Graph coloring applied to secure computation in non-Abelian groups

We study the natural problem of secure n-party computation (in the computationally unbounded attack model) of circuits over an arbitrary finite non-Abelian group (G,⋅), which we call G-circuits. Besides its intrinsic interest, this problem is also motivating by a completeness result of Barrington, stating that such protocols can be applied for general secure computation of arbitrary functions. For flexibility, we are interested in protocols which only require black-box access to the group G (i.e. the only computations performed by players in the protocol are a group operation, a group inverse, or sampling a uniformly random group element). Our investigations focus on the passive adversarial model, where up to t of the n participating parties are corrupted.

Active security in multiparty computation over black-box groups

Most previous work on unconditionally secure multiparty computation has focused on computing over a finite field (or ring). Multiparty computation over other algebraic structures has not received much attention, but is an interesting topic whose study may provide new and improved tools for certain applications. At CRYPTO 2007, Desmedt et al introduced a construction for a passive-secure multiparty multiplication protocol for black-box groups, reducing it to a certain graph coloring problem, leaving as an open problem to achieve security against active attacks. We present the first n-party protocol for unconditionally secure multiparty computation over a black-box group which is secure under an active attack model, tolerating any adversary structure Δ satisfying the Q 3 property (in which no union of three subsets from Δ covers the whole player set), which is known to be necessary for achieving security in the active setting. Our protocol uses Maurer’s Verifiable Secret Sharing (VSS) but preserves the essential simplicity of the graph-based approach of Desmedt et al, which avoids each shareholder having to rerun the full VSS protocol after each local computation. A corollary of our result is a new active-secure protocol for general multiparty computation of an arbitrary Boolean circuit.

Phosphorus-based functional groups as hydrogen bonding templates for rotaxane formation

We report on the use of the hydrogen bond acceptor properties of some phosphorus-containing functional groups for the assembly of a series of [2]rotaxanes. Phosphinamides, and the homologous thio– and selenophosphinamides, act as hydrogen bond acceptors that, in conjunction with an appropriately positioned amide group on the thread, direct the assembly of amide-based macrocycles around the axle to form rotaxanes in up to 60% yields. Employing solely phosphorus-based functional groups as the hydrogen bond accepting groups on the thread, a bis(phosphinamide) template and a phosphine oxide-phosphinamide template afforded the corresponding rotaxanes in 18 and 15 % yields, respectively. X-Ray crystallography of the rotaxanes shows the presence of up to four intercomponent hydrogen bonds between the amide groups of the macrocycle and various hydrogen bond accepting groups on the thread, including rare examples of amide-to-phosphonamide, -thiophosphinamide and -selenophosphinamide groups. With a phosphine oxide-phosphinamide thread, the solid state structure of the rotaxane is remarkable, featuring no direct intercomponent hydrogen bonds but rather a hydrogen bond network involving water molecules that bridge the H-bonding groups of the macrocycle and thread through bifurcated hydrogen bonds. The incorporation of phosphorus-based functional groups into rotaxanes may prove useful for the development of molecular shuttles in which the macrocycle can be used to hinder or expose binding ligating sites for metal-based catalysts.

An examination of microfinance self-help groups and the poorest of the poor women in Tamil Nadu, India

This study examined the formation and operation of women's microfinance self-help groups in southern India and investigated whether or not the poorest of the poor women were accepted as members of those groups. The study found that caste was used as a selection criterion. Many eligible women excluded themselves from joining the self-help group due to their own lack of education, age, poor health, poverty and lack of trust in the system. The research revealed that self-help groups enhanced women's income and education, improved village infrastructure, and reduced household conflict. Factors that might prevent inclusion of the poorest of the poor in future microfinance programs were identified.

The renormalization group: A perturbation method for the graduate curriculum

In this paper the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. Lett., 73 (1994), pp.1311-1315; Phys. Rev. E, 54 (1996), pp.376-394] is presented in a pedagogical way to increase its visibility in applied mathematics and to argue favorably for its incorporation into the corresponding graduate curriculum.The method is illustrated by some linear and nonlinear singular perturbation problems. Key word. © 2012 Society for Industrial and Applied Mathematics.

A Combined Renormalization Group-Multiple Scale Method for Singularly Perturbed Problems

This paper introduces a straightforward method to asymptotically solve a variety of initial and boundary value problems for singularly perturbed ordinary differential equations whose solution structure can be anticipated. The approach is simpler than conventional methods, including those based on asymptotic matching or on eliminating secular terms. © 2010 by the Massachusetts Institute of Technology.

Examples illustrating the use of renormalization techniques for singularly perturbed differential equations

With nine examples, we seek to illustrate the utility of the Renormalization Group approach as a unification of other asymptotic and perturbation methods.

Reduction of amplitude equations by the renormalization group approach

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.

The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

Secular series and renormalization group for amplitude equations

We have developed a technique that circumvents the process of elimination of secular terms and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems. © 2008 The American Physical Society.

Keyword field-free conjunctive keyword searches on encrypted data and extension for dynamic groups

We consider the following problem: a user stores encrypted documents on an untrusted server, and wishes to retrieve all documents containing some keywords without any loss of data confidentiality. Conjunctive keyword searches on encrypted data have been studied by numerous researchers over the past few years, and all existing schemes use keyword fields as compulsory information. This however is impractical for many applications. In this paper, we propose a scheme of keyword field-free conjunctive keyword searches on encrypted data, which affirmatively answers an open problem asked by Golle et al. at ACNS 2004. Furthermore, the proposed scheme is extended to the dynamic group setting. Security analysis of our constructions is given in the paper.

On secure multi-party computation in black-box groups

We study the natural problem of secure n-party computation (in the passive, computationally unbounded attack model) of the n-product function f G (x 1,...,x n ) = x 1 ·x 2 ⋯ x n in an arbitrary finite group (G,·), where the input of party P i is x i  ∈ G for i = 1,...,n. For flexibility, we are interested in protocols for f G which require only black-box access to the group G (i.e. the only computations performed by players in the protocol are a group operation, a group inverse, or sampling a uniformly random group element). Our results are as follows. First, on the negative side, we show that if (G,·) is non-abelian and n ≥ 4, then no ⌈n/2⌉-private protocol for computing f G exists. Second, on the positive side, we initiate an approach for construction of black-box protocols for f G based on k-of-k threshold secret sharing schemes, which are efficiently implementable over any black-box group G. We reduce the problem of constructing such protocols to a combinatorial colouring problem in planar graphs. We then give two constructions for such graph colourings. Our first colouring construction gives a protocol with optimal collusion resistance t < n/2, but has exponential communication complexity O(n*2t+1^2/t) group elements (this construction easily extends to general adversary structures). Our second probabilistic colouring construction gives a protocol with (close to optimal) collusion resistance t < n/μ for a graph-related constant μ ≤ 2.948, and has efficient communication complexity O(n*t^2) group elements. Furthermore, we believe that our results can be improved by further study of the associated combinatorial problems.

Securing multicast groups in ad hoc networks

We propose a reliable and ubiquitous group key distribution scheme that is suitable for ad hoc networks. The scheme has self-initialisation and self-securing features. The former feature allows a cooperation of an arbitrary number of nodes to initialise the system, and it also allows node admission to be performed in a decentralised fashion. The latter feature allows a group member to determine the group key remotely while maintaining the system security. We also consider a decentralised solution of establishing secure point-to-point communication. The solution allows a new node to establish a secure channel with every existing node if it has pre-existing secure channels with a threshold number of the existing nodes.

Using the Event Analysis of Systemic Teamwork (EAST) to explore conflict between different road user groups when making right hand turns at urban intersections

Collisions between different types of road users at intersections form a substantial component of the road toll. This paper presents an analysis of driver, cyclist, motorcyclist and pedestrian behaviour at intersections that involved the application of an integrated suite of ergonomics methods, the Event Analysis of Systemic Teamwork (EAST) framework, to on-road study data. EAST was used to analyse behaviour at three intersections using data derived from an on-road study of driver, cyclist, motorcyclist and pedestrian behaviour. The analysis shows the differences in behaviour and cognition across the different road user groups and pinpoints instances where this may be creating conflicts between different road users. The role of intersection design in creating these differences in behaviour and resulting conflicts is discussed. It is concluded that currently intersections are not designed in a way that supports behaviour across the four forms of road user studied. Interventions designed to improve intersection safety are discussed.

Online Customer Experience : What is the Experience and how is it Difference for Frequent and Infrequent Purchasers, Age Cohorts and Gender Groups?

What do we know? • Customer Experience is increasingly becoming the new standard for differentiation in both offline and online retailing, and offers a sustainable competitive advantage. o The economic value of a company’s offering has been observed to increase when the customer has a fulfilling shopping experience (Pine & Gilmore, 1998) o Crafting engaging and customer experience is a known method of generating loyalty, advocacy and word of mouth (Tynan & McKechnie, 2009). o A good experience can entice consumers to shop for longer and spend more (Kim, 2001). • The customer’s experience is made up of diverse elements occurring before, during and after the purchase itself. (Discussed further on page 5). It is cumulative over time and can be influenced by touch points across multiple channels. What remains unclear? • How do Coles customers respond to the elements of online customer experience? • How does the online customer experience differ for frequent and infrequent purchasers? • Do differences between genders and age cohorts for online customer experience exist?