A novel symmetric cryptography based on the hybrid Haar wavelets encoder and chaotic masking scheme

In this scheme, the authors use the seven chaotic parameters (a,β,a,b,x₀,y₀,z₀) and the dimension of Haar wavelet encoder matrix H_n, the combining form of H_n with subwavelet basis {h₀,h₁,...,h_n-1}, the prespecified time span t_s, as well as the coefficients a_i,i=1,...,n, and the prime number k of the collision-free one-way function to serve as the "encryption keys." The security property of the proposed cryptosystem results from two main parts: first, the high sensitivity of synchronization versus parameter or initial condition with small variation. It is sensitive enough to make the state trajectories separate from each other at an exponential rate. The second part depends on the Haar wavelets encoder H_n with its various combining form from the subwavelets basis {h₀,h₁,...,h_n-1}; it is composed the same way as the lottery. Furthermore, due to the collision-free one-way function, the chaotic behavior control parameters are always different. Therefore, the system can be secured as long as the first chaotic parameters are kept secret. Moreover, the transmitting error-detection function of the proposed cryptosystem is also addressed.