Research And Applications Of Permutation Group Theory Based Cryptosystem

In recent years,with the rapid development of Internet?Internet of Things,cloud computing and other information technologies,the degree of social in-formatization has been rapidly improved,and human beings have come to the era of big data.However,social informatization produces serious infor-mation security problems wile it promotes economic and social development and improves people's lives.In the era of big data,information security is an important issue of common concern in different fields of society.The cryp-tosystems are the key to realize and guarantee information security,and plays a key role in protecting the confidentiality and integrity of information.The construction of the cryptosystems is closely related to the permutation group theory because the cryptosystems are usually defined on a finite set.In this thesis,we apply the ideas and methods of the permutation group theory to the field of the research and application of the cryptosystems.We research the key problems faced in constructing a secure and efficient cryptosystem,and will construct an S-boxes with good cryptographic properties.Mean-while,a group-based NTRU-like cryptosystem and a searchable encryption scheme that supports personalized privacy requirements are proposed.The main works and the results are summarized as follows:In terms of construction of S-boxes,firstly,an S-boxes construction method based on chaos and transpositions is proposed,which can construct S-boxes with better cryptographic properties than the existing chaotic-based S-boxes;secondly,an S-boxes construction method based on the Cayley graph and transpositions is proposed,which can construct S-boxes with better crypto-graphic properties than the existing optimization based S-boxes.In terms of differential uniformity of functions,firstly,we propose a cal-culation method of the differential uniformity based on the conjugate permu-tation and construct three kinds of new differential 4 uniform permutation on F22n for any integer n;then,we research the differential uniformity of the composition of a function and a permutation,construct two kinds of new dif-ferential 4 uniform permutation on F22 for any integer n,and find a necessary condition for the existence of APN permutation on the finite field F22n for any integer m.In terms of post-quantum public-key cryptosystem,we extend the lattice-based public key cryptosystem NTRU which is defined on the truncated poly-nomial ring to the poly-Z group,propose a poly-Z group based NTR.U-like public key cryptosystem and show that the non-abelian poly-Z group based NTRU-like public key cryptosystem is more secure than NTRU against lattice-based attacks.In terms of searchable encryption schemes,a searchable encryption scheme based on CT-AES algorithm is proposed to solve the problem of privacy pro-tection in the data storage phase of big deta life cycle,we show that the proposed scheme can resist the inside keyword guessing attack and protect the privacy of users while utilizing the huge value of big data.