Abstract: Attribute based encryption from lattices has the property of resisting quantum attacks,and achieves fine-grained access control of attributes by cleverly embedding access control policies into ciphertext or keys.However,due to the inherent weaknesses of attribute based encryption,users with the same attribute may leak the key.To avoid key leakage,attribute based encryption schemes need to implement the function of tracking and revoking specific user decryption permissions.However,illegal users may still attempt to recover the keys of past sessions by collecting large amounts of encrypted data.To effectively resist such attacks,the scheme must implement forward security.In response to the current demands and challenges in the field of lattices cryptography,this paper proposes a multi-functional attribute based encryption scheme based on the Decisional Learning with Errors(DLWE) problem from lattices that can prove security.The scheme uses a complete binary tree to track the identity matrices related to the users in the decryption key(such as the values of the leaf nodes of the complete binary tree) in order to track malicious users.Introducing a user revocation mechanism that allows attribute authority to revoke user permissions in a timely and effective manner without generating new keys for the users.Using tag puncturing method to ensure that even if the current key is leaked,the past ciphertext remains secure and achieves forward security.In addition,due to the uncertainty of the upsampling algorithm from lattice,it is currently difficult to achieve experiments on attribute based encryption from lattice.Therefore,the security and correctness of the scheme are verified through theoretical analysis.The scheme not only optimizes space storage efficiency,but also compensates for the shortcomings caused by the lack of functions of attribute based encryption schemes on lattice cryptography.

Key words: Lattice,Attribute based encryption,Traceable,Forward security,User revocation