Xiaole Fang

Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems

Traditionally, chaotic systems are built on the domain of infinite precision in mathematics. However, the quantization is inevitable for any digital devices, which causes dynamical degradation. To cope with this problem, many methods were proposed, such as perturbing chaotic states and cascading multiple chaotic systems. This paper aims at developing a novel methodology to design the higher-dimensional digital chaotic systems (HDDCS) in the domain of finite precision. The proposed system is based on the chaos generation strategy controlled by random sequences. It is proven to satisfy the Devaneys definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The application of HDDCS in image encryption is demonstrated via FPGA platform. As each operation of HDDCS is executed in the same fixed precision, no quantization loss occurs. Therefore, it provides a perfect solution to the dynamical degradation of digital chaos.

Noise and Chaos Contributions in Fast Random Bit Sequence Generated From Broadband Optoelectronic Entropy Sources

During the last 4 years, chaotic waveforms for random number generation found a deep interest within the community of analogue broadband chaotic optical systems. Earlier investigations on chaos-based RNG were proposed in the 90s and early 2000, however mainly based on piecewise linear (PL) 1D map, with bit rate determined by analog electronic processing capabilities to provide the PL nonlinear function of concern. Optical chaos came with promises for much higher bit rate, and entropy sources based on high complexity (high dimensional) continuous time (differential) dynamics. More specifically in 2009, Reidler published a paper entitled “An optical ultrafast random bit generator”, in which they presented a physical system for a random number generator based on a chaotic semiconductor laser. This generator is claimed to reach potentially the extremely high rate of 300 Gb/s. We report on analysis and experiments of their method, which leads to the discussion about the actual origin of the obtained randomness. Through standard signal theory arguments, we show that the actual binary randomness quality obtained from this method, can be interpreted as a complex mixing operated on the initial analogue entropy source. Our analysis suggests an explanation about the already reported issue that this method does not necessarily require any specific deterministic property (i.e., chaos) from the physical signal used as the source of entropy. The bit stream randomness quality is found to result from “aliasing” phenomena performed by the post-processing method, both for the sampling and the quantization operations. As an illustration, such random bit sequences extracted from different entropy sources are investigated. Optoelectronic noise is used as a non deterministic entropy source. Electro-optic phase chaotic signal, as well as simulations of its deterministic model, are used as deterministic entropy sources. In all cases, the extracted bit sequence reveals excellent randomness.

Randomness Quality of CI Chaotic Generators: Applications to Internet Security

Due to the rapid development of the Internet in recent years, the need to find new tools to reinforce trust and security through the Internet has became a major concern. The discovery of new pseudo-random number generators with a strong level of security is thus becoming a hot topic, because numerous cryptosystems and data hiding schemes are directly dependent on the quality of these generators. At the conference Internet`09, we have described a generator based on chaotic iterations, which behaves chaotically as defined by Devaney. In this paper, the proposal is to improve the speed and the security of this generator, to make its use more relevant in the Internet security context. To do so, a comparative study between various generators is carried out and statistical results are given. Finally, an application in the information hiding framework is presented, to give an illustrative example of the use of such a generator in the Internet security field.

Theoretical Design and Circuit Implementation of Integer Domain Chaotic Systems

In this paper, a new approach for constructing integer domain chaotic systems (IDCS) is proposed, and its chaotic behavior is mathematically proven according to the Devaneys definition of chaos. Furthermore, an analog-digital hybrid circuit is also developed for realizing the designed basic IDCS. In the IDCS circuit design, chaos generation strategy is realized through a sample-hold circuit and a decoder circuit so as to convert the uniform noise signal into a random sequence, which plays a key role in circuit implementation. The experimental observations further validate the proposed systematic methodology for the first time.

FPGA acceleration of a pseudorandom number generator based on chaotic iterations

As any well-designed information security application uses a very large quantity of good pseudorandom numbers, inefficient generation of these numbers can be a significant bottleneck in various situations. In previous research works, a technique that applies well-defined discrete iterations, satisfying the reputed Devaneys definition of chaos, has been developed. It has been proven that the generators embedding these chaotic iterations (CIs) produce truly chaotic random numbers. In this new article, these generators based on chaotic iterations are redesigned specifically for Field Programmable Gate Array (FPGA) hardware, leading to an obvious improvement of the generation rate. Analyses illustrate that statistically perfect and chaotic random sequences are produced. Additionally, such generators can also be cryptographically secure. To show the effectiveness of the method, an application in the information hiding domain is finally proposed.

Suitability of chaotic iterations schemes using XORshift for security applications

The design and engineering of original cryptographic solutions is a major concern to provide secure information systems. In a previous study, we have described a generator based on chaotic iterations, which uses the well-known XORshift generator. By doing so, we have improved the statistical performances of XORshift and make it behave chaotically, as defined by Devaney. The speed and security of this former generator have been improved in a second study, to make its usage more relevant in the Internet security context. In this paper, these contributions are summarized and a new version of the generator is introduced. It is based on a new Lookup Table implying a large improvement of speed. A comparison and a security analysis between the XORshift and these three versions of our generator are proposed, and various new statistical results are given. Finally, an application in the information hiding framework is presented, to give an illustrative example of the use of such a generator in the Internet security field.