Research On Boolean Functions Generation And Cryptanalysis Based On Heuristics And Machine Learning Algorithms

Cryptographic functions are an important part of the design and analysis of cryptographic algorithms.The search for Boolean functions with good performance considering various cryptographic properties has been a hot and difficult research area in the field of cryptography.Therefore,this paper aims to explore and study two areas of cryptographic research,namely Boolean function generation and cryptanalysis,with the help of emerging computer technologies such as machine learning.The main work of the article has the following three aspects.(1)A study related to Boolean functions using heuristic algorithms was carried out.A new algorithm for searching Boolean functions is designed based on the gravitational search algorithm,supplemented by other heuristic algorithms such as simulated annealing.The algorithm exploits the one-to-one correspondence between n-element Boolean functions and points in a 2n-dimensional space,simulates the motion in nature following Newton’s law of gravity,uses the change in coordinates before and after the motion of each point in space to represent the change in the truth table of its corresponding n-element Boolean function,and then searches deeply for the proximity function in its surrounding space after the motion has converged.For different search objectives,the algorithm is also designed to combine different safety metrics such as high non-linearity,high algebraic count and low autocorrelation absolute value,sum of squares,etc.The experimental results show that the algorithm can generate Boolean functions of 8,9 and 10 variables with excellent overall performance,and can also directly obtain functions of high non-linearity with 1st order elasticity or meeting the 1st order diffusion criterion without considering the linear transformation condition.The algorithm implements a direct computer search to generate 2-output balanced Boolean functions.(2)Research related to cryptographic functions was carried out using machine learning algorithms.Attempts were made to design reinforcement learning algorithms that can quickly obtain Boolean functions with good performance and neural network models that can generate Bent functions based on the DDQN(Double Deep Q Network)algorithm and GAN(Generative Adversarial Networks)algorithms in machine learning,respectively,and new target The performance of the new target fitness function and the neural network structure that is isomorphic or similar to the task target is experimentally corroborated.The experiments show that the isomorphic fitting network can quickly generate 8-variable Boolean functions with a nonlinearity of 116 or 9-variable Boolean functions with a nonlinearity of 238 with the help of the new target function;also the GAN network can generate a large number of Bent functions after a short training period using a network structure designed with the isomorphic fitting principle.3)A study related to grouped cryptanalysis using generative adversarial network algorithms was conducted.The similarities in structure and computational processes between neural networks and packet cipher algorithms in machine learning means were observed in focus.A cryptanalysis method based on the GAN algorithm is proposed by considering the design of the network structure from this aspect and fitting the decryption network with a neural network.The method trains the network for a fixed encryption algorithm,using ciphertext-plaintext pairs as data set inputs,and is eventually able to obtain a neural network that can input ciphertexts and output plaintexts.In the experiments,an attempt was made to produce 200,000 sets of random ciphertext-plaintext data sets using DES encryption in ECB(Electronic Codebook)mode as an example,and the average error between the data obtained by the network after decrypting the ciphertext and the real plaintext data after training was around 22.0%.