Secret-Sharing Schemes for General and Uniform Access Structures

Applebaum, Benny; Beimel, Amos; Farràs, Oriol; Nir, Oded; Peter, Naty

doi:10.1007/978-3-030-17659-4_15

Cited by 39 publications

(13 citation statements)

References 38 publications

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“…The DNF construction from [10] has information ratio at most n−1 k−1 . Observe that if k = ln n ln ln n , then n k < n k e k k k = n k e ln n ln ln n e ln n ln ln n ln( ln n ln ln n ) = n k n 1 ln ln n n 1− ln ln ln n ln ln n = n k−1+o (1) , and so n−1 k−1 = n k−2+o (1) . Therefore, our construction is useful if k is constant or k ln n ln ln n .…”

Section: Ports Of Matroids Of Higher Rankmentioning

confidence: 99%

“…+ o(1)). If k is close n/2, then the schemes in [1,25] have smaller information ratio. In this work, we denote the logarithmic function with base 2 and base e by log and ln, respectively.…”

Section: Secret Sharing Schemesmentioning

confidence: 99%

“…In general, for a given access structure, it is not known what the scheme with smallest information ratio is. By means of general constructions, we know that every access structure on a set of n participants admits a scheme with information ratio O(2 cn ) for some c < 1 [1,25]. On the other hand, Csirmaz proved that there exists a family of access structures that require schemes with information ratio O(n/ log n) [14].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Secret sharing schemes for ports of matroids of rank 3

Farràs¹

2020

Kybernetika

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Section: Ports Of Matroids Of Higher Rankmentioning

confidence: 99%

“…+ o(1)). If k is close n/2, then the schemes in [1,25] have smaller information ratio. In this work, we denote the logarithmic function with base 2 and base e by log and ln, respectively.…”

Section: Secret Sharing Schemesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Secret sharing schemes for ports of matroids of rank 3

Farràs¹

2020

Kybernetika

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“…Attribute-based encryption (ABE) [1,2] was introduced in 2006 as a generalization of identity-based encryption (IBE) [3,4]. ABE exists in two forms key-policy ABE (KP-ABE) and ciphertext-policy ABE (CP-ABE).…”

Section: Introductionmentioning

confidence: 99%

A Novel Implementation of Attribute Based Encryption for Query Optimization in Big Data Using Mapreduce

Bharati¹,

Ravi²,

Kumari³

2021

ITII

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Data increased daily and has a significant role in every field, like industries, medical, etc. The data is captured, stored, and it is processed to retrieve the necessary data. Security and privacy play an essential role when critical data is shared among users in a distributed environment. These challenges are to be addressed. Mainly they are highly required during sharing and storing vast amounts of data. This paper presents a novel solution to secure the vast data with Attribute-based encryption (ABE), providing access control that prevents unauthorized user's access. Moreover, query optimization is provided in this paper to retrieve the required encrypted data from the big data quickly.

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“…The parties are allowed to send a single message to Carol which may depend on their "shares" and shared randomness. CDS has found multiple applications in cryptography, including private information retrieval [58], attribute-based encryption [56], priced oblivious transfer [8] and secret sharing for uniform/general/forbidden/graph access structures [18,17,10,78,11].…”

Section: Introductionmentioning

confidence: 99%

Function-private Conditional Disclosure of Secrets and Multi-evaluation Threshold Distributed Point Functions

Miranda¹,

Yeo²,

Sehrawat³

2021

Preprint

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Conditional disclosure of secrets (CDS) allows multiple parties to reveal a secret to a third party if and only if some pre-decided condition is satisfied. In this work, we bolster the privacy guarantees of CDS by introducing function-private CDS wherein the pre-decided condition is never revealed to the third party. We also derive a function secret sharing scheme from our function-private CDS solution. The second problem that we consider concerns threshold distributed point functions, which allow one to split a point function such that at least a threshold number of shares are required to evaluate it at any given input. We consider a setting wherein a point function is split among a set of parties such that multiple evaluations do not leak non-negligible information about it. Finally, we present a provably optimal procedure to perform threshold function secret sharing of any polynomial in a finite field. † The is the full version of the paper that will appear in Cryptology and Network Security (CANS), 2021.

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Secret-Sharing Schemes for General and Uniform Access Structures

Cited by 39 publications

References 38 publications

Secret sharing schemes for ports of matroids of rank 3

Secret sharing schemes for ports of matroids of rank 3

A Novel Implementation of Attribute Based Encryption for Query Optimization in Big Data Using Mapreduce

Function-private Conditional Disclosure of Secrets and Multi-evaluation Threshold Distributed Point Functions

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