequency determine, in order to establish a new Chen-Mobiusencryption algorithm system model.Ⅲ. New Chen-Mobius encryption algorithm simulation to achieve: theChen-Mobius transformation properties and build encryption algorithmsystem model of the Chen-Mobius, the utilize of Matlab and atleradevelopment software DSP Builder structures Chen-Mobius waveformgenerator model.Ⅳ. The application of the Chen-Mobius encryption algorithms in hardware:DSP Builder design process made HDL program packaged into modules andproduced structures of other modules in the system. Test the effect of the newChen-Mobius encryption algorithm, and test the encryption algorithms voiceencryption effect.Ⅴ. The Chen-Mobius encryption algorithms in voice applications: the use ofhardware packaged as a module of the Chen-Mobius encryption algorithm,and the algorithm is applied to the field of voice encryption. |
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