Do All Elliptic Curves of the Same Order Have the Same Difficulty of Discrete Log?

The aim of this paper is to justify the common cryptographic practice of selecting elliptic curves using their order as the primary criterion. We can formalize this issue by asking whether the discrete log problem (DLOG) has the same difficulty for all curves over a given finite field with the same order. We prove that this is essentially true by showing polynomial time random reducibility of DLOG among such curves, assuming the Generalized Riemann Hypothesis (GRH). We do so by constructing certain expander graphs, similar to Ramanujan graphs, with elliptic curves as nodes and low degree isogenies as edges. The result is obtained from the rapid mixing of random walks on this graph. Our proof works only for curves with (nearly) the same endomorphism rings. Without this technical restriction such a DLOG equivalence might be false; however, in practice the restriction may be moot, because all known polynomial time techniques for constructing equal order curves produce only curves with nearly equal endomorphism rings.Comment: 26 pages, revised, to appear in Advances in Cryptology -- Asiacrypt 200

Facets of sovereignty. Institutions that Spur and Institutions that Retard Tribal Development.

That so many of their assets continue to be held in governmental trusts under outdated policy rationales creates great difficulty for indigenous peoples. But restoring control of those assets to their rightful owners will impose daunting responsibilities on judiciaries. Exchanging assets for a residual share of returns from a joint venture exposes one to shirking by co-investors. Judiciaries known reliably to penalize those who renege on commitments help investors persuade others to sink complementary assets in promising projects. But a court is an arm of the sovereign. Across history and geography justifiable rulings adverse to sovereigns have so often been honored in the breach that private parties are especially leery of sovereigns as co-investors. To attract assets into its realm a sovereign may thus invest in a reputation for abiding by waivers of sovereign immunity, or rely on a still stronger sovereign to bond its waivers. Reputations arise from observed court successes by aggrieved co-investors when their suits against the sovereign are meritorious. But many tribal reservations are small and poor, have offered few investment opportunities, and hence possess thin legal histories. At the same time, investors are skeptical that courts of more powerful sovereigns such as Canada and the United States dependably bond tribal waivers. Thus tribes often must pay investors high risk-premiums, resort to costly tribal ownership, or even forego promising opportunities altogether. The Sovereign’s Paradox refers to the difficulty that an entity with power to compel involuntary outcomes has in negotiating voluntary ones. This chapter explores ways to ameliorate that Paradox and thus improve returns from reservation assets.

Analysis of Linsker's simulations of Hebbian rules

Linsker has reported the development of center-surround receptive fields and oriented receptive fields in simulations of a Hebb-type equation in a linear network. The dynamics of the learning rule are analyzed in terms of the eigenvectors of the covariance matrix of cell activities. Analytic and computational results for Linsker's covariance matrices, and some general theorems, lead to an explanation of the emergence of center-surround and certain oriented structures. We estimate criteria for the parameter regime in which center-surround structures emerge

Relationships between land use and nitrogen and phosphorus in New Zealand lakes

Developing policies to address lake eutrophication requires an understanding of the relative contribution of different nutrient sources and of how lake and catchment characteristics interact to mediate the source–receptor pathway. We analysed total nitrogen (TN) and total phosphorus (TP) data for 101 New Zealand lakes and related these to land use and edaphic sources of phosphorus (P). We then analysed a sub-sample of lakes in agricultural catchments to investigate how lake and catchment variables influence the relationship between land use and in-lake nutrients. Following correction for the effect of co-variation amongst predictor variables, high producing grassland (intensive pasture) was the best predictor of TN and TP, accounting for 38.6% and 41.0% of variation, respectively. Exotic forestry and urban area accounted for a further 18.8% and 3.6% of variation in TP and TN, respectively. Soil P (representing naturally-occurring edaphic P) was negatively correlated with TP, owing to the confounding effect of pastoral land use. Lake and catchment morphology (zmax and lake : catchment area) and catchment connectivity (lake order) mediated the relationship between intensive pasture and in-lake nutrients. Mitigating eutrophication in New Zealand lakes requires action to reduce nutrient export from intensive pasture and quantifying P export from plantation forestry requires further consideration

Use of operational analyses to study the dynamics of troposphere-stratosphere interactions in polar regions

Operational analyses produced by large weather centers have been used in the past to monitor various aspects of the general circulation as well as address dynamical questions. For a number years researchers have been monitoring National Meteorological Center (NMC) analyses at 100 millibars because it is the level from which stratospheric analyses are built. In particular, they closely examined the pressure-work term at that level which is an important parameter related to the forcing of the stratosphere by the troposphere. Rapid fluctuations typically seen in this quanity during the months of July-November, and similarly noted by Randel et al., (1987) may raise some concern about the quality of the analyses. Researchers investigated the behavior of the term mainly responsible for these variations, namely the eddy flux of heat, and furthermore have corroborated the presence of these variations in contemporaneous analyses produced by the European Centre for Medium Range Forecasts (ECMWF). Researchers demonstrated that fluctuations in standing eddy heat fluxes, related to the forcing of the stratosphere by the troposphere, agree in two largely independent meteorological analyses. Researchers believe, that these fluctuations are mostly real

Jet substructure and probes of CP violation in Vh production

We analyse the hVV (V = W, Z) vertex in a model independent way using Vh production. To that end, we consider possible corrections to the Standard Model Higgs Lagrangian, in the form of higher dimensional operators which parametrise the effects of new physics. In our analysis, we pay special attention to linear observables that can be used to probe CP violation in the same. By considering the associated production of a Higgs boson with a vector boson (W or Z), we use jet substructure methods to define angular observables which are sensitive to new physics effects, including an asymmetry which is linearly sensitive to the presence of CP odd effects. We demonstrate how to use these observables to place bounds on the presence of higher dimensional operators, and quantify these statements using a log likelihood analysis. Our approach allows one to probe separately the hZZ and hWW vertices, involving arbitrary combinations of BSM operators, at the Large Hadron Collider.Comment: 37 pages, 17 figures; v3 matches published versio