On Using Expansions to the Base of -2

This short note investigates the effects of using expansions to the base of -2. The main applications we have in mind are cryptographic protocols, where the crucial operation is computation of scalar multiples. For the recently proposed groups arising from Picard curves this leads to a saving of at least 7% for the computation of an m-fold. For more general non-hyperelliptic genus 3 curves we expect a larger speed-up.Comment: 5 page

A Salad of Block Ciphers

This book is a survey on the state of the art in block cipher design and analysis. It is work in progress, and it has been for the good part of the last three years -- sadly, for various reasons no significant change has been made during the last twelve months. However, it is also in a self-contained, useable, and relatively polished state, and for this reason I have decided to release this \textit{snapshot} onto the public as a service to the cryptographic community, both in order to obtain feedback, and also as a means to give something back to the community from which I have learned much. At some point I will produce a final version -- whatever being a ``final version\u27\u27 means in the constantly evolving field of block cipher design -- and I will publish it. In the meantime I hope the material contained here will be useful to other people

The QARMA Block Cipher Family. Almost MDS Matrices Over Rings With Zero Divisors, Nearly Symmetric Even-Mansour Constructions With Non-Involutory Central Rounds, and Search Heuristics for Low-Latency S-Boxes

This paper introduces QARMA, a new family of lightweight tweakable block ciphers targeted at applications such as memory encryption, the generation of very short tags for hardware-assisted prevention of software exploitation, and the construction of keyed hash functions. QARMA is inspired by reflection ciphers such as PRINCE, to which it adds a tweaking input, and MANTIS. However, QARMA differs from previous reflector constructions in that it is a three-round Even-Mansour scheme instead of a FX-construction, and its middle permutation is non-involutory and keyed. We introduce and analyse a family of Almost MDS matrices defined over a ring with zero divisors that allows us to encode rotations in its operation while maintaining the minimal latency associated to {0, 1}-matrices. The purpose of all these design choices is to harden the cipher against various classes of attacks. We also describe new S-Box search heuristics aimed at minimising the critical path. QARMA exists in 64- and 128-bit block sizes, where block and tweak size are equal, and keys are twice as long as the blocks. We argue that QARMA provides sufficient security margins within the constraints determined by the mentioned applications, while still achieving best-in-class latency. Implementation results on a state-of-the art manufacturing process are reported. Finally, we propose a technique to extend the length of the tweak by using, for instance, a universal hash function, which can also be used to strengthen the security of QARMA

On multi-exponentiation in cryptography

We describe and analyze new combinations of multi-exponentiation algorithms with representations of the exponents. We deal mainly but not exclusively with the case where the inversion of group elements is fast: These methods are most attractive with exponents in the range from 80 to 256 bits, and can also be used for computing single exponentiations in groups which admit an automorphism satisfying a monic equation of small degree over the integers. The choice of suitable exponent representations allows us to match or improve the running time of the best multi-exponentiation techniques in the aforementioned range, while keeping the memory requirements as small as possible. Hence some of the methods presented here are particularly attractive for deployment in memory constrained environments such as smart cards. By construction, such methods provide good resistance against side channel attacks. We also describe some applications of these algorithms

The influence of the geological and geomorphological settings on shallow landslides. An example in a temperate climate environment: the June 19th, 1996 event in north-western Tuscany (Italy)

On June 19, 1996, an extremely heavy rainstorm hit a restricted area in the Apuan Alps (northwestern Tuscany, Italy). Its max intensity concentrated over an area of about 150 km2 astride the Apuan chain, where 474 mm was recorded in about 12 h (21% of the mean annual precipitation, with an intensity up to 158 mm/h). The storm caused floods and hundreds of landslides and debris flows, which produced huge damage (hundreds of millions of Euros), partially destroyed villages and killed 14 people. This paper reports the results obtained from a detailed field survey and aerial view interpretation. In the most severely involved area, 647 main landslides were investigated, mapped and related to the geologic, geomorphic and vegetational factors of the source areas. This was in order to define the influence of these factors and contribute to an evaluation of the landslide hazard in the study area. An assessment was also made of the total area and volume of material mobilised by landsliding. The study area, about 46 km2 wide, includes three typically mountainous basins, characterised by narrow, deep cut valleys and steep slopes, where many rock types outcrop. Most of the landslides were shallow and linear, referable to complex, earth and debris translational slide, which quickly developed into flow (soil slip – debris flow). Usually, they involved colluvium and started in hollows underlain by metamorphic rock (metasandstone and phyllite), often dipping downslope. Therefore, bedrock lithology and impermeability appeared to be important factors in the localisation of the landslide phenomena. The investigation of the geomorphic and land use features in the source areas also frequently highlighted a rectilinear profile of the slope, a high slope gradient (31–45j) and dense chestnut wood cover. In the area, about 985,000 m2 (2.1% of 46 km2) was affected by landsliding and about 700,000 m2 of this area was covered by chestnut forest. The landslides removed about 7000 trees. The volume of mobilised material was about 1,360,000 m3; about 220,000 m3 remained on the slopes, while the rest poured into the streams. In addition, about 945,000 m3 was mobilised by the torrential erosion in the riverbeds. D 2004 Elsevier B.V. All rights reserved

Preliminary analysis of the November 10, 2014 rainstorm and related landslides in the lower Lavagna valley (eastern Liguria)

On the evening of November 10, 2014, eight rainfall-induced shallow landslides were triggered on a slope in the lower Lavagna valley (eastern Liguria, Italy). Most of the shallow landslides were channelled as flows into steep hollows and reached the toe of the slope, where some sparse houses were built. One of these landslides impacted and destroyed a building located just at a steep channel outlet, causing two fatalities. Damage affected also agricultural terracing as well as some other buildings and a road running at the toe of the slope, which was buried for long tracts by landslide deposits. Since a few days after the landslides occurrence, various activities were carried out, with the aim of better understanding both the triggering and predisposing factors of landslides. These activities included field surveys, rainfall data analysis, topographic/thematic maps, DEM and aerial photo analyses, preliminary laboratory tests on soil samples. From the analyses performed, it seems that, in addition to the rainfall characteristics of the November 10, 2014 event, the antecedent rainfall may have played an important role as landslides predisposing factor. Other relevant predisposing factors can be referred to slope steepness, presence of hollows, stratigraphic and structural settings at the source areas and lack of maintenance of terracing. Investigations are still in progress to achieve a complete geotechnical and hydraulic characterization of soils. Furthermore, it is also expected to extend the analyses performed to the whole area affected by shallow landslides. However, we believe the results of this study can be helpful in shallow landslide modelling, hazard assessment and planning of appropriate risk mitigation measures

Probabilistic rainfall thresholds for triggering debris flows in a human-modified landscape

Abstract In the Carrara Marble Basin (CMB; Apuan Alps, Italy) quarrying has accumulated widespread and thick quarry waste, lying on steep slopes and invading valley bottoms. The Apuan Alps are one of the rainiest areas in Italy and rainstorms often cause landslides and debris flows. The stability conditions of quarry waste are difficult to assess, owing to its textural, geotechnical and hydrogeological variability. Therefore, empirical rainfall thresholds may be effective in forecasting the possible occurrence of debris flows in the CMB. Three types of thresholds were defined for three rain gauges of the \CMB\ and for the whole area: rainfall intensity–rainfall duration (ID), cumulated event rainfall–rainfall duration (ED), and cumulated event rainfall normalized by the mean annual precipitation–rainfall intensity (EMAPI). The rainfall events recorded from 1950 to 2005 was analyzed and compared with the occurrence of debris flows involving the quarry waste. They were classified in events that triggered one or more debris flows and events that did not trigger debris flows. This dataset was fitted using the logistic regression method that allows us to define a set of thresholds, corresponding to different probabilities of failure (from 10% to 90%) and therefore to different warning levels. The performance of the logistic regression in defining probabilistic thresholds was evaluated by means of contingency tables, skill scores and receiver operating characteristic (ROC) analysis. These analyses indicate that the predictive capability of the three types of threshold is acceptable for each rain gauge and for the whole CMB. The best compromise between the number of correct debris flow predictions and the number of wrong predictions is obtained for the 40% probability thresholds. The results obtained can be tested in an experimental debris flows forecasting system based on rainfall thresholds, and could have implications for the debris flow hazard and risk assessment in the CMB

Preliminary analysis of the November 10, 2014 rainstorm and related landslides in the lower Lavagna valley (eastern Liguria)

On the evening of November 10, 2014, eight rainfall-induced shallow landslides were triggered on a slope in the lower Lavagna valley (eastern Liguria, Italy). Most of the shallow landslides were channelled as flows into steep hollows and reached the toe of the slope, where some sparse houses were built. One of these landslides impacted and destroyed a building located just at a steep channel outlet, causing two fatalities. Damage affected also agricultural terracing as well as some other buildings and a road running at the toe of the slope, which was buried for long tracts by landslide deposits. Since a few days after the landslides occurrence, various activities were carried out, with the aim of better understanding both the triggering and predisposing factors of landslides. These activities included field surveys, rainfall data analysis, topographic/thematic maps, DEM and aerial photo analyses, preliminary laboratory tests on soil samples. From the analyses performed, it seems that, in addition to the rainfall characteristics of the November 10, 2014 event, the antecedent rainfall may have played an important role as landslides predisposing factor. Other relevant predisposing factors can be referred to slope steepness, presence of hollows, stratigraphic and structural settings at the source areas and lack of maintenance of terracing. Investigations are still in progress to achieve a complete geotechnical and hydraulic characterization of soils. Furthermore, it is also expected to extend the analyses performed to the whole area affected by shallow landslides. However, we believe the results of this study can be helpful in shallow landslide modelling, hazard assessment and planning of appropriate risk mitigation measures

Response to 'comment on "The influence of geological–morphological and land use settings on shallow landslides in the Pogliaschina T. basin (northern Apennines, Italy)" by Bartelletti et al. (2017)'

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Minimality of the Hamming Weight of the \tau-NAF for Koblitz Curves and Improved Combination with Point Halving

In order to efficiently perform scalar multiplications on elliptic Koblitz curves, expansions of the scalar to a complex base associated with the Frobenius endomorphism are commonly used. One such expansion is the $\tau$-adic NAF, introduced by Solinas. Some properties of this expansion, such as the average weight, are well known, but in the literature there is no proof of its {\em optimality}, i.e.~that it always has minimal weight. In this paper we provide the first proof of this fact. Point halving, being faster than doubling, is also used to perform fast scalar multiplications on generic elliptic curves over binary fields. Since its computation is more expensive than that of the Frobenius, halving was thought to be uninteresting for Koblitz curves. At PKC 2004, Avanzi, Ciet, and Sica combined Frobenius operations with one point halving to compute scalar multiplications on Koblitz curves using on average 14\% less group additions than with the usual $\tau$-and-add method without increasing memory usage. The second result of this paper is an improvement over their expansion, that is simpler to compute, and optimal in a suitable sense, i.e.\ it has minimal Hamming weight among all $\tau$-adic expansions with digits $\{0,\pm1\}$ that allow one halving to be inserted in the corresponding scalar multiplication algorithm. The resulting scalar multiplication requires on average 25\% less group operations than the Frobenius method, and is thus 12.5\% faster than the previous known combination