Research On Certificateless Cryptographic Mechanism Based On Lattic

As the world becomes more diverse and open,the security of data has been the focus of attention.As an important part of public key cryptography,certificateless cryptography(CLC)is a research hotspot in recent years.The emergence of certificateless cryptography not only avoids the cost of digital certificate distribution and maintenance,but also solves the identity-based cryptography’s(IBC)key escrow problem.However,the security of conventional certificateless schemes is threatened by the development of quantum computers.Lattice cryptography has received extensive attention as one of the four types of anti-quantum algorithm attacks.An important point that makes the lattice cryptography regime a good security guarantee is that the lattice hard problem has a unique worst case to average case reductive relationship.Therefore,the construction of the certificateless cryptographic scheme that is resistant to quantum attacks has become the focus of public attention and has significant value of theoretical research.In order to improve the efficiency of signature schemes against quantum attacks and solve the problem of heterogeneity of signcryption schemes,this dissertation conducts research on the lattice-based certificateless cryptography.First,the certificateless cryptography is introduced into the traditional lattice-based proxy signature scheme,and the generation process of the proxy signature key is optimized.Then a lattice-based certificateless proxy signature scheme is proposed,and it overcomes the key escrow problem of the traditional proxy signature scheme.Secondly,in order to realize the signcryption process between heterogeneous cryptosystems,by improving the lattice-based IBC signcryption scheme and designing the key generation process of CLC users,a lattice-based efficient heterogeneous signcryption scheme is proposed.Finally,the lattice-based certificateless proxy signature scheme and the lattice-based efficient heterogeneous signcryption scheme are applied to federated learning,realize the secure proxy delegation process of the client to agent and the upload and distribution process of the gradient respectively.Then a federated learning mechanism with post-quantum security is proposed and it ensures the quantum security of data transmission.The main research content of this dissertation are as follows:(1)A lattice-based certificateless proxy signature scheme is proposed.In order to realize the secure proxy delegation process in quantum environment,the certificateless cryptography is introduced into the traditional lattice-based proxy signature scheme,and the generation process of the proxy signature key is optimized.Then a lattice-based certificateless proxy signature scheme is proposed.The original signer generates the proxy signature key using the proxy signer’s identity and its own secret value,and sends the proxy signature key to the proxy signer over a secure channel.The message is signed by the proxy signer using both its own private key and the proxy signature private key.The quantum security of the scheme is proved with the assumption of the difficulty of the small integer solution problem(SIS).This scheme avoids the huge overhead of maintaining certificates,improves the verification speed,and has good anti-quantum security.(2)A lattice-based efficient heterogeneous signcryption scheme is proposed.In order to realize efficient signcryption communication between certificateless cryptosystem and identity-based cryptosystem in quantum environment,by improving the lattice-based IBC signcryption scheme and designing the key generation process of CLC users,then a lattice-based efficient heterogeneous signcryption scheme is proposed.The sender generates signcryption ciphertext through the hash function and matrix operation,and the signcryption of message is realized through the XOR operation.Under the assumption of the difficulty of learning with errors(LWE)problem and SIS problem,the indistinguishability under chosen ciphertext attack(IND-CCA)and the existential unforgeability under adaptive chosen message attack(EUF-CMA)of the scheme are proved.The scheme realizes signcryption communication between heterogeneous cryptosystems,avoids complex signcryption operations and realizes a lightweight signcryption process.(3)A federated learning mechanism with post-quantum security is proposed.In order to realize the federated learning process against quantum attacks,the lattice-based certificateless proxy signature scheme and the lattice-based efficient heterogeneous signcryption scheme are applied to federated learning,and a federated learning mechanism with post-quantum security is proposed.The lattice-based certificateless proxy signature scheme is used to complete the proxy delegation process from the client to agent,the agent replaces the client to communicate with the server.This method improves the efficiency of data transmission.The lattice-based efficient heterogeneous signcryption scheme is used to complete the gradient upload and distribution process between the client and the server,which overcomes the heterogeneity between the client and server.The process realizes the confidential communication process with authentication function between heterogeneous entities.