LNT: a logical neighbor tree secure group communication scheme for wireless sensor networks

Secure group communication is a paradigm that primarily designates one-to-many communication security. The proposed works relevant to secure group communication have predominantly considered the whole network as being a single group managed by a central powerful node capable of supporting heavy communication, computation and storage cost. However, a typical Wireless Sensor Network (WSN) may contain several groups, and each one is maintained by a sensor node (the group controller) with constrained resources. Moreover, the previously proposed schemes require a multicast routing support to deliver the rekeying messages. Nevertheless, multicast routing can incur heavy storage and communication overheads in the case of a wireless sensor network. Due to these two major limitations, we have reckoned it necessary to propose a new secure group communication with a lightweight rekeying process. Our proposal overcomes the two limitations mentioned above, and can be applied to a homogeneous WSN with resource-constrained nodes with no need for a multicast routing support. Actually, the analysis and simulation results have clearly demonstrated that our scheme outperforms the previous well-known solutions.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.