Differential and invertibility properties of BLAKE (full version)

BLAKE is a hash function selected by NIST as one of the 14 second round candidates for the SHA-3 Competition. In this paper, we follow a bottom-up approach to exhibit properties of BLAKE and of its building blocks: based on differential properties of the internal function G, we show that a round of BLAKE is a permutation on the message space, and present an efficient inversion algorithm. For 1.5 rounds we present an algorithm that finds preimages faster than in previous attacks. Discovered properties lead us to describe large classes of impossible differentials for two rounds of BLAKE’s internal permutation, and particular impossible differentials for five and six rounds, respectively for BLAKE- 32 and BLAKE-64. Then, using a linear and rotation-free model, we describe near-collisions for four rounds of the compression function. Finally, we discuss the problem of establishing upper bounds on the probability of differential characteristics for BLAKE

Extractability of elements in sugar maple xylem along a gradient of soil acidity

Dendrochemistry has been used for the historical dating of pollution. Its reliability is questionable due primarily to the radial mobility of elements in sapwood. In the present study, the extractability of seven elements was characterized to assess their suitability for the monitoring of environmental conditions. Nine mature sugar maple trees (Acer saccharum Marsh.), a wide-ranging species in eastern North America that has suffered decline in past decades, were sampled in three Quebec watersheds along a soil acidity gradient. Five-year groups of annual tree rings were treated by sequential chemical extractions using extractants of varying strength (deionized H2O, 0.05 M HCl, and concentrated HNO3) to selectively solubilize the elements into three fractions (water-soluble, acid-soluble, and residual). Monovalent K; divalent Ba, Ca, Cd, Mg, Mn; and trivalent Al cations were found mostly in the water-soluble, acid-soluble, and residual fractions, respectively. Forms more likely to be mobile within the tree (water-soluble and acid-soluble) do not seem to be suitable for temporal monitoring because of potential lateral redistribution in sapwood rings. However, certain elements (Cd, Mn) were responsive to current soil acidity and could be used in spatial variation monitoring. Extractability of Al varied according to soil acidity; at less acidic sites, up to 90% of Al was contained in the residual form, whereas on very acidic soils, as much as 45% was found in the water-soluble and acid-soluble fractions. Sequential extractions can be useful for determining specific forms of metals as key indicators of soil acidification