How to share a quantum secret

We investigate the concept of quantum secret sharing. In a ((k,n)) threshold scheme, a secret quantum state is divided into n shares such that any k of those shares can be used to reconstruct the secret, but any set of k-1 or fewer shares contains absolutely no information about the secret. We show that the only constraint on the existence of threshold schemes comes from the quantum "no-cloning theorem", which requires that n < 2k, and, in all such cases, we give an efficient construction of a ((k,n)) threshold scheme. We also explore similarities and differences between quantum secret sharing schemes and quantum error-correcting codes. One remarkable difference is that, while most existing quantum codes encode pure states as pure states, quantum secret sharing schemes must use mixed states in some cases. For example, if k <= n < 2k-1 then any ((k,n)) threshold scheme must distribute information that is globally in a mixed state.Comment: 5 pages, REVTeX, submitted to PR

How to Share a Secret, Infinitely

Secret sharing schemes allow a dealer to distribute a secret piece of information among several parties such that only qualified subsets of parties can reconstruct the secret. The collection of qualified subsets is called an access structure. The best known example is the $k$-threshold access structure, where the qualified subsets are those of size at least $k$. When $k=2$ and there are $n$ parties, there are schemes for sharing an $\ell$-bit secret in which the share size of each party is roughly $\max\{\ell,\log n\}$ bits, and this is tight even for secrets of 1 bit. In these schemes, the number of parties $n$ must be given in advance to the dealer. In this work we consider the case where the set of parties is not known in advance and could potentially be infinite. Our goal is to give the $t$-th party arriving the smallest possible share as a function of $t$. Our main result is such a scheme for the $k$-threshold access structure and 1-bit secrets where the share size of party $t$ is $(k-1)\cdot \log t + \mathsf{poly}(k)\cdot o(\log t)$. For $k=2$ we observe an equivalence to prefix codes and present matching upper and lower bounds of the form $\log t + \log\log t + \log\log\log t + O(1)$. Finally, we show that for any access structure there exists such a secret sharing scheme with shares of size $2^{t-1}$

How to infinitely share a secret more efficiently

We device a general secret sharing scheme for evolving access structures (following [KNY16]). Our scheme has (sub)exponentially smaller share complexity (share of $i$\u27th party) for certain access structures compared to the general scheme in ~\cite{KNY16}. We stress that unlike ~\cite{KNY16}\u27s scheme, our scheme requires that the entire evolving access structure is known in advance. Revising, ~\cite{KNY16}\u27s scheme (in its most optimized form) is based on a representation of the access structure by an ordered (possibly infinite) oblivious, read once decision tree. Each node is associated with an output of the function (0 or 1). The tree is augmented to cut paths that reach a node where $f$ evaluates to 1 at that node (works for evolving access structures, in which the descendants of all 1-nodes must be 1). Each party $P_i$ receives a (single-bit) share for each edge exiting a node labeled by $x_i$. Generally, the scheme of ~\cite{KNY16} has share complexity $O(w_T(i))$, where $w_T(i)$ is the width of layer $i$ relevant decision tree. In general, this width can reach $\Omega(2^i)$. To get non trivial share complexity, $e^{n^{o(1)}}$, a \emph{tree} of width $e^{n^{o(1)}}$ is required. Our scheme is based on a generalized (infinite) tree representation of the access structure. The main difference is that vertices are labeled with sequences of variables, rather than a single variable. As a result, we often get smaller trees, and the edges $e$ are labeled by more complex (non-evloving) monotone functions $g_e$ of the variables in the sequence. The share associated with the edge is shared (among the parties in the relevant sequence). As a result, the tree is smaller, while the shares received for every edge in it are bigger. Still, the tradeoff is often on our side. Namely, for access structures with ordered read-once \emph{branching programs} with relatively small width, $e^{O(i^c)}$ for $c<0.25$, share complexity of $e^{n^{o(1)}}$ is achieved. More specifically, the resulting share complexity is $(iw_{BP}(i^2))^{O(\log{i} + \log{w_{BP}(i^2)})}$. In particular, for $w=\Omega(i)$, we get share complexity of $w_{BP}(i^2)^{O(\log{w_{BP}(i^2)})}$. Finally, a further improved variant of our scheme for a special class of ``counting\u27\u27 access structures yields polynomial share complexity. In particular, we obtain an evolving secret sharing scheme for \emph{evolving majority} with share complexity $\tilde{O}(n^6)$, answering an open question of~\cite{KNY16}

A Call to Action: Organizing to Increase the Effectiveness and Impact of Foundation Grantmaking

Many nonprofit organizations are constantly struggling to find enough resources to make their organizations more effective and sustainable. A Call to Action illustrates how the lack of core operating support is at the center of this struggle. It tells of the needs and aspirations of nonprofits by enabling them, in their own words, to share their stories

On-the job knowledge sharing: how to train employees to share job knowledge

One of the challenging issues many organizations are facing is to find the best ways to encourage employees share what they have learned on their jobs. Rewarding employees may be one of the techniques used to promote knowledge sharing but there are still psychological barriers preventing employees from sharing knowledge. In many cases, rewarding employees for sharing knowledge ends up in developing the behaviour of hoarding knowledge among employees. Based on a review of existing literature, this article explains how employers can make employees practice knowledge sharing in their daily work activities. The article introduces 12 approaches on how knowledge sharing can be cultivated in the job and train employees to accept that it is their job to share knowledge. Some of the methods discussed include; peer assist, training and mentoring, challenging projects, job description, job rotation, cross training, and sharing sessions. The article also discusses how on-the-job knowledge sharing can promote individual performance among employees. The intention of this article is to provide a framework that helps organizations to choose various methods of knowledge sharing that suit the organization’s needs in order to cultivate sharing of job knowledge and to save the knowledge as an asset

Secure secret sharing in the cloud

In this paper, we show how a dealer with limited resources is possible to share the secrets to players via an untrusted cloud server without compromising the privacy of the secrets. This scheme permits a batch of two secret messages to be shared to two players in such a way that the secrets are reconstructable if and only if two of them collaborate. An individual share reveals absolutely no information about the secrets to the player. The secret messages are obfuscated by encryption and thus give no information to the cloud server. Furthermore, the scheme is compatible with the Paillier cryptosystem and other cryptosystems of the same type. In light of the recent developments in privacy-preserving watermarking technology, we further model the proposed scheme as a variant of reversible watermarking in the encrypted domain

Verifying Privacy-Type Properties in a Modular Way

Formal methods have proved their usefulness for analysing the security of protocols. In this setting, privacy-type security properties (e.g. vote-privacy, anonymity, unlink ability) that play an important role in many modern applications are formalised using a notion of equivalence. In this paper, we study the notion of trace equivalence and we show how to establish such an equivalence relation in a modular way. It is well-known that composition works well when the processes do not share secrets. However, there is no result allowing us to compose processes that rely on some shared secrets such as long term keys. We show that composition works even when the processes share secrets provided that they satisfy some reasonable conditions. Our composition result allows us to prove various equivalence-based properties in a modular way, and works in a quite general setting. In particular, we consider arbitrary cryptographic primitives and processes that use non-trivial else branches. As an example, we consider the ICAO e-passport standard, and we show how the privacy guarantees of the whole application can be derived from the privacy guarantees of its sub-protocols

"Colearning" - Collaborative Open Learning through OER and Social Media

This chapter introduces the concept of coLearning as well as discussing how open learning networks can produce, share and reuse OER collaboratively through social media. COLEARNING OBJECTIVES The aim of this investigation is to identify new forms of collaboration, as well as strategies that can be used to make the production and adaptation processes of OER more explicit for anyone in a social network to contribute. REUSABILITY This open content is an adapted version of a conference paper for OCW conference 2012, which was created by the same authors. This chapter can be reused by: Educators who would like to create reusable OER (images, videos, maps, units) Learners who are interested in tools for reusing and adapting OER Content developers who are looking for different media to enrich OER Social network users who would like to produce and share open media conten

Harnessing and Sharing the Benefits of State Sponsored Research

In recent years data-sharing has been a recurring focus of struggle within the scientific research community as improvements in information technology and digital networks have expanded the ways that data can be produced, disseminated, and used. Information technology makes it easier to share data in publicly accessible archives that aggregate data from multiple sources. Such sharing and aggregation facilitate observations that would otherwise be impossible. But data disclosure poses a dilemma for scientists. Data have long been the stock in trade of working scientists, lending credibility to their claims while highlighting new questions that are worthy of future research funding. Some disclosure is necessary in order to claim these benefits, but data disclosure may also benefit one\u27s research competitors. Scientists who share their data promptly and freely may find themselves at a competitive disadvantage relative to free riders in the race to make future observations and thereby to earn further recognition and funding. The possibility of commercial gain further raises the competitive stakes. This article discusses data sharing in California\u27s stem cell initiative against the background of other data sharing efforts and in light of the competing interests that the California Institute for Regenerative Medicine (CIRM) is directed to balance. We begin by considering how IP law affects data-sharing. We then assess the strategic considerations that guide the IP and data policies and strategies of federal, state, and private research sponsors. With this background, we discuss four specific sets of issues that public sponsors of data-rich research, including CIRM, are likely to confront: (1) how to motivate researchers to contribute data; (2) who may have access to the data and on what conditions; (3) what data get deposited and when do they get deposited; and (4) how to establish database architecture and curate and maintain the database