A commercial process for bioreactor leaching of a nickel concentrate by-product of talc mining has been described previously. It was developed and operated (2016-2018) at about 45-46 degrees C. Further features of bioleaching that concentrate have now been investigated in laboratory-scale reactors with continuous feeds of up to 10% (w/v) solids and an emphasis on temperatures at and a few degrees above that of the commercial process. The sulfur-oxidizing At. caldus was more abundant than the sulfide mineral-oxidizing S. thermosulfidooxidans and Atm. siderophilum at 48 degrees C but was essentially lost with a 3 degrees C temperature rise, simultaneously with a rise in pH and in iron precipitation from solution, without adversely affecting nickel leaching. The relative abundance among bacteria was similar between two reactors operated in series but there was more than a fourfold increase in the relative abundance of the ferrous-iron oxidizing, heterotrophic archaeon Ac. cupricumulans in the secondary reactor, most likely in response to an increase in the acidity as the sulfide concentrate oxidation proceeded.

Rare earth element (REE)-bearing carbonatite deposits commonly contain a wide range of different REE- and REE-bearing minerals associated with various gangue matrices. In order to select the most-suitable mineral processing technique for these deposits, it is essential to identify and quantify the minerals of interest, including their liberation, associations and grain size distribution, along with whole rock compositions. These data are also vital for ore feed optimisation and metallurgical troubleshooting during and after designing a mineral processing flowsheet. This paper summarises the key mineralogical parameters needed before conducting metallurgical beneficiation tests, using the Songwe Hill carbonatite deposit as an example. This REE ore deposit consists of poorly-liberated synchysite-(Ce), which hosts the light rare earth elements including Nd plus some heavy rare earths and well-liberated apatite, which hosts 50% of Gd, 63% of Dy and 71% of Y (heavy rare earth elements) in the deposit. For all REE heavier than Gd, apatite is the most important REE host, however, for the two REE where data are available in both synchysite-(Ce) and apatite (Dy and Y), synchysite-(Ce) still accommodates >25% of the whole-rock HREE content. Both of these ore minerals are associated with ankerite, calcite, and to a lesser extent with iron oxides/carbonates, K-feldspar, strontianite and baryte. According to the quantitative mineralogical data, the possibility of using gravity separation, magnetic separation, froth flotation and leaching to process Songwe Hill carbonatite ore is discussed and a potential beneficiation flowsheet is presented.

Apatite subspecies depend on their halogen and hydroxyl content; chlorapatite, hydroxylapatite and fluorapatite, with additional substitution of other elements within the lattice such as rare earth elements (REE), sodium, strontium and manganese also possible. Rare earth elements are vital to green and emerging technologies, with demand set to outstrip supply. Apatite provides a possible future source of REE. Processing rare earth deposits is often complex, with surface behaviour having a significant effect on the optimization of a process flow sheet. The effect of enrichment of natural apatite and the doping of synthetic apatite on surface behaviour can be determined by measuring the zeta potential and the isoelectric point of the mineral. In this paper, we review zeta potential studies of natural and synthetic apatite to determine the effect of elemental enrichment on surface behaviour. Fifty three studies of natural apatite and forty four studies of synthetic apatite were reviewed. The isoelectric point of apatite varied from pH 1 to pH 8.7, with studies of apatite specified to be >90% pure reducing the variation to pH 3 to pH 6.5. Of the four studies of rare earth enriched apatite found, three had IEP values between pH 3 and pH 4. A study of synthetic apatite showing enrichment of between 1 and 10% by the REE europium does not affect surface behaviour. However, no studies were found that investigated the effect of common REE processing reagents on REE enriched apatite zeta potentials. Therefore, in addition to comparing previous studies we also therefore present new zeta potential measurements of apatite from a REE enriched deposit under water and common flotation collector conditions. The IEP value of this apatite under water conditions was at pH 3.6, shifting to <3.5 under both hydroxamic acid and betacol conditions. When compared to previous studies, the behaviour of REE enriched apatite under collector conditions is similar to non-REE apatite. This result could be important for future processing of apatite enriched with REE, and therefore global apatite and rare earth supply.

Tungsten is considered by the European Union as a critical raw material for future development due to its expected demand and scarcity of resource within Europe. It is therefore, critical to optimize European tungsten operations and maximise recoveries. The role of enhanced gravity/centrifugal concentrators in recovering tungsten from ultra-fine fractions should form an important part of this aim. Reported herein are the results of investigations to improve efficiency of Wolf Minerals' Draklends mine, a major European tungsten mine, by recovering saleable material from a magnetic waste stream of a low-intensity magnetic separator using an enhanced gravity concentrator. The mine hosts wolframite and ferberite as the main tungsten bearing mineral species. A Mozley multi-gravity separator (MGS) C-900 was selected as it is suited to exploiting small variations in mineral density to affect a separation. Working with a current manufacturer, a novel scraping blade system was tested. To assess the MGS in a statistically valid manner, a response surface methodology was followed to determine optimal test conditions. The test programme showed that the most important parameters were drum speed and wash water rate. Under optimal conditions the model predicted that 40% of the tungsten could be recovered above the required grade of 43% WO3.

This work presents a study of the complexity of the Blum–Kalai–Wasserman (BKW) algorithm when applied to the Learning with Errors (LWE) problem, by providing refined estimates for the data and computational effort requirements for solving concrete instances of the LWE problem. We apply this refined analysis to suggested parameters for various LWE-based cryptographic schemes from the literature and compare with alternative approaches based on lattice reduction. As a result, we provide new upper bounds for the concrete hardness of these LWE-based schemes. Rather surprisingly, it appears that BKW algorithm outperforms known estimates for lattice reduction algorithms starting in dimension \(n \approx 250\) when LWE is reduced to SIS. However, this assumes access to an unbounded number of LWE samples.

The learning with errors (LWE) problem is one of the most attractive problems that lattice-based cryptosystems base their security on. Thus, assessing the hardness in theory and practice is of prime importance. Series of work investigated the hardness of LWE from a theoretical point of view. However, it is quite common that in practice one can solve lattice problems much faster than theoretical estimates predict.The most promising approach to solve LWE is the decoding method, which converts an LWE instance to an instance of the closest vector problem (CVP). The latter instance can then be solved by a CVP solver. In this work, we investigate how the nearest planes algorithm proposed by Lindner and Peikert (CT-RSA 2011) performs in practice. This algorithm improves an algorithm by Babai, and is a state-of-the-art CVP solver.We present the first parallel version of the nearest planes algorithm. Our implementation achieves speedup factors of more than 11x on a machine with four CPU-chips totaling 16 cores. In fact, to the best of our knowledge, there is not even a single parallel implementation publicly available of any LWE solver so far. We also compare our results with heuristics on the running time of a single nearest planes run claimed by Lindner and Peikert and subsequently used by others for runtime estimations.

We analyse the complexity of algebraic algorithms for solving systems of linear equations with \emph{noise}. Such systems arise naturally in the theory of error-correcting codes as well as in computational learning theory. More recently, linear systems with noise have found application in cryptography. The \emph{Learning with Errors} (LWE) problem has proven to be a rich and versatile source of innovative cryptosystems, such as fully homomorphic encryption schemes. Despite the popularity of the LWE problem, the complexity of algorithms for solving it is not very well understood, particularly when variants of the original problem are considered. Here, we focus on and generalise a particular method for solving these systems, due to Arora \& Ge, which reduces the problem to non-linear but noise-free system solving. Firstly, we provide a refined complexity analysis for the original Arora-Ge algorithm for LWE. Secondly, we study the complexity of applying algorithms for computing Grobner basis, a fundamental tool in computational commutative algebra, to solving Arora-Ge-style systems of non-linear equations. We show positive and negative results. On the one hand, we show that the use of Grobner bases yields an exponential speed-up over the basic Arora-Ge approach. On the other hand, we give a negative answer to the natural question whether the use of such techniques can yield a subexponential algorithm for the LWE problem. Under a mild algebraic assumption, we show that it is highly unlikely that such an improvement exists. We also consider a variant of LWE known as BinaryError-LWE introduced by Micciancio and Peikert recently. By combining Grobner basis algorithms with the Arora-Ge modelling, we show under a natural algebraic assumption that BinaryError-LWE can be solved in subexponential time as soon as the number of samples is quasi-linear, e.g. m=O(nloglog⁡n)m=O(n \log \log n). We also derive precise complexity bounds for BinaryError-\LWE with m=O(n)m=O(n), showing that this new approach yields better results than best currently-known generic (exact) CVP solver as soon as m/n≥6.6m/n \geq 6.6. More generally, our results provide a good picture of the hardness degradation of BinaryError-LWE for a number of samples ranging from m=n(1+Ω(1/log(n))m=n\left(1+\Omega\big(1/{\rm log}(n)\right) (a case for which BinaryError-\LWE{} is as hard as solving some lattice problem in the worst case) to m=O(n2)m=O(n^2) (a case for which it can be solved in polynomial-time). This addresses an open question from Micciancio and Peikert. Whilst our results do not contradict the hardness results obtained by Micciancio and Peikert, they should rule out BinaryError-\LWE for many cryptographic applications. The results in this work depend crucially on the assumption the algebraic systems considered systems are not easier and not harder to solve than a random system of equations. We have verified experimentally such hypothesis. We also have been able to prove formally the assumptions is several restricted situations. We emphasize that these issues are highly non-trivial since proving our assumptions in full generality would allow to prove a famous conjecture in commutative algebra known as Froberg's Conjecture.

The area of lattice-based cryptography is growing ever-more prominent as a paradigm for quantum-resistant cryptography. One of the most important hard problem underpinning the security of lattice-based cryptosystems is the shortest vector problem (SVP). At present, two approaches dominate methods for solving instances of this problem in practice: enumeration and sieving. In 2010, Micciancio and Voulgaris presented a heuristic member of the sieving family, known as GaussSieve, demonstrating it to be comparable to enumeration methods in practice. With contemporary lattice-based cryptographic proposals relying largely on the hardness of solving the shortest and closest vector problems in ideal lattices, examining possible improvements to sieving algorithms becomes highly pertinent since, at present, only sieving algorithms have been successfully adapted to solve such instances more efficiently than in the random lattice case. In this paper, we propose a number of heuristic improvements to GaussSieve, which can also be applied to other sieving algorithms for SVP.

In this paper, we investigate the security of a public-key encryption scheme introduced by Huang, Liu and Yang (HLY) at PKC’12. This new scheme can be provably reduced to the hardness of solving a set of quadratic equations whose coefficients of highest degree are chosen according to a discrete Gaussian distributions. The other terms being chosen uniformly at random. Such a problem is a variant of the classical problem of solving a system of non-linear equations (PoSSo), which is known to be hard for random systems. The main hypothesis of Huang, Liu and Yang is that their variant is not easier than solving PoSSo for random instances. In this paper, we disprove this hypothesis. To this end, we exploit the fact that the new problem proposed by Huang, Liu and Yang reduces to an easy instance of the Learning With Errors (LWE) problem. The main contribution of this paper is to show that security and efficiency are essentially incompatible for the HLY proposal. That is, one cannot find parameters which yield a secure and a practical scheme. For instance, we estimate that a public-key of at least 1.03 GB is required to achieve 80-bit security against the simplest of our attacks. As a proof of concept, we present 3 practical attacks against all the parameters proposed by Huang, Liu and Yang. With the most efficient attack, we have been able to recover the private-key in roughly 5 minutes for the first challenge (i.e. Case 1) proposed by HLY and less than 30 minutes for the second challenge (i.e. Case2).

We present a study of the concrete complexity of solving instances of the unique shortest vector problem (uSVP). In particular, we study the complexity of solving the Learning with Errors (LWE) problem by reducing the Bounded-Distance Decoding (BDD) problem to uSVP and attempting to solve such instances using the 'embedding' approach. We experimentally derive a model for the success of the approach, compare to alternative methods and demonstrate that for the LWE instances considered in this work, reducing to uSVP and solving via embedding compares favorably to other approaches.

Some recent constructions based on LWE do not sample the secret uniformly at random but rather from some distribution which produces small entries. The most prominent of these is the binary-LWE problem where the secret vector is sampled from {0,1} ∗ or { − 1,0,1} ∗ . We present a variant of the BKW algorithm for binary-LWE and other small secret variants and show that this variant reduces the complexity for solving binary-LWE. We also give estimates for the cost of solving binary-LWE instances in this setting and demonstrate the advantage of this BKW variant over standard BKW and lattice reduction techniques applied to the SIS problem. Our variant can be seen as a combination of the BKW algorithm with a lazy variant of modulus switching which might be of independent interest.

We introduce software for the generation of instances of the LWE and Ring-LWE problems, allowing both the generation of generic instances and also particular instances closely-related to those arising from cryptomania proposals in the literature. Our goal is to allow researchers to attack different instances in order to assess the practical hardness of LWE and Ring-LWE. This will in turn give insight to the practical security of cryptographic systems based on both problems.

Arora & Ge recently showed that solving LWE can be reduced to solve a high-degree non-linear system of equations. They used a linearization to solve the systems. We investigate here the possibility of using Gr¨obner bases to improve Arora & Ge approach.

Creating dramatic and engaging characters is one of the ‘holy grail’ issues in video games. Another – related – focus is the implementation of morality in game characters. We look into a combination of these two issues inside the game character’s definition. This character data set forms the backbone of the game entity and a basis from which behavioral engines can operate. Some of these data features refer to established character definitions from traditional media, including physiology, sociology and psychology as three defining elements of dramatic characters. Historically, games have developed game character physiology, but how do data sets provide for the other two elements? We refer to three games (Chrono Trigger, Fable and Ultima Online) and examine their character data sets in regard to: a) their range, limitations and contents b) ways in which they mimic social and ethical references Based on the analysis we suggest a basic rethinking of a character’s data set combining the elements of consistency and granularity that allow for a clearer tracking and representation of moral behavior as “parameterized morality”.