Algebra Encryption Algorithm Based On Gray Theory Realization

With the rapid development of Internet, people's life is more convenient and efficient, but the security of network is threatened. So public key cryptography produces, which is an effective solution scheme of ensuring information confidential in the process of transmission. Although public key cryptography is already mature in theory and practice, many sides can be improved. Therefore, the paper implements a new algebra encryption algorithm based on the grey system theory, whose main research results are as follows:(1) Based on the grey system theory and information security, the paper studies the grey system theory in the application of information security. Get grey all generation series through the grey modeling. Using its extrapolative and irreversible characteristics, the paper develops a key seed as the initial sequence. And it can construct a scheme of the low level reversible matrix. These matrixes can be the private key of the algebra encryption system.(2) Combined with the matrix of the Kronecker product and Drazin inverse, the paper puts forward a scheme of using the low level matrix to construct high level matrix and proves the irreversible characteristic of the high level matrix. On the basis, construct a public key cryptosystem using the low level matrix as the private key and the high level matrix as the public key. Moreover, the paper proves the effectiveness of the cryptography.(3) According to the cryptanalysts may put forward several attacking schemes, the paper brings forward the solution schemes of several difficult problems using the high level irreversible matrix with the current difficult problems. And the paper proves the cryptanalysts can't decipher the ciphertexts in the limited time using the high level matrix as the public key of the algebra encryption system to encrypt the texts. At the same time, the paper deeply elaborates the key management in the algebra encryption system.(4) In view of different users focusing on security or effectiveness of encryption differently, in the paper, according to the time/space trade-off curve of NP complete problem, the users of using the algebra encryption system are graded, can meet the users of different groups having different demands of security or effectiveness of encryption, and respectively analyzes the time of deciphering the different groups of the algebra encryption system.(5) Using Matlab simulation, the paper accomplishes the whole process of the algebra encryption system, deeply analyzes the details in the process of the encryption and decryption, and verifies the effectiveness of the encryption algorithm.