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Journal of Computers

Improvement on a Fuzzy Identity-based Encryption Scheme

Guoyan Zhang, Feng Wang

Published Nov 1, 2014• 3 citations

Abstract

Abstract—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.

DOI: 10.4304/jcp.9.11.2727-2732

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Abstract. In this paper, we present an identity-based encryption (IBE) scheme from lattices with efficient key revocation. We adopt multiple trapdoors from the Agrawal-Boneh-Boyen and Gentry-Peikerty-Vaikuntanathan lattice IBE schemes to realize key revocation, which in turn, makes use of binary-tree data structure. Using our scheme, key update requires logarithmic complexity in the maximal number of users and linear in the number of revoked users for the relevant key authority. We prove that our scheme is selective secure in the standard model and under the LWE assumption, which is as hard as the worst-case approximating short vectors on arbitrary lattices. Moreover, our key revocation techniques from lattices can be applied to obtain revocable functional encryption schemes in the similar setting.

Fuzzy identity based encryption (FIBE), proposed by Sahai and Waters, is a new kind of identity based encryption. It allows users with identity w can decrypt ciphertext for w' if and only if w is close enough to w'. Recently, Ren et al. proposed a new FIBE scheme and claimed it is fully CCA2 secure in the standard model with a tight reduction. However, in this paper we will show that their scheme is not correct. Furthermore, the key generation process of their scheme cannot resist the collusion attack, which is a basic security requirement for FIBE. At last, we propose a new fully secure FIBE scheme based on the Sahai–Waters FIBE scheme and prove its security by using the “dual system encryption” technique.

Due to their conjectured resistance to quantum cryptanalysis, strong worst-case/average-case security guarantees, ease of implementation and increasing practicality, lattice-based cryptography is one of the hottest and fastest moving areas in mathematical cryptography today. In this paper, we give a fuzzy certificateless identity-based encryption scheme from lattice, whose security is based on the hardness of the Learning With Errors (LWE) problem. In the scheme, the user can choose his own secret key that the KGC cannot obtain, which is an efficient approach to mitigate the key escrow problem in fuzzy identity-based encryption scheme.

An efficient identity-based encryption (IBE) scheme over lattice is proposed in this paper. Under the hardness of the learning with errors (LWE) problem, the proposed scheme is semantic secure against adaptive chosen identity and chosen plaintext attack in the standard model. To improve the efficiency of the lattice-based IBE scheme, unlike the identity string is encoded into a matrix by a group of public matrices in several known constructions, the identity string of l bits is encoded into a vector with the help of l+1 vectors in this paper. With the help of this idea, we achieve the private key extraction of IBE scheme at the same lattice. Then, the public key of the proposed scheme only consists of one n×m matrix and l+1 vectors, compared with that the public keys of the known lattice-based IBE schemes all consist as a group of n×m matrices. Hence, the public key size of this scheme is shorter than that of the known constructions.

At present, most of the identity based encryption (IBE) schemes from the lattice originate from the results of Gentry et.al., and regard each identity as a bit string with equal length and then map a matrix to every bit of identity string. Consequently, they are considerably less efficient. In our paper, we construct an IBE which is efficient from standard learning with errors problem and handles identities as a chunk for performance. In the standard model, our paper gives a proof which our IBE is IND-sID-CCA secure. Mean-while, we also show which our IBE construction is also IND-ID-CCA secure via the technique i.e., imposing additional restrictions on the identities, presented by Boyen and Boneh.