Reach On Two Cryptographic Algorithms From Lattice Assumptions

In recent years,the development of quantum computing has posed a threat to the security of present cryptographic systems,and designing secure cryptographic systems that can resist quantum computing has become the focus of cryptography.Among post-quantum cryptographic systems,lattice-based cryptographic systems based on the NP-hard lattice problems have many advantages,such as resistance to quantum computing,provable security,efficient and simple operations,and reductions from worst-case to average-case.These systems have received widespread attention from scholars,and have obtained theoretical research results.However,existing lattice-based cryptographic algorithms have not yet reached the security requirements for communication in a quantum computing environment.Therefore,based on existing research,thesis conducts research on lattice-based cryptographic algorithms with novel security features.The main results are specified as follows:1.A lattice-based anonymous signcryption algorithm,called LASC,is constructed based on the Ring-Learning with Errors problem(RLWE).LASC utilizes error-coordination techniques and rejection sampling techniques in the lattice,and allows a sender and a receiver to complete the signature and encryption operations in one logical step during communication.The identity of the sender is embedded in the signcryptext.Only the receiver participating in the communication can decrypt the signcryptext and obtain the data and sender’s identity.LASC provides anonymity that third parties will not obtain any information about the communication participants’ identities except for the sender and the receiver participating in the communication.In addition,LASC achieves forward security and x-security.The provable security of LASC are formalized in the random oracle model,and LASC’ security depends on the RLWE problem.The performance of LASC shows that it is efficient in terms of computation and communication costs.2.A password-based threshold single sign-on authentication scheme,called LPb TSSO,is based on Learning with Errors problem(LWE).LPb T-SSO introduces multiple identity servers to authenticate a user’s identity through the user’s password and issues a token after accomplishing authentication,which the user can use the token to access the application server.The user evaluates a one-way function of the password and the secret deployed in multiple identity servers using threshold secret sharing,which the function is based on the LWE problem,and takes the function output as a credential,so that quantum adversaries cannot recover the user’s password from the credential by offline dictionary guessing attacks.In addition,this method solves the single-point failure problem.Even if some identity servers are compromised,the adversary cannot recover the secrets stored on the identity server,providing a stronger security guarantee for passwords.LPb T-SSO utilizes a lattice-based threshold signature scheme to issue tokens,ensuring that any adversary cannot forge valid tokens.The provable security of LPb T-SSO are formalized in the random oracle model,and its security depends on the LWE problem.Performance evaluation shows that LPb T-SSO is efficient in terms of computation,storage,and communication costs.