Yet having a very long history, how to generating good random number sequences still remains as a technical challenge. Although some mechanical ways, such as tossing a coin or rolling a dice, are commonly accepted as good random sources, they are obviously not been able to fulfill the requirements of most of the real-world applications, in which high throughput and good quality are generally required.
For more than half century, different random number generators have been proposed. Recently, we have witnessed an active involvement of another branch of sciences in this topic, in particularly, aiming for cryptographical applications. Due to the distinct properties of chaos, including random-like dynamics, continuous broadband frequency spectrum, high sensitivity on initial conditions and system parameters, etc, the use of chaos in random number generation and cryptographical applications has aroused tremendous interests.
However, the actual realization environment is usually ignored in most of the chaos-based designs, for which an infinite precision is commonly assumed. As pointed out by some researchers, if a chaotic system is to be implemented in finite precision, its dynamics will be greatly deviated from its original one, and hence some nice properties will be vanished.
In this thesis, the use of chaotic maps or chaotic systems for the generation of random number under a finite precision environment is to be studied. Firstly, the adverse effects on the characteristics of the chaotic maps and chaos-based random number generators are investigated in details, when quantization errors occur through the evolution of the associated chaotic maps. In order to tackle with these effects, a novel high-dimensional chaos-based post-processing function is designed. With such data post-processing, the statistical quality of the generated random sequence can be greatly improved and can fulfill the up-to-date standards. From the experiments, it shows that the newly designed technique outperforms all the other existing post-processing methods, both in terms of performance and speed.
Finally, two practical designs of chaos-based random number generators are suggested for 32-bit and 8-bit precision environments. With a simple cascade structure of a chaotic map and the chaos-based post-processing function, a fast and simple chaos-based random number generator is designed in a 32-bit machine. An UDP secure chatting system is then developed, in which an effective encryption scheme is designed based on the 32-bit chaos-based random number generator. For the 8-bit environment, a chaotic circuit together with the proposed post-processing function is used. Good random number sequences can be generated and its quality is confirmed by statistical tests. This provides a unique solution for such a low precision system environment, which is still commonly found in industrial and consumer markets.
Author: Tang Kwok Wah
Source: City University of Hong Kong