Xiaole Fang

Jacques M. Bahi, Xiaole Fang, Christophe Guyeux

Internet communication systems involving cryptography and data hiding often require billions of random numbers. In addition to the speed of the algorithm, the quality of the pseudo-random number generator and the ease of its implementation are common practical aspects. In this work we will discuss how to improve the quality of random numbers independently from their generation algorithm. We propose an additional implementation technique in order to take advantage of some chaotic properties. The statistical quality of our solution stems from some well-defined discrete chaotic iterations that satisfy the reputed Devaney's definition of chaos, namely the chaotic iterations technique. Pursuing recent researches published in the previous International Conference on Evolving Internet (Internet 09, 10, and 11), three methods to build pseudorandom generators by using chaotic iterations are recalled. Using standard criteria named NIST and DieHARD (some famous batteries of tests), we will show that the proposed technique can improve the statistical properties of a large variety of defective pseudorandom generators, and that the issues raised by statistical tests decrease when the power of chaotic iterations increase.

Xiaole Fang, Christophe Guyeux, Qianxue Wang et al.

Design and cryptanalysis of chaotic encryption schemes are major concerns to provide secured information systems. Pursuing our previous research works, some well-defined discrete chaotic iterations that satisfy the reputed Devaney's definition of chaos have been proposed. In this article, we summarize these contributions and propose applications in the fields of pseudorandom number generation, hash functions, and symmetric cryptography. For all these applications, the proofs of chaotic properties are outlined.

Qianxue Wang, Simin Yu, Christophe Guyeux et al.

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 Devaney's 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.

Jacques M. Bahi, Xiaole Fang, Christophe Guyeux et al.

Lots of researches indicate that the inefficient generation of random numbers is a significant bottleneck for information communication applications. Therefore, Field Programmable Gate Array (FPGA) is developed to process a scalable fixed-point method for random streams generation. In our previous researches, we have proposed a technique by applying some well-defined discrete chaotic iterations that satisfy the reputed Devaney's definition of chaos, namely chaotic iterations (CI). We have formerly proven that the generator with CI can provide qualified chaotic random numbers. In this paper, this generator based on chaotic iterations is optimally redesigned for FPGA device. By doing so, the generation rate can be largely improved. Analyses show that these hardware generators can also provide good statistical chaotic random bits and can be cryptographically secure too. An application in the information hiding security field is finally given as an illustrative example.