Fast formulas for computing cryptographic pairings

The most powerful known primitive in public-key cryptography is undoubtedly elliptic curve pairings. Upon their introduction just over ten years ago the computation of pairings was far too slow for them to be considered a practical option. This resulted in a vast amount of research from many mathematicians and computer scientists around the globe aiming to improve this computation speed. From the use of modern results in algebraic and arithmetic geometry to the application of foundational number theory that dates back to the days of Gauss and Euler, cryptographic pairings have since experienced a great deal of improvement. As a result, what was an extremely expensive computation that took several minutes is now a high-speed operation that takes less than a millisecond. This thesis presents a range of optimisations to the state-of-the-art in cryptographic pairing computation. Both through extending prior techniques, and introducing several novel ideas of our own, our work has contributed to recordbreaking pairing implementations.

On Ordinal VC-Dimension and Some Notions of Complexity

We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.

Faster pairings on special Weierstrass curves

This paper presents efficient formulas for computing cryptographic pairings on the curve y 2 = c x 3 + 1 over fields of large characteristic. We provide examples of pairing-friendly elliptic curves of this form which are of interest for efficient pairing implementations.

A method of lines approach for modelling saltwater intrusion in coastal aquifiers

The equations governing saltwater intrusion in coastal aquifers are complex. Backward Euler time stepping approaches are often used to advance the solution to these equations in time, which typically requires that small time steps be taken in order to ensure that an accurate solution is obtained. We show that a method of lines approach incorporating variable order backward differentiation formulas can greatly improve the efficiency of the time stepping process.

Layered titanate nanofibers as efficient adsorbents for removal of toxic radioactive and heavy metal ions from water

Titanate nanofibers with two formulas, Na2Ti3O7 and Na1.5H0.5Ti3O7, respectively, exhibit ideal properties for removal of radioactive and heavy metal ions in wastewater, such as Sr2+ , Ba2+ (as substitute of 226Ra2+), and Pb2+ ions. These nanofibers can be fabricated readily by a reaction between titania and caustic soda and have structures in which TiO6 octahedra join each other to form layers with negative charges; the sodium cations exist within the interlayer regions and are exchangeable. They can selectively adsorb the bivalent radioactive ions and heavy metal ions from water through ion exchange process. More importantly, such sorption finally induces considerable deformation of the layer structure, resulting in permanent entrapment of the toxic bivalent cations in the fibers so that the toxic ions can be safely deposited. This study highlights that nanoparticles of inorganic ion exchangers with layered structure are potential materials for efficient removal of the toxic ions from contaminated water.

Zernike radial slope polynomials for wavefront reconstruction and refraction

Ophthalmic wavefront sensors typically measure wavefront slope, from which wavefront phase is reconstructed. We show that ophthalmic prescriptions (in power-vector format) can be obtained directly from slope measurements without wavefront reconstruction. This is achieved by fitting the measurement data with a new set of orthonormal basis functions called Zernike radial slope polynomials. Coefficients of this expansion can be used to specify the ophthalmic power vector using explicit formulas derived by a variety of methods. Zernike coefficients for wavefront error can be recovered from the coefficients of radial slope polynomials, thereby offering an alternative way to perform wavefront reconstruction.

The Impact of Globalization and Corruption on Extraordinary Wealth: An Empirical Analysis

The billionaires of the world attract significant attention from the media and the public. The popular press is full of books selling formulas on how to become rich. Surprisingly, only a limited number of studies have explored empirically the determinants of extraordinary wealth. Using a large data set we explore whether globalization and corruption affect extreme wealth accumulation. We find evidence that an increase in globalization increases super-richness. In addition, we also find that an increase in corruption leads to an increase in the creation of super fortune. This supports the argument that in kleptocracies large sums are transferred into the hands of a small group of individuals.

Avoiding full extension field arithmetic in pairing computations

The most costly operations encountered in pairing computations are those that take place in the full extension field Fpk . At high levels of security, the complexity of operations in Fpk dominates the complexity of the operations that occur in the lower degree subfields. Consequently, full extension field operations have the greatest effect on the runtime of Miller’s algorithm. Many recent optimizations in the literature have focussed on improving the overall operation count by presenting new explicit formulas that reduce the number of subfield operations encountered throughout an iteration of Miller’s algorithm. Unfortunately, almost all of these improvements tend to suffer for larger embedding degrees where the expensive extension field operations far outweigh the operations in the smaller subfields. In this paper, we propose a new way of carrying out Miller’s algorithm that involves new explicit formulas which reduce the number of full extension field operations that occur in an iteration of the Miller loop, resulting in significant speed ups in most practical situations of between 5 and 30 percent.

Faster pairing computations on curves with high-degree twists

Research on efficient pairing implementation has focussed on reducing the loop length and on using high-degree twists. Existence of twists of degree larger than 2 is a very restrictive criterion but luckily constructions for pairing-friendly elliptic curves with such twists exist. In fact, Freeman, Scott and Teske showed in their overview paper that often the best known methods of constructing pairing-friendly elliptic curves over fields of large prime characteristic produce curves that admit twists of degree 3, 4 or 6. A few papers have presented explicit formulas for the doubling and the addition step in Miller’s algorithm, but the optimizations were all done for the Tate pairing with degree-2 twists, so the main usage of the high- degree twists remained incompatible with more efficient formulas. In this paper we present efficient formulas for curves with twists of degree 2, 3, 4 or 6. These formulas are significantly faster than their predecessors. We show how these faster formulas can be applied to Tate and ate pairing variants, thereby speeding up all practical suggestions for efficient pairing implementations over fields of large characteristic.

Hollywood dominance : will it continue?

Hollywood has dominated the global film business since the First World War. Economic formulas used by governments to assess levels of industry dominance typically measure market share to establish the degree of industry concentration. The business literature reveals that a marketing orientation strongly correlates with superior market performance and that market leaders that possess a set of six superior marketing capabilities are able to continually outperform rival firms. This paper argues that the historical evidence shows that the Hollywood Majors have consistently outperformed rival firms and rival film industries in each of those six marketing capabilities and that unless rivals develop a similarly integrated and cohesive strategic marketing management approach to the movie business and match the Major studios’ superior capabilities, then Hollywood’s dominance will continue. This paper also proposes that in cyberspace, whilst the Internet does provide a channel that democratises film distribution, the flat landscape of the world wide web means that in order to stand out from the clutter of millions of cyber-voices seeking attention, independent film companies need to possess superior strategic marketing management capabilities and develop effective e-marketing strategies to find a niche, attract a loyal online audience and prosper. However, mirroring a recent CIA report forecasting a multi-polar world economy, this paper also argues that potentially serious longer-term rivals are emerging and will increasingly take a larger slice of an expanding global box office as India, China and other major developing economies and their respective cultural channels grow and achieve economic parity with or surpass the advanced western economies. Thus, in terms of global market share over time, Hollywood’s slice of the pie will comparatively diminish in an emerging multi-polar movie business.

Web searching and Σ2 queries

In the terminology of Logic programming, current search engines answer Sigma1 queries (formulas of the form where is a boolean combination of attributes). Such a query is determined by a particular sequence of keywords input by a user. In order to give more control to users, search engines will have to tackle more expressive queries, namely, Sigma2 queries (formulas of the form ). The purpose of the talk is to examine which directions could be explored in order to move towards more expressive languages, more powerful search engines, and the benefits that users should expect.

Tyrosine monitoring in children with early and continuously treated phenylketonuria: Results of an international practice survey

Investigations into the biochemical markers associated with executive function (EF) impairment in children with early and continuously treated phenylketonuria (ECT-PKU) remain largely phenylalanine-only focused, despite experimental data showing that a high phenylalanine:tyrosine (phe:tyr) ratio is more strongly associated with EF deficit than phe alone. A high phe:tyr ratio is hypothesized to lead to a reduction in dopamine synthesis within the brain, which in turn results in the development of EF impairment. This paper provides a snapshot of current practice in the monitoring and/or treatment of tyrosine levels in children with PKU, across 12 countries from Australasia, North America and Europe. Tyrosine monitoring in this population has increased over the last 5 years, with over 80% of clinics surveyed reporting routine monitoring of tyrosine levels in infancy alongside phe levels. Twenty-five percent of clinics surveyed reported actively treating/managing tyrosine levels (with supplemental tyrosine above that contained in PKU formulas) to ensure tyrosine levels remain within normal ranges. Anecdotally, supplemental tyrosine has been reported to ameliorate symptoms of both attention deficit hyperactivity disorder and depression in this population. EF assessment of children with ECT-PKU was likewise highly variable, with 50% of clinics surveyed reporting routine assessments of intellectual function. However when function was assessed, test instruments chosen tended towards global measures of IQ prior to school entry, rather than specific assessment of EF development. Further investigation of the role of tyrosine and its relationship with phe and EF development is needed to establish whether routine tyrosine monitoring and increased supplementation is recommended.

Thermal analysis of hydrotalcite synthesised from aluminate solutions

The aluminate hydrotalcites are proposed to have either of the following formulas: Mg4Al2(OH)12(CO3 2-)·xH2O or Mg4Al2(OH)12(CO3 2-, SO4 2-)·xH2O. A pure hydrotalcite phase forms when magnesium chloride and aluminate solns. are mixed at a 1:1 volumetric ratio at pH 14. The synthesis of the aluminate hydrotalcites using seawater results in the formation of an impurity phase bayerite. Two decompn. steps have been identified for the aluminate hydrotalcites: (1) removal of interlayer water (230 °C) and (2) simultaneous dehydroxylation and decarbonation (330 °C).

Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Knowledge and attitudes of paediatric nurses related to breastfeeding

Introduction: Almost 90% of Australian mothers are exclusively breastfeeding when they discharge from maternity hospitals but by six months of age breastfeeding infants have reduced to 32% nationally and 19% in Queensland, far below the national target of 80%. Many factors influence the choice to breastfeed, including health care provision, therefore the knowledge and attitudes of paediatric nurses have the potential to affect breastfeeding duration. Aims: To assess current breastfeeding knowledge and attitudes of paediatric nurses in metropolitan and regional Queensland settings. Method: The study used a cross-sectional survey design. The tool was developed from several documented health professional questionnaires about breastfeeding, with permission from authors. Survey items relating breastfeeding physiology, factors relating to breastfeeding success, and local, national and international policies were also included. Ethics approval was granted from the appropriate Ethics Committees to conduct the survey through tertiary metropolitan and regional hospital settings. Results: A total of 241 surveys were returned, achieving a response rate of 53%. Nurses acknowledged breastmilk as the best source of nutrition for infants (99%, n=238) and that mothers should be encouraged to breastfeed (92%, n=221). However, many respondents considered infant formula a nutritional equivalent (44%, n=105) and (47%, n=113) were unaware that supplemental formulas interfered with successful breastfeeding. Most nurses recognised that stress (e.g. infant hospitalisation) impacts on the success of breastfeeding (90%, n=216). Knowledge of breastfeeding anatomy and physiology was poor and a substantial number of nurses did not identify correct attachment in response to two diagrammatic representations (76%, n=183 and 45%, n=109). Survey results demonstrated deficiencies in knowledge that would impact on support provided to breastfeeding mothers. Knowledge deficits were also identified relating to local, national and international policies and protocols concerning breastfeeding and breastmilk substitutes. Conclusion: Breastfeeding knowledge and attitudes were exceptional in areas related to general breastfeeding knowledge. However, in areas directly related to nursing practice, considerable deficits in paediatric nurses' knowledge and attitudes were identified. Lack of appropriate skills, knowledge and varying attitudes amongst paediatric nurses has the potential to negatively impact on the education, advice and support provided to breastfeeding mothers and their families whilst their infant is in hospital. These study findings will guide future research and strategies to improve knowledge and policy statements to assist paediatric nurses in fulfilling their role.