Revisiting LFSMs

Linear Finite State Machines (LFSMs) are particular primitives widely used in information theory, coding theory and cryptography. Among those linear automata, a particular case of study is Linear Feedback Shift Registers (LFSRs) used in many cryptographic applications such as design of stream ciphers or pseudo-random generation. LFSRs could be seen as particular LFSMs without inputs. In this paper, we first recall the description of LFSMs using traditional matrices representation. Then, we introduce a new matrices representation with polynomial fractional coefficients. This new representation leads to sparse representations and implementations. As direct applications, we focus our work on the Windmill LFSRs case, used for example in the E0 stream cipher and on other general applications that use this new representation. In a second part, a new design criterion called diffusion delay for LFSRs is introduced and well compared with existing related notions. This criterion represents the diffusion capacity of an LFSR. Thus, using the matrices representation, we present a new algorithm to randomly pick LFSRs with good properties (including the new one) and sparse descriptions dedicated to hardware and software designs. We present some examples of LFSRs generated using our algorithm to show the relevance of our approach.Comment: Submitted to IEEE-I

Construction of self-dual normal bases and their complexity

Recent work of Pickett has given a construction of self-dual normal bases for extensions of finite fields, whenever they exist. In this article we present these results in an explicit and constructive manner and apply them, through computer search, to identify the lowest complexity of self-dual normal bases for extensions of low degree. Comparisons to similar searches amongst normal bases show that the lowest complexity is often achieved from a self-dual normal basis

Noise-induced stabilization of dynamical states in a non-Markovian system

A Josephson junction subject to an external RF excitation may experience the inverse AC Josephson effect, where the phase across the junction locks to the drive. The resulting ``Shapiro steps'' of quantized voltage are currently utilized in primary voltage standards. The effect has also been a key technique in the search for topological superconductivity. Here, we study a particularly interesting regime in which the zero voltage state becomes unstable at zero DC bias, and the junction spontaneously develops the first Shapiro step with a voltage $V=\pm \hbar \omega /2e$. The switching time between the $+ \hbar \omega /2e$ and $- \hbar \omega /2e$ states ranges from milliseconds to hours. Most interestingly, we find a surprising regime with a non-monotonic temperature dependence, in which the switching time demonstrates a pronounced minimum at intermediate temperatures. Tuning of the measurement parameters is also shown to give rise to a tristable switching behavior, showcasing the potential for further experiments in stochastic physics and quantum thermodynamics

Ex situ mineral carbonation for CO2 mitigation: Evaluation of mining waste resources, aqueous carbonation processability and life cycle assessment (Carmex project)

This article presents the main outputs from the multidisciplinary Carmex project (2009–2012), which was concerned with the possibility of applying ex situ mineral carbonation concepts to mafic/ultramafic mining wastes. Focus points of the project included (i) matching significant and accessible mining wastes to large CO2 emitters through a dedicated geographical information system (GIS), (ii) analysis of aqueous carbonation mechanisms of mining waste and process development and (iii) environmental assessment of ex situ mining waste carbonation through life cycle assessment (LCA) methodology. With a number of materials associated with the mining sector, the project took a close look at the aqueous carbonation mechanisms for these materials and obtained unexpected carbonation levels (up to 80%) by coupling mechanical exfoliation and reactive carbonation. Results from this work support the possibility of processing serpentine-rich peridotites without applying the classical first step of heat activation. Perspectives are also given for the carbonation of Ni-pyrometallurgical slag available closed to ultramafic mining residues. LCA of the mining waste carbonation system as a whole made it clear that the viability of this CO2 storage option lies with the carbonation process itself and optimisation of its operating conditions. By combining the body of knowledge acquired by this project, it is concluded that New Caledonia, with its insularity and local abundance of ‘carbonable’ rocks and industrial wastes coupled with significant greenhouse gas (GHG) emissions from world-class nickel pyro and hydrometallurgical industries stands out as a strong potential candidate for application of ex situ mineral carbonation

The Virgo data acquisition system

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The gravitational wave detector VIRGO

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