The Implementation And Theory Of The Tensor Product Of Matrices Encryption

With the development at full speed in computer network technology and the wide application of computer network, the network security problem is increasingly pop out and information security is becoming one of popular fields that current domestic and international scholar. The development of information security is base on cryptography research such as information encryption digital signature,digital seal,identity authentication, so cryptography is active domains in the study of computer science recently, spring up a number of new encryption technologies, at the same time Chaos cryptology develops rapidly. Chaos cryptology is one of main research field during the writer's graduate student period, in the paper, introduce Chaos arithmetic in the Application of Image Encryption in brief. The writer design a scheme of produce key which base on one-dimensional chaos system and three-dimensional chaos system. The scheme is very safe. The chaos encrypting arithmetic has very good performance through testing encrypting every image's pixel, its speed is quickThe arithmetic of the Tensor Product of Matrices Encryption (TPME) base on the problem of solving reversible matrix of large-scale matrix has very good encryption effect and security effect. The author studies the arithmetic of the Tensor Product of Matrices Encryption, improves the performance of the Tensor Product of Matrices Encryption partly and presents a scheme of produce key which base on sharing data, improve the speed of encryption and deciphering.The introduction part of this paper present the new development of cryptography such as the online/offline cryptography,embargo permit security cryptography chaos cryptography,Elliptic Curve cryptography. The main body of this paper, we introduce theory of matrix product and its mathematical property, then discuss the feasibility of TPME and the content of key management such as producing key,modification key,deleting key. On that basis, the writer puts the scheme of key management of TPME. The scheme of produce key is one of innovations of this article, which base on sharing data. In this paper, encryption key is large-scale matrix which is the tensor product of some small matrices, and decryption Key is inverse matrix of large-scale matrix. They are different, but have intimacy, so we can find some sharing data of them. We can get the sequence of produce inverse matrix by recording the sequence of the tensor product of some small matrices and can get inverse matrix when produce two dimension matrix or three dimension matrix. So we can immediately get decryption Key when server produce encryption key. At last, according to Software Engineering we analyses functional requirement and performance requirements of TPME, and demonstrate the encryption procedure of TPME in mode of C/S. The experiment results show that the TPME has high speed and high performance.