Designing Multi dimensiona Quadratic Map with Fixed Point Finite Precision

Abstract

The resistance to cryptanalysis in cryptography can be achieved with aperiodic and highly non-linear random sequences. Chaotic ITlapS over real space exhibit the properties for encryp tion key gen eration in cryptography. Chaotic maps are sensitive to the parame ter selection and initial condition in order to make chaotic trajectory aperiodic and unpredictable. In discrete domain, chaotic maps can visit finite set of sample space, whi ch 111akes the chaotic trajectory compact and periodic orbits. Non-linearity feedback and cascad ing of the multiple chaotic maps are the two main factors which can decelerate the dynamic degradation of digital chaotic maps un der finite precision. In this work, we propose multidimensional modified quadra tic chaotic map under finite precision. The pro posed cascaded quadratic maps with non-linear feedback enhances period length of the digital chaotic map. We also analyzed the pro posed map using well-known Liapunov Exponent Toolbox (LET), NIST statistical test, and auto-correlation. The analysis suggests tha t the proposed modified quadratic map under finite precision has low complexity and exhibits the characteristics for cryptogra phy.