On the bound for anonymous secret sharing schemes

AbstractIn anonymous secret sharing schemes, the secret can be reconstructed without knowledge of which participants hold which shares. In this paper, we derive a tighter lower bound on the size of the shares than the bound of Blundo and Stinson for anonymous (k,n)-threshold schemes with 1<k<n. Our bound is tight for k=2. We also show a close relationship between optimum anonymous (2,n)-threshold secret schemes and combinatorial designs

Octopus: A Secure and Anonymous DHT Lookup

Distributed Hash Table (DHT) lookup is a core technique in structured peer-to-peer (P2P) networks. Its decentralized nature introduces security and privacy vulnerabilities for applications built on top of them; we thus set out to design a lookup mechanism achieving both security and anonymity, heretofore an open problem. We present Octopus, a novel DHT lookup which provides strong guarantees for both security and anonymity. Octopus uses attacker identification mechanisms to discover and remove malicious nodes, severely limiting an adversary's ability to carry out active attacks, and splits lookup queries over separate anonymous paths and introduces dummy queries to achieve high levels of anonymity. We analyze the security of Octopus by developing an event-based simulator to show that the attacker discovery mechanisms can rapidly identify malicious nodes with low error rate. We calculate the anonymity of Octopus using probabilistic modeling and show that Octopus can achieve near-optimal anonymity. We evaluate Octopus's efficiency on Planetlab with 207 nodes and show that Octopus has reasonable lookup latency and manageable communication overhead

Quantum protocols for anonymous voting and surveying

We describe quantum protocols for voting and surveying. A key feature of our schemes is the use of entangled states to ensure that the votes are anonymous and to allow the votes to be tallied. The entanglement is distributed over separated sites; the physical inaccessibility of any one site is sufficient to guarantee the anonymity of the votes. The security of these protocols with respect to various kinds of attack is discussed. We also discuss classical schemes and show that our quantum voting protocol represents a N-fold reduction in computational complexity, where N is the number of voters.Comment: 8 pages. V2 includes the modifications made for the published versio

Almost-perfect secret sharing

Splitting a secret s between several participants, we generate (for each value of s) shares for all participants. The goal: authorized groups of participants should be able to reconstruct the secret but forbidden ones get no information about it. In this paper we introduce several notions of non- perfect secret sharing, where some small information leak is permitted. We study its relation to the Kolmogorov complexity version of secret sharing (establishing some connection in both directions) and the effects of changing the secret size (showing that we can decrease the size of the secret and the information leak at the same time).Comment: Acknowledgments adde

Bounds for Visual Cryptography Schemes

In this paper, we investigate the best pixel expansion of the various models of visual cryptography schemes. In this regard, we consider visual cryptography schemes introduced by Tzeng and Hu [13]. In such a model, only minimal qualified sets can recover the secret image and that the recovered secret image can be darker or lighter than the background. Blundo et al. [4] introduced a lower bound for the best pixel expansion of this scheme in terms of minimal qualified sets. We present another lower bound for the best pixel expansion of the scheme. As a corollary, we introduce a lower bound, based on an induced matching of hypergraph of qualified sets, for the best pixel expansion of the aforementioned model and the traditional model of visual cryptography realized by basis matrices. Finally, we study access structures based on graphs and we present an upper bound for the smallest pixel expansion in terms of strong chromatic index

Communication Efficient Secret Sharing

A secret sharing scheme is a method to store information securely and reliably. Particularly, in a threshold secret sharing scheme, a secret is encoded into $n$ shares, such that any set of at least $t_1$ shares suffice to decode the secret, and any set of at most $t_2 < t_1$ shares reveal no information about the secret. Assuming that each party holds a share and a user wishes to decode the secret by receiving information from a set of parties; the question we study is how to minimize the amount of communication between the user and the parties. We show that the necessary amount of communication, termed "decoding bandwidth", decreases as the number of parties that participate in decoding increases. We prove a tight lower bound on the decoding bandwidth, and construct secret sharing schemes achieving the bound. Particularly, we design a scheme that achieves the optimal decoding bandwidth when $d$ parties participate in decoding, universally for all $t_1 \le d \le n$. The scheme is based on Shamir's secret sharing scheme and preserves its simplicity and efficiency. In addition, we consider secure distributed storage where the proposed communication efficient secret sharing schemes further improve disk access complexity during decoding.Comment: submitted to the IEEE Transactions on Information Theory. New references and a new construction adde