Quantum resource estimates for computing elliptic curve discrete logarithms

We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point addition, implemented within the framework of the quantum computing software tool suite LIQ$Ui|\rangle$. We determine circuit implementations for reversible modular arithmetic, including modular addition, multiplication and inversion, as well as reversible elliptic curve point addition. We conclude that elliptic curve discrete logarithms on an elliptic curve defined over an $n$-bit prime field can be computed on a quantum computer with at most $9n + 2\lceil\log_2(n)\rceil+10$ qubits using a quantum circuit of at most $448 n^3 \log_2(n) + 4090 n^3$ Toffoli gates. We are able to classically simulate the Toffoli networks corresponding to the controlled elliptic curve point addition as the core piece of Shor's algorithm for the NIST standard curves P-192, P-224, P-256, P-384 and P-521. Our approach allows gate-level comparisons to recent resource estimates for Shor's factoring algorithm. The results also support estimates given earlier by Proos and Zalka and indicate that, for current parameters at comparable classical security levels, the number of qubits required to tackle elliptic curves is less than for attacking RSA, suggesting that indeed ECC is an easier target than RSA.Comment: 24 pages, 2 tables, 11 figures. v2: typos fixed and reference added. ASIACRYPT 201

Supersingular Isogeny Diffie-Hellman Authenticated Key Exchange

We propose two authenticated key exchange protocols from supersingular isogenies. Our protocols are the first post-quantum one-round Diffie-Hellman type authenticated key exchange ones in the following points: one is secure under the quantum random oracle model and the other resists against maximum exposure where a non-trivial combination of secret keys is revealed. The security of the former and the latter is proven under isogeny versions of the decisional and gap Diffie-Hellman assumptions, respectively. We also propose a new approach for invalidating the Galbraith-Vercauteren-type attack for the gap problem

Light interception principally drives the understory response to boxelder invasion in riparian forests

Since several decades, American boxelder (Acer negundo) is replacing white willow (Salix alba) riparian forests along southern European rivers. This study aims to evaluate the consequences of boxelder invasion on understory community in riparian areas. We determined the understory species richness, composition and biomass in boxelder and white willow stands located in three riparian forests, representative of three rivers with distinct hydrological regimes. We investigated correlation of these variables to soil moisture and particle size, main soil nutrient stocks, potential nitrification and denitrification, tree canopy cover and photosynthetic active radiation (PAR) at the ground level. A greenhouse experiment was then conducted to identify the causal factors responsible for changes in the understory. The effect of soil type, PAR level and water level on the growth and the biomass production of Urtica dioica were examined. A lower plant species richness and biomass, and a modification of community composition were observed for boxelder understory in all sites, regardless of their environmental characteristics. The strongest modification that follows boxelder invasion was the decline in U. dioica, the dominant species of the white willow forest understory. These differences were mainly correlated with a lower incident PAR under boxelder canopy. The greenhouse experiment identified PAR level as the main factor responsible for the changes in U. dioica stem number and biomass. Our results indicate that adult boxelder acts as an ecosystem engineer that decreases light availability. The opportunistic invasion by boxelder leads to important understory changes, which could alter riparian ecosystem functioning

Processes and patterns of oceanic nutrient limitation

Microbial activity is a fundamental component of oceanic nutrient cycles. Photosynthetic microbes, collectively termed phytoplankton, are responsible for the vast majority of primary production in marine waters. The availability of nutrients in the upper ocean frequently limits the activity and abundance of these organisms. Experimental data have revealed two broad regimes of phytoplankton nutrient limitation in the modern upper ocean. Nitrogen availability tends to limit productivity throughout much of the surface low-latitude ocean, where the supply of nutrients from the subsurface is relatively slow. In contrast, iron often limits productivity where subsurface nutrient supply is enhanced, including within the main oceanic upwelling regions of the Southern Ocean and the eastern equatorial Pacific. Phosphorus, vitamins and micronutrients other than iron may also (co-)limit marine phytoplankton. The spatial patterns and importance of co-limitation, however, remain unclear. Variability in the stoichiometries of nutrient supply and biological demand are key determinants of oceanic nutrient limitation. Deciphering the mechanisms that underpin this variability, and the consequences for marine microbes, will be a challenge. But such knowledge will be crucial for accurately predicting the consequences of ongoing anthropogenic perturbations to oceanic nutrient biogeochemistry. © 2013 Macmillan Publishers Limited. All rights reserved

Integrin Clustering Is Driven by Mechanical Resistance from the Glycocalyx and the Substrate

Integrins have emerged as key sensory molecules that translate chemical and physical cues from the extracellular matrix (ECM) into biochemical signals that regulate cell behavior. Integrins function by clustering into adhesion plaques, but the molecular mechanisms that drive integrin clustering in response to interaction with the ECM remain unclear. To explore how deformations in the cell-ECM interface influence integrin clustering, we developed a spatial-temporal simulation that integrates the micro-mechanics of the cell, glycocalyx, and ECM with a simple chemical model of integrin activation and ligand interaction. Due to mechanical coupling, we find that integrin-ligand interactions are highly cooperative, and this cooperativity is sufficient to drive integrin clustering even in the absence of cytoskeletal crosslinking or homotypic integrin-integrin interactions. The glycocalyx largely mediates this cooperativity and hence may be a key regulator of integrin function. Remarkably, integrin clustering in the model is naturally responsive to the chemical and physical properties of the ECM, including ligand density, matrix rigidity, and the chemical affinity of ligand for receptor. Consistent with experimental observations, we find that integrin clustering is robust on rigid substrates with high ligand density, but is impaired on substrates that are highly compliant or have low ligand density. We thus demonstrate how integrins themselves could function as sensory molecules that begin sensing matrix properties even before large multi-molecular adhesion complexes are assembled

Temperature sensitivity of soil respiration rates enhanced by microbial community response

Soils store about four times as much carbon as plant biomass(1), and soil microbial respiration releases about 60 petagrams of carbon per year to the atmosphere as carbon dioxide(2). Short-term experiments have shown that soil microbial respiration increases exponentially with temperature(3). This information has been incorporated into soil carbon and Earth-system models, which suggest that warming-induced increases in carbon dioxide release from soils represent an important positive feedback loop that could influence twenty-first-century climate change(4). The magnitude of this feedback remains uncertain, however, not least because the response of soil microbial communities to changing temperatures has the potential to either decrease(5-7) or increase(8,9) warming-induced carbon losses substantially. Here we collect soils from different ecosystems along a climate gradient from the Arctic to the Amazon and investigate how microbial community-level responses control the temperature sensitivity of soil respiration. We find that the microbial community-level response more often enhances than reduces the mid-to long-term (90 days) temperature sensitivity of respiration. Furthermore, the strongest enhancing responses were observed in soils with high carbon-to-nitrogen ratios and in soils from cold climatic regions. After 90 days, microbial community responses increased the temperature sensitivity of respiration in high-latitude soils by a factor of 1.4 compared to the instantaneous temperature response. This suggests that the substantial carbon stores in Arctic and boreal soils could be more vulnerable to climate warming than currently predicted.Output Type: Lette