—Sahai and Waters introduced a fuzzy id-based encryption (FIBE) scheme in which an identity was viewed as a set of descriptive attributes, and any user with a private key for an identity ID was allowed to decrypt a ciphertext encrypted with an identity ID′ , if and only if the identity ID and ID′ were close to each other as measured by the “set overlap” distance metric. After that, Shweta Agrawal, Xavier Boyen, Vinod Vaikuntanathan, Panagiotis Voulgaris and Hoeteck Weeto constructed a fuzzy id-based encryption scheme from the hardness of the Learning With Errors ( LWE ) problem. The two schemes both had more longer public and private keys, and it was not very efficient. This paper gives more efficient fuzzy id-based encryption scheme from lattice, in which the public keys are greatly reduced, and there are two vectors corresponding to each bit of the identity by using of the algorithm Sampleleft introduced by Shweta Agrawal, Dan Boneh and Xavier Boyen, and only a trapdoor basis is the secret key. Furthermore, the scheme is dealing with N − bit information and is also secure from the hardness of the Learning With Errors ( LWE ) problem, and all these greatly raise efficiency.
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