Abstract-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.

In-network data aggregation is considered an effective technique for conserving energy communication in wireless sensor networks. It consists in eliminating the inherent redundancy in raw data collected from the sensor nodes. Prior works on data aggregation protocols have focused on the measurement data redundancy. In this paper, our goal in addition of reducing measures redundancy is to identify near duplicate nodes that generate similar data sets. We consider a tree based bi-level periodic data aggregation approach implemented on the source node and on the aggregator levels. We investigate the problem of finding all pairs of nodes generating similar data sets such that similarity between each pair of sets is above a threshold t. We propose a new frequency filtering approach and several optimizations using sets similarity functions to solve this problem. To evaluate the performance of the proposed filtering method, experiments on real sensor data have been conducted. The obtained results show that our approach offers significant data reduction by eliminating in network redundancy and outperforms existing filtering techniques.

In this paper, a novel formulation of discrete chaotic iterations in the field of dynamical systems is given. Their topological properties are studied: it is mathematically proved that, under some conditions, these iterations have a chaotic behavior in the meaning of Devaney. This chaotic behavior allows us to propose a way to generate new hash functions. An illustration example is detailed in order to show how to use our theoretical study in practice.