Chaotic map implementation based on digital-analog hybrid method

Abstract

Random number generator plays an important role in many domains, including secret communication, radar waveform generation, etc. However, the existing methods for generating random numbers cannot meet the actual demand for speed. Even worse, the use of analog device will restrict the speed of generator and robustness of system. As a result, researchers start to turn their eyes to digital implementation which is stabler and more efficient than the analog counterpart. Unfortunately, digital methods still have the disadvantages of dynamical degradation because of word length limitation effect. Though some remedies, such as increasing computing precision, cascading multiple chaotic systems, pseudo-randomly perturbing the chaotic system, the switching multiple chaotic systems and error compensation method are proposed, but the limitations are still inevitable. In recent researches, continuous-time chaotic oscillators are used with digital devices to realize random number generator, and a new approach is proposed to solve the dynamical degradation of digital chaotic system by coupling the given digital chaotic map with an analog chaotic system, where the analog chaotic system is applied to anti-control the given digital chaotic map. However, this method also requires a whole continuous-time system realized with analog devices, which confines the system performance. In this paper, a new digital-analog hybrid chaotic map with only one analog capacitor is constructed to produce random numbers. Firstly, the block diagram of digital-analog hybrid system based on the single capacitance feedback is given, and the model of the system is derived from the block diagram. Secondly, the simple logistic map is applied to the model and its nonlinear dynamics behaviors are analyzed and compared to verify the correctness and effectiveness of the proposed method. Then a more complex two-way coupled saw tooth map is used to produce pseudorandom sequences through simulation smoothly. When designing the circuits of the system, a digital-analog hybrid implementation with field programmable logic gate array and a single analog capacitor is used to realize chaotic maps, showing that it can overcome the finite word length effect of digital implementation. NIST, a general statistical test suiting for random and pseudorandom number generator cryptographic applications, is used to test the sequences produced by the new system. The results show that the new hybrid system is insensitive to the evolution of circuit parameters and the randomness of sequence is in accordance with the practical application. The circuit implementation verifies the numerical simulation and theoretical results. The high speed digital devices and a single analog capacitance are applied to the proposed random sequence generator, and therefore it can be integrated easily into the systems of digital encryption, secure communication and radar waveform generation.