Twisted Edwards curves revisited

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 for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature use . It is also shown that the new addition algorithm can be implemented with four processors dropping the effective cost to . 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).

Not drowning, (hand)waving? Molecular phylogenetics, biogeography and evolutionary tempo of the ‘Gondwanan’ midge Stictocladius Edwards (Diptera: Chironomidae)

Many insect clades, especially within the Diptera (true flies), have been considered classically ‘Gondwanan’, with an inference that distributions derive from vicariance of the southern continents. Assessing the role that vicariance has played in the evolution of austral taxa requires testing the location and tempo of diversification and speciation against the well-established predictions of fragmentation of the ancient super-continent. Several early (anecdotal) hypotheses that current austral distributions originate from the breakup of Gondwana derive from studies of taxa within the family Chironomidae (non-biting midges). With the advent of molecular phylogenetics and biogeographic analytical software, these studies have been revisited and expanded to test such conclusions better. Here we studied the midge genus Stictocladius Edwards, from the subfamily Orthocladiinae, which contains austral-distributed clades that match vicariance-based expectations. We resolve several issues of systematic relationships among morphological species and reveal cryptic diversity within many taxa. Time-calibrated phylogenetic relationships among taxa accorded partially with the predicted tempo from geology. For these apparently vagile insects, vicariance-dated patterns persist for South America and Australia. However, as often found, divergence time estimates for New Zealand at c. 50 mya post-date separation of Zealandia from Antarctica and the remainder of Gondwana, but predate the proposed Oligocene ‘drowning’ of these islands. We detail other such ‘anomalous’ dates and suggest a single common explanation rather than stochastic processes. This could involve synchronous establishment following recovery from ‘drowning’ and/or deleteriously warming associated with the mid-Eocene climatic optimum (hence ‘waving’, which refers to cycles of drowning events) plus new availability of topography providing of cool running waters, or all these factors in combination. Alternatively a vicariance explanation remains available, given the uncertain duration of connectivity of Zealandia to Australia–Antarctic–South America via the Lord Howe and Norfolk ridges into the Eocene.

Romano-British wall-painting fragments: a spectroscopic analysis

Raman spectroscopic analyses of fragmented wall-painting specimens from a Romano-British villa dating from ca. 200 AD are reported. The predominant pigment is red haematite, to which carbon, chalk and sand have been added to produce colour variations, applied to a typical Roman limewash putty composition. Other pigment colours are identified as white chalk, yellow (goethite), grey (soot/chalk mixture) and violet. The latter pigment is ascribed to caput mortuum, a rare form of haematite, to which kaolinite (possibly from Cornwall) has been added, presumably in an effort to increase the adhesive properties of the pigment to the substratum. This is the first time that kaolinite has been reported in this context and could indicate the successful application of an ancient technology discovered by the Romano-British artists. Supporting evidence for the Raman data is provided by X-ray diffraction and SEM-EDAX analyses of the purple pigment.