This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses 1 8M for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature use 9M + 1S. It is also shown that the new addition algorithm can be implemented with four processors dropping the effective cost to 2M. This implies an effective speed increase by the full factor of 4 over the sequential case. Our results allow faster implementation of elliptic curve scalar multiplication. In addition, the new point addition algorithm can be used to provide a natural protection from side channel attacks based on simple power analysis (SPA).

Abstract. We use a coupled atmosphere-ocean global climate model (CSIRO-Mk3.6) to investigate the drivers of trends in summer rainfall and circulation in the vicinity of northern Australia. As part of the Coupled Model Intercomparison Project Phase 5 (CMIP5), we perform a 10-member 21st century ensemble driven by Representative Concentration Pathway 4.5 (RCP4.5). To investigate the roles of different forcing agents, we also perform multiple 10-member ensembles of historical climate change, which are analysed for the period 1951–2010. The historical runs include ensembles driven by "all forcings" (HIST), all forcings except anthropogenic aerosols (NO_AA) and forcing only from long-lived greenhouse gases (GHGAS). Anthropogenic aerosol-induced effects in a warming climate are calculated from the difference of HIST minus NO_AA. CSIRO-Mk3.6 simulates a strong summer rainfall decrease over north-western Australia (NWA) in RCP4.5, whereas simulated trends in HIST are weakly positive (but insignificant) during 1951–2010. The weak rainfall trends in HIST are due to compensating effects of different forcing agents: there is a significant decrease in GHGAS, offset by an aerosol-induced increase. Observations show a significant increase of summer rainfall over NWA during the last few decades. The large magnitude of the observed NWA rainfall trend is not captured by 440 unforced 60-yr trends calculated from a 500-yr pre-industrial control run, even though the model's decadal variability appears to be realistic. This suggests that the observed trend includes a forced component, despite the fact that the model does not simulate the magnitude of the observed rainfall increase in response to "all forcings" (HIST). We investigate the mechanism of simulated and observed NWA rainfall changes by exploring changes in circulation over the Indo-Pacific region. The key circulation feature associated with the rainfall increase in reanalyses is a lower-tropospheric cyclonic circulation trend off the coast of NWA, which enhances the monsoonal flow. The model shows an aerosol-induced cyclonic circulation trend off the coast of NWA in HIST minus NO_AA, whereas GHGAS shows an anticyclonic circulation trend. This explains why the aerosol-induced effect is an increase of rainfall over NWA, and the greenhouse gas-induced effect is of opposite sign. Possible explanations for the cyclonic (anticyclonic) circulation trend in HIST minus NO_AA (GHGAS) involve changes in the Walker circulation or the local Hadley circulation. In either case, a plausible atmospheric mechanism is that the circulation anomaly is a Rossby wave response to convective heating anomalies south of the Equator. We also discuss the possible role of air-sea interactions, e.g. an increase (decrease) of sea-surface temperatures off the coast of NWA in HIST minus NO_AA (GHGAS). Further research is needed to better understand the mechanisms and the extent to which these are model-dependent. In summary, our results suggest that anthropogenic aerosols may have "masked" greenhouse gas-induced changes in rainfall over NWA and in circulation over the wider Indo-Pacific region. Due to the opposing effects of greenhouse gases and anthropogenic aerosols, future trends may be very different from trends observed over the last few decades.

No abstract

No abstract

No abstract