Research On Digital Cryptography Algorithm Based On Complex Logistic Chaotic System

Chaos,represents the seeming random but irregular motion.As one of the three greatest revolutions in physics in the 20 th century,chaos has attracted a wide spread attention by scientists and scholars since it was discovered and proposed.The complex chaotic system is derived from the real chaotic system,by extending the parameters from the real number domain to the complex number domain.Compared with the real chaotic system,the complex chaotic system has more variables,wider dimensions,more complicated chaotic characteristics,and stronger information carrying capacity.Meanwhile,its trajectory will be more difficult to predict.Cryptography,as the research core of information security,plays a critical role in the era of big data.The similarities in structure between chaotic system and traditional cryptography make chaotic cryptography come into being.Therefore,after constructing two new complex logistic mapping systems,the thesis proposes two lightweight cryptograpic algorithms by combining the mapping system with traditional block cipher and traditional stream cipher.The main contents and innovations of this thesis are as follows:(1)Research on complex Logistic mapping and its characteristic analysisFirst,we extend the variables of the real Logistic map from the real number domain to the complex number domain,and construct a two-dimensional lag complex Logistic chaotic system(2D-lag complex Logistic map,2D-LCLM).The characteristics of the 2D-LCLM include: fixed points and their stability,bifurcation diagram,Lyapunov exponents diagram,and phase diagram are all analysed.Secondly,we present a two-dimensional lag complex Logistic chaotic system with complex parameters(2D-lag complex Logistic map with complex parameters,2D-LMCP)on the basis of the 2D-LCLM,and analyze the chaotic characteristics of the system.(2)2D-LCLM-based stream cipherStream cipher,whose length of the plaintext is the same as the key,is easy to implement and has fast speed in encryption and decryption.We propose a 2D-LCLM and stream cipher-based color image cryptography algorithm.Firstly,the color image is divided into R,G,and B three channels,and then the grayscale value of pixels in each channel are converted into 8-bit binary numbers to form the plaintext stream;secondly,we choose the initial value and parameter values of 2D-LCLM,and the sum of the grayscale value as the key,so that the “one-time keys” of the system can well resist the chosen-plaintext attack;thirdly,the pseudo-random sequence generated by the chaotic system is used to construct the integer sequence and the position sequence through mathematical operation,and the value and position of the pixel in the image are replaced and scrambled in units of bits.Simulations and performance analysis results show that the algorithm is superior to other algorithms.(3)2D-LCLM-based digital block cipherIn order to make up for the shortcomings of stream ciphers that the plaintext and key must be of equal length and have poor scalability,we propose a 2D-LCLM and block cipher-based digital cryptography algorithm.The block cipher,whose length of the seed key is arbitrary,has strong adaptability.Confusion and diffusion operations are used to obfuscate the plaintext and the key in this algorithm.In this algorithm,we mainly adopt the Feistel-like structure,and perform nonlinear operations on the data through the dynamic S-box and DNA algorithm in round function F.Then,the scrambling effect is achieved through the swap-place operation in each round and the permutation at the input and output.The initial value and parameters in 2D-LCLM and the round number are treated as “one-time keys”,who changes adaptively with the plaintext,and shared between the sending and receiving end.The 64bit-block length,16 bit round-key length,and 6 rounds ensuring the simple and easy implementation of the algorithm under the condition of limited resources.Simulations and performance analysis results of text and images show that the algorithm has a great encryption effect.To sum up,in this thesis we mainly studys the complex Logistic chaotic system and its implementation in digital cryptographic algorithms.Firstly,we propose the two-dimensional lag complex Logistic map with real and complex parameters.Then,we construct the stream cipher algorithm and block cipher algorithm based on two-dimensional lag complex Logistic map,which providing new ideas for the research of lightweight chaotic cryptographic algorithms.