Lattice-Based Public Key Cryptography

In recent years,although lattice-based public key cryptography has made great progress as the representative of post-quantum cryptography,there are still many problems to be solved in lattice-based cryptography.For example,one of the problems is that the size of the lattice-based public key is large,resulting in low space efficiency.Therefore,the lattice-based cryptographic algorithms with shorter key need to be designed to increase the space utilization efficiency.Another problem is that the application of lattice-based cryptography needs to be expanded.Security models and applications related to lattice-based cryptography need to be explored continuously.The other problem is that the high-dimensional lattice-based key and huge amount of data will bring heavy burden to the transmission and management of information in the process of application.Effective methods need to be adopted in order to compress the data.In order to solve the above problems,a public key cryptosystem with integrated lattice is proposed in this paper,in which the traditional public key cryptosystem and the characteristics of lattice are combined.First of all,public decisions were negotiated through a social platform,which includes the processing of identity information,the method of key exchange and the matrixequation for integration.Then,the identity information was compressed by discrete cosine transform.And then,the keys for integration were exchanged by using the elliptic curve cryptography.At last,the plaintext,the keys and the compressed identity information were integrated in matrix equation.The encryption and decryption processes were simulated in MATLAB.The simulation results show that the public key cryptosystem with integrated lattice can not only avoid the transmission and preservation of large-size public keys,but also have the function of authentication while transmitting information.The algorithm proposed in this paper is simple and feasible in practical application and has strong security.The compressive sensing theory breaks through the limitation of Nyquist sampling rate and has been applied in the field of image compression and cryptography.Both the compressive sensing model and lattice-based cryptography are matrix equation operations.They have some relevance.A third-party lattice-based identity authentication scheme based on compressive sensing theory is proposed in this paper,in which the lattice-based public key cryptography algorithm and the compressive sensing theory are combined.There are two core algorithms in the scheme.One is the algorithm for generating the user's identification information,which combines the compressive sensing theory.The other is the algorithm for generating the user's certificates and keys.In the process of generating the user's identificationinformation,the encryption matrix library used by the trusted authority which is the third party is designed as a paging form in this paper.On the one hand,the paging form facilitates the indexing operation of the encryption matrix and the management of the third party.On the other hand,the operation rules of combining the user's password and the application date can be changed periodically according to the needs,which can greatly increase the security performance of authentication.The functions of this scheme include the certificate issuance,key management,identity authentication,password retrieval and certificate revocation.According to different needs,three identity authentication processes are designed in this paper.They are the unilateral identity authentication process,the interactive identity authentication process and strong security interactive identity authentication process.In the forward operation,on the one hand,the lattice-based authentication scheme can avoid using the large-size lattice-based public key by combining with traditional public key cryptography,on the other hand,the large amount information data is compressed to a great extent by combining with the compressive sensing model.It makes the reverse operation impossible to succeed and achieves the purpose of resisting quantum attacks.