Chaos-based Cryptography Design And Research

With the deepening research into the chaos theory in recent years, various chaotic systems are widely applied into modern cryptography. Chaotic code has become a brand-new and effective encryption. Chaotic cryptography has attracted wide attention at home and abroad. Chaotic cryptography, an interdisciplinary study crossing two fields—chaos and cryptography, is a new branch of cryptography. This paper has made a thorough study on chaotic cryptography, and for the degradation of chaotic dynamics behavior caused by the finite precision of computer to digital chaos, some new chaotic cryptographic algorithms and chaotic disturbance programs has been designed, the superiority of which has been confirmed by means of mathematical proofs and data simulated experiments. The main points are as follows:(1) An encryption algorithm based on the disturbed Lorenz system is proposed. This encryption algorithm firstly perturbs system parameters b in Lorenz system by means of Legendre polynomials, and then uses random sequences generated by Lorenz to conduct a range of operational transformation to original information, which makes the encrypted information more secure. As a result, degradation behavior of chaotic systems caused by the finite precision of computer has been got the effective compensation by disturbance.(2) An image encryption algorithm based on chaos and magic cubes is proposed. This algorithm not only changes the image pixel values, but also achieves image scrambling by rearranging the locations of the image pixels, and finally in the three-dimension brings about the implementation of encryption to the image data information by breaking the features of the original images. Encryption process is that key and chaotic map generate chaotic sequences, and then the chaotic sequences control transformation of the magic cubes to do the image encryption.(3) A new perturbation method to the Tent chaotic map is proposed. This method firstly evenly divides the Tent map domain into 2N parts, and achieve the entire system disturbance by proliferating the Tent map mapping trajectory of one of those parts. The mathematical analysis and simulation experiment results prove that, the disturbed Tent map has the property of uniform invariant distribution, and can produce good cryptographic properties of pseudo-random sequence, which avoid the phenomenon of short-period caused by the computer's finite precision and reduce the sequence's dependence on the disturbance signal. Thus, the digital chaotic system dynamics degradation has been got the effective compensation.