In this paper, we consider the problem of (t, δ) robust secret sharing secure against rushing adversary. We design a simple t-out-of-n secret sharing scheme, which can reconstruct the secret in presence of t cheating participants except with probability at most δ, provided t < n/2. The later condition on cheater resilience is optimal for the case of public reconstruction of the secret, on which we focus in this work.

Our construction improves the share size of Cevallos et al. (EUROCRYPT-2012) robust secret sharing scheme by applying the “authentication tag compression” technique devised by Carpentieri in 1995. Our improvement is by a constant factor that does not contradict the asymptotic near-optimality of the former scheme. To the best of our knowledge, the proposed scheme has the smallest share size, among other efficient rushing (t, δ) robust secret sharing schemes with optimal cheater resilience.

AVISHEK ADHIKARI

Pure Mathematics

P S ROY

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

&nbsp;

The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

&nbsp;

It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

An Efficient Robust Secret Sharing Scheme with Optimal Cheater Resiliency

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Threshold access structures of secret sharing schemes capture a scenario in which all the participants have the same weight (or power) and their contributions are equal. However, in some situations such as gradation among officials in an organization, the participants have different weights. Hierarchical access structures capture those natural scenarios, where different levels of hierarchy are present and a participant belongs precisely to one of them. Although an extensive research addressing the issues of cheater identifiability and robustness have been done for threshold secret sharing, no such research has been carried out for hierarchical secret sharing (HSS). This paper resolves this long-standing open issue by presenting definitions and constructions of both cheater identifiable and robust HSS schemes secure against rushing adversary, in the information-theoretic setting. © Springer Nature Switzerland AG 2018.

Hierarchical secret sharing schemes secure against rushing adversary: Cheater identification and robustness

In this paper, we consider two very important issues namely detection and identification of k-out-of-n secret sharing schemes against rushing cheaters who are allowed to submit (possibly forged) shares after observing shares of the honest users in the reconstruction phase. Towards this, we present four different schemes. Among these, first we present two k-out-of-n secret sharing schemes, the first one being capable of detecting (k − 1)/3 cheaters such that |Vi| = |S|/∊3 and the second one being capable of detecting n − 1 cheaters such that |Vi| = |S|/∊k+1, where S denotes the set of all possible secrets, ∊ denotes the successful cheating probability of cheaters and Vi denotes set all possible shares. Next we present two k-out-of-n secret sharing schemes, the first one being capable of identifying (k−1)/3 rushing cheaters with share size |Vi| that satisfies |Vi| = |S|/∊k. This is the first scheme, whose size of shares does not grow linearly with n but only with k, where n is the number of participants. For the second one, in the setting of public cheater identification, we present an efficient optimal cheater resilient k-out-of-n secret sharing scheme against rushing cheaters having the share size |Vi| = (n−t)n+2t|S|/∊n+2t. The proposed scheme achieves flexibility in the sense that the security level (i.e., the cheater(s) success probability) is independent of the secret size. Each of the four proposed schemes has the smallest share size among the existing schemes having the mentioned properties in the respective models. © Springer International Publishing AG 2016.

Fulltext

Efficient threshold secret sharing schemes secure against rushing cheaters

Secret sharing scheme plays a crucial role in distributed cryptosystems. Due to its extensive use in numerous applications, an important goal in this area is to minimize trust among the participants. To remove this bottleneck, robust secret sharing, which allows the correct secret to be recovered even when some of the shares presented during an attempted reconstruction are incorrect, can be an efficient tool. However, as unconditional security demands honest majority and share size to be at least equal to the size of the secret, the need for computational security of such schemes has been felt over the years, specially in case of multi-secret sharing schemes. In this paper, we provide a notion of computationally robust multi-secret sharing scheme for general access structure. We also propose a robust multi-secret sharing scheme for general access structure and prove its computational security under the proposed notation. © Springer India 2015.

Journal	Data powered by TypesetLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publisher	Data powered by TypesetSpringer Verlag
ISSN	0302-9743