Fuzzy Identity-Based Signature from Lattices for Identities in a Large Universe

Zhang, Yanhua; Gan, Yong; Yin, Yawei; Jia, Huiwen; Meng, Yunlong

doi:10.1007/978-3-030-00012-7_52

Cited by 2 publications

(3 citation statements)

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“…In a FIBS scheme, a signature produced using an identity id can be verified by the receiver using an identity id † as long as id and id † are within a certain distance of each other. Over recent years, several FIBS schemes [11][12][13][14][15][16] have been proposed from the SIS problem. In these schemes, the identities are strings of length ℓ, and when verifying a signature σ of identity id = (id 1 , .…”

Section: Introductionmentioning

confidence: 99%

“…That is, in these schemes, the signature σ is verified by using the identity id instead of by using the identity id † . Consequently, these schemes [11][12][13][14][15][16] are not the fuzzy identity-based signature schemes. A leveled FIBFHS scheme [17] has been proposed from the SIS problem.…”

Section: Introductionmentioning

confidence: 99%

“…A leveled FIBFHS scheme [17] has been proposed from the SIS problem. Unfortunately, this FIBFHS scheme [17] suffers from the same mistake as the previous FIBS schemes [11][12][13][14][15][16]. Therefore, our FIBFHS scheme is not only the first leveled FIBFHS scheme but also the first FIBS scheme from the SIS problem.…”

Section: Introductionmentioning

confidence: 99%

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Leveled Fuzzy Identity-Based Fully Homomorphic Signatures

2023

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In fuzzy identity-based fully homomorphic signature (FIBFHS), the output of homomorphic computation, which is related to the identity id, can be verified by the receiver using the identity id^ as long as id and id^ are within a certain distance of each other. Gorbunov, Vaikuntanathan and Wichs (STOC 2015) introduced a new notion called homomorphic trapdoor functions (HTDFs) and constructed the first leveled fully homomorphic signature (FHS) scheme from HTDFs. In this paper, firstly, we extend the notion of HTDFs to fuzzy identity-based homomorphic trapdoor functions (FIBHTDFs). Next, we construct a FIBHTDF based on the small integer solution (SIS) problem by borrowing ideas from the secret-sharing techniques developed by Agrawal et al. (PKC 2012) and Boyen (TCC 2013) and prove that it is selective-identity secure in the standard model. Finally, we construct the first leveled FIBFHS scheme from FIBHTDFs and prove that it satisfies existential unforgeability under selective-identity and static chosen-message attacks in the standard model.

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