Nearly optimal robust secret sharing

Cheraghchi, Mahdi

doi:10.1007/s10623-018-0578-y

Cited by 12 publications

(8 citation statements)

References 28 publications

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“…In particular,[3,7,9,11] use partly similar tools than we do but achieve weaker or incomparable results.…”

mentioning

confidence: 75%

“…, H i , the E j 's for j ∈ H i \ H i−1 are random and independent for any i. 7 Therefore, we can apply Lemma 3 to…”

Section: Proposition 4 At the End Of Step II With Probability At Leastmentioning

confidence: 99%

“…Thus, the interesting region is n/3 ≤ t < n/2, respectively n = 2t + 1 if we want t maximal, where robust secret sharing is possible but only up to a small error probability 2 −κ (which can be controlled by a statistical security parameter κ) and only with some overhead in the share size (beyond the size of the "ordinary", e.g., Shamir share). There are many works [2,3,[5][6][7][8][9]11,13] in this direction. 1 The classical scheme proposed by Rabin and BenOr [13] has an overhead in share size of O(κn), i.e., next to the actual share of the secret, each player has to hold an additional O(κn) bits of information as part of his share.…”

Section: Introductionmentioning

confidence: 99%

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Towards Optimal Robust Secret Sharing with Security Against a Rushing Adversary

Fehr

Yuan

2019

Lecture Notes in Computer Science

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Robust secret sharing enables the reconstruction of a secretshared message in the presence of up to t (out of n) incorrect shares. The most challenging case is when n = 2t + 1, which is the largest t for which the task is still possible, up to a small error probability 2 −κ and with some overhead in the share size. Recently, Bishop, Pastro, Rajaraman and Wichs [3] proposed a scheme with an (almost) optimal overhead of O(κ). This seems to answer the open question posed by Cevallos et al. [6] who proposed a scheme with overhead of O(n + κ) and asked whether the linear dependency on n was necessary or not. However, a subtle issue with Bishop et al.'s solution is that it (implicitly) assumes a non-rushing adversary, and thus it satisfies a weaker notion of security compared to the scheme by Cevallos et al. [6], or to the classical scheme by Rabin and BenOr [13]. In this work, we almost close this gap. We propose a new robust secret sharing scheme that offers full security against a rushing adversary, and that has an overhead of O(κn ε), where ε > 0 is arbitrary but fixed. This n ε-factor is obviously worse than the polylog(n)-factor hidden in the O notation of the scheme of Bishop et al. [3], but it greatly improves on the linear dependency on n of the best known scheme that features security against a rushing adversary (when κ is substantially smaller than n). A small variation of our scheme has the same O(κ) overhead as the scheme of Bishop et al. and achieves security against a rushing adversary, but suffers from a (slightly) superpolynomial reconstruction complexity.

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“…In particular,[3,7,9,11] use partly similar tools than we do but achieve weaker or incomparable results.…”

mentioning

confidence: 75%

“…, H i , the E j 's for j ∈ H i \ H i−1 are random and independent for any i. 7 Therefore, we can apply Lemma 3 to…”

Section: Proposition 4 At the End Of Step II With Probability At Leastmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Towards Optimal Robust Secret Sharing with Security Against a Rushing Adversary

Fehr

Yuan

2019

Lecture Notes in Computer Science

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“…However, such algorithms with side information were not developed for FRS codes in the literature. Listdecoding of FRS codes has been also incorporated in the context of secret sharing to enhance the security [20]- [22]. However, these works do not consider computations over data and are only concerned with recovering the data from the secret shares.…”

Section: B Related Workmentioning

confidence: 99%

List-Decodable Coded Computing: Breaking the Adversarial Toleration Barrier

Soleymani¹,

Ali²,

Mahdavifar³

et al. 2021

Preprint

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We consider the problem of coded computing where a computational task is performed in a distributed fashion in the presence of adversarial workers. We propose techniques to break the adversarial toleration threshold barrier previously known in coded computing. More specifically, we leverage list-decoding techniques for folded Reed-Solomon (FRS) codes and propose novel algorithms to recover the correct codeword using side information. In the coded computing setting, we show how the master node can perform certain carefully designed extra computations in order to obtain the side information. This side information will be then utilized to prune the output of list decoder in order to uniquely recover the true outcome. We further propose folded Lagrange coded computing, referred to as folded LCC or FLCC, to incorporate the developed techniques into a specific coded computing setting. Our results show that FLCC outperforms LCC by breaking the barrier on the number of adversaries that can be tolerated. In particular, the corresponding threshold in FLCC is improved by a factor of two compared to that of LCC.

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“…This scheme can verify for n 3 ≤ t ≤ (1 − ε) • n 2 corrupted shares, while the size of each share is O(L + λ ), where λ is the security parameter, larger than that of secret O(L). Cheraghchi [22] showed a nearly optimal secret sharing method, which employs Reed-Solomon codes to tag a secret image to verify δ n, δ ∈ (0, 1 2) unreliable partners or shares and the size of shares is L…”

Section: A Related Workmentioning

confidence: 99%

Robust Secret Image Sharing Scheme Against Noise in Shadow Images

Sun

Yan

et al. 2021

IEEE Access

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The (k, n)-threshold secret image sharing scheme is an image protection method, whose security comes partly from precise mathematical calculations, and even a little change in shadow images will lead to a false recovered image. Thus, it is crucial to recover the secret image information in the presence of possible noise on shadow images, which has rarely been considered in previous work. In this paper, a robust (k, n)-threshold polynomial-based secret image sharing scheme(RPSIS) against noise on shadow images is proposed, which depends on the randomness of the sharing phase without any other techniques, such as steganography. Additionally, pixel expansion caused by the direct application of error correction codes is avoided. Experimental results and theoretical proof confirm the effectiveness of our scheme. The shadow images of the scheme are of the same size as secret image and the security of the scheme is also maintained with no information leakage. Even though the shadow images are modified by noise, the original secret image can be reconstructed without loss under the error correction capability, which provides more possibilities for the practical application of secret image sharing.

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Nearly optimal robust secret sharing

Cited by 12 publications

References 28 publications

Towards Optimal Robust Secret Sharing with Security Against a Rushing Adversary

Towards Optimal Robust Secret Sharing with Security Against a Rushing Adversary

List-Decodable Coded Computing: Breaking the Adversarial Toleration Barrier

Robust Secret Image Sharing Scheme Against Noise in Shadow Images

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