Performance Comparison of Spline Curves and Chebyshev Polynomials for Managing Keys in MANETs

The dynamic and unstable nature of Mobile Ad hoc Networks (MANETs) does not support the existence of a centralized key server to govern keys. There exist two hierarchical key management techniques which are based on Polynomial Interpolation methods i.e. Lagrange's Polynomial interpolation and Curve fitting method. Both these techniques require high computational costs for higher-order polynomials as well as they suffer from Runge's problem. So, other polynomial interpolation methods were tried. In this work, key management is implemented using Spline Curves and Chebyshev Polynomials interpolation method and simulated in various settings. The key shares by Security Association Members (SAMs) are generated, distributed and secret key is built using any of the two polynomial interpolation methods. It is analyzed from the simulation results that the power and memory consumption in MANETs is decreased by using these methods. Spline Curves and Chebyshev polynomials both are more accurate, secure and stable as they not only provide security but they also impose no restriction to the order of the Polynomial. Hence, the key management schemes using these methods provide better cryptography. The results of their comparison have been analysed on various parameters. The significant property of Chebyshev polynomials is its recursive nature which outperforms it over Spline Curves.