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Authenticated Key Exchange (AKE) between any two entities is one of the most important security protocols available for securing our digital networks and infrastructures. In PQCrypto 2023, Bruckner, Ramacher and Striecks proposed a novel hybrid AKE (HAKE) protocol, dubbed Muckle+, that is particularly useful in large quantum-safe networks consisting of a large number of nodes. Their protocol is hybrid in the sense that it allows key material from conventional and post-quantum primitives, as well as from quantum key distribution, to be incorporated into a single end-to-end shared key. To achieve the desired authentication properties, Muckle+ utilizes post-quantum digital signatures. However, available instantiations of such signatures schemes are not yet efficient enough compared to their post-quantum key-encapsulation mechanism (KEM) counterparts, particularly in large networks with potentially several connections in a short period of time. To mitigate this gap, we propose Muckle# that pushes the efficiency boundaries of currently known HAKE constructions. Muckle# uses post-quantum key-encapsulating mechanisms for implicit authentication inspired by recent works done in the area of Transport Layer Security (TLS) protocols, particularly, in KEMTLS (CCS'20). We port those ideas to the HAKE framework and develop novel proof techniques on the way. Due to our novel KEM-based approach, the resulting protocol has a slightly different message flow compared to prior work that we carefully align with the HAKE framework and which makes our changes to the Muckle+ non-trivial.

Vlasiator is a space plasma simulation code which models near-Earth ion-kinetic dynamics in three spatial and three velocity dimensions. It is highly parallelized, modeling the Vlasov equation directly through the distribution function, discretized on a Cartesian grid, instead of the more common particle-in-cell approach. Modeling near-Earth space, plasma properties span several orders of magnitude in temperature, density, and magnetic field strength. In order to fit the required six-dimensional grids in memory, Vlasiator utilizes a sparse block-based velocity mesh, where chunks of velocity space are added or deleted based on the advection requirements of the Vlasov solver. In addition, the spatial mesh is adaptively refined through cell-based octree refinement. In this paper, we describe the design choices of porting Vlasiator to heterogeneous CPU/GPU architectures. We detail the memory management, algorithmic changes, and kernel construction as well as our unified codebase approach, resulting in portability to both NVIDIA and AMD hardware (CUDA and HIP languages, respectively). In particular, we showcase a highly parallel block adjustment approach allowing efficient re-ordering of a sparse velocity mesh. We detail pitfalls we have overcome and lay out a plan for optimization to facilitate future exascale simulations using multi-node GPU supercomputing., Comment: 31 pages, 12 figures, submitted to ASTRONUM 2024 - the 16th International Conference on Numerical Modeling of Space Plasma Flows

In this paper, we present a new diverse class of post-quantum group-based Digital Signature Schemes (DSS). The approach is significantly different from previous examples of group-based digital signatures and adopts the framework of group action-based cryptography: we show that each finite group defines a group action relative to the semidirect product of the group by its automorphism group, and give security bounds on the resulting signature scheme in terms of the group-theoretic computational problem known as the Semidirect Discrete Logarithm Problem (SDLP). Crucially, we make progress towards being able to efficiently compute the novel group action, and give an example of a parameterised family of groups for which the group action can be computed for any parameters, thereby negating the need for expensive offline computation or inclusion of redundancy required in other schemes of this type.

Solar wind charge exchange produces emissions in the soft X-ray energy range which can enable the study of near-Earth space regions such as the magnetopause, the magnetosheath and the polar cusps by remote sensing techniques. The Solar wind-Magnetosphere-Ionosphere Link Explorer (SMILE) and Lunar Environment heliospheric X-ray Imager (LEXI) missions aim to obtain soft X-ray images of near-Earth space thanks to their Soft X-ray Imager (SXI) instruments. While earlier modeling works have already simulated soft X-ray images as might be obtained by SMILE SXI during its mission, the numerical models used so far are all based on the magnetohydrodynamics description of the space plasma. To investigate the possible signatures of ion-kinetic-scale processes in soft X-ray images, we use for the first time a global hybrid-Vlasov simulation of the geospace from the Vlasiator model. The simulation is driven by fast and tenuous solar wind conditions and purely southward interplanetary magnetic field. We first produce global X-ray images of the dayside near-Earth space by placing a virtual imaging satellite at two different locations, providing meridional and equatorial views. We then analyze regional features present in the images and show that they correspond to signatures in soft X-ray emissions of mirror-mode wave structures in the magnetosheath and flux transfer events (FTEs) at the magnetopause. Our results suggest that, although the time scales associated with the motion of those transient phenomena will likely be significantly smaller than the integration time of the SMILE and LEXI imagers, mirror-mode structures and FTEs can cumulatively produce detectable signatures in the soft X-ray images. [...], Comment: Accepted for publication in Earth and Planetary Physics. 28 pages, 10 figures

The precipitation of charged particles from the magnetosphere into the ionosphere is one of the crucial coupling mechanisms between these two regions of geospace and is associated with multiple space weather effects, such as global navigation satellite system signal disruption and geomagnetically induced currents at ground level. While precipitating particle fluxes have been measured by numerous spacecraft missions over the past decades, it often remains difficult to obtain global precipitation patterns with a good time resolution during a substorm. Numerical simulations can help to bridge this gap and improve the understanding of mechanisms leading to particle precipitation at high latitudes through the global view they offer on the near-Earth space system. We present the first results on auroral (0.5-50 keV) proton precipitation within a 3-dimensional simulation of the Vlasiator hybrid-Vlasov model. The run is driven by southward interplanetary magnetic field conditions with constant solar wind parameters. We find that, on the dayside, cusp proton precipitation exhibits the expected energy-latitude dispersion and takes place in the form of successive bursts associated with the transit of flux transfer events formed through dayside magnetopause reconnection. On the nightside, the precipitation takes place within the expected range of geomagnetic latitudes, and it appears clearly that the precipitating particle injection is taking place within a narrow magnetic local time span, associated with fast Earthward plasma flows in the near-Earth magnetotail. Finally, the simulated precipitating fluxes are compared to observations from Defense Meteorological Satellite Program spacecraft during driving conditions similar to those in the simulation and are found to be in good agreement with the measurements., Comment: Accepted for publication in the Journal of Space Weather and Space Climate (JSWSC). 35 pages, 15 figures

Group-based cryptography is a relatively unexplored family in post-quantum cryptography, and the so-called Semidirect Discrete Logarithm Problem (SDLP) is one of its most central problems. However, the complexity of SDLP and its relationship to more well-known hardness problems, particularly with respect to its security against quantum adversaries, has not been well understood and was a significant open problem for researchers in this area. In this paper we give the first dedicated security analysis of SDLP. In particular, we provide a connection between SDLP and group actions, a context in which quantum subexponential algorithms are known to apply. We are therefore able to construct a subexponential quantum algorithm for solving SDLP, thereby classifying the complexity of SDLP and its relation to known computational problems.

We define new families of Tillich-Z\'emor hash functions, using higher dimensional special linear groups over finite fields as platforms. The Cayley graphs of these groups combine fast mixing properties and high girth, which together give rise to good preimage and collision resistance of the corresponding hash functions. We justify the claim that the resulting hash functions are post-quantum secure., Comment: 18 pages, an appendix with a python/sage implementation of the hash functions

Of the many families of cryptographic schemes proposed to be post-quantum, a relatively unexplored set of examples comes from group-based cryptography. One of the more central schemes from this area is the so-called Semidirect Product Key Exchange (SDPKE), a generalisation of Diffie-Hellman Key Exchange that is plausibly post-quantum. In this report we survey the state of the literature relating to SDPKE, providing a high-level discussion of security, as well as a comprehensive overview of the proposed platforms and the main cryptanalytic ideas relevant to each.

All instances of the semidirect key exchange protocol, a generalisation of the famous Diffie-Hellman key exchange protocol, satisfy the so-called "telescoping equality"; in some cases, this equality has been used to construct an attack. In this report we present computational evidence suggesting that an instance of the scheme called `MOBS' is an example of a scheme where the telescoping equality has too many solutions to be a practically viable means to conduct an attack., Comment: 10 pages, 6 figures

It was recently demonstrated that the Matrix Action Key Exchange (MAKE) algorithm, a new type of key exchange protocol using the semidirect product of matrix groups, is vulnerable to a linear algebraic attack if the matrices are over a commutative ring. In this note, we establish conditions under which protocols using matrices over a non-commutative ring are also vulnerable to this attack. We then demonstrate that group rings $R[G]$ are examples of non-commutative rings that satisfy these conditions., Comment: 11 pages

Context. Solar Energetic Particles (SEPs) with energy in the GeV range can propagate to Earth from their acceleration region near the Sun and produce Ground Level Enhancements (GLEs). The traditional approach to interpreting and modelling GLE observations assumes particle propagation only parallel to the magnetic field lines of interplanetary space, i.e. it is spatially 1D. Recent measurements by PAMELA have characterised SEP properties at 1 AU for the ~100 MeV-1 GeV range at high spectral resolution. Aims. We model the transport of GLE-energy solar protons through the Interplanetary Magnetic Field (IMF) using a 3D approach, to assess the effect of the Heliospheric Current Sheet (HCS) and drifts associated to the gradient and curvature of the Parker spiral. The latter are influenced by the IMF polarity. We derive 1 AU observables and compare the simulation results with data from PAMELA. Methods. We use a 3D test particle model including a HCS. Monoenergetic populations are studied first to obtain a qualitative picture of propagation patterns and numbers of crossings of the 1 AU sphere. Simulations for power law injection are used to derive intensity profiles and fluence spectra at 1 AU. A simulation for a specific event, GLE 71, is used to compare with PAMELA data. Results. Spatial patterns of 1 AU crossings and the average number of crossings are strongly influenced by 3D effects, with significant differences between periods of A+ and A- polarities. The decay time constant of 1 AU intensity profiles varies depending on the polarity and position of the observer, and it is not a simple function of the mean free path as in 1D models. Energy dependent leakage from the injection flux tube is particularly important for GLE energy particles, in many cases resulting in a roll-over in the fluence spectrum., Comment: Accepted by A&A (revised version, 9 pages, 6 figures)

Solar energetic particles (SEPs) are an important product of solar activity. They are connected to solar active regions and flares, coronal mass ejections (CMEs), EUV waves, shocks, Type II and III radio emissions, and X-ray bursts. These phenomena are major probes of the partition of energy in solar eruptions, as well as for the organization, dynamics, and relaxation of coronal and interplanetary magnetic fields. Many of these phenomena cause terrestrial space weather, posing multiple hazards for humans and their technology from space to the ground. Since particular flares, shocks, CMEs, and EUV waves produce SEP events but others do not, since propagation effects from the low corona to 1 AU appear important for some events but not others, and since Type II and III radio emissions and X-ray bursts are sometimes produced by energetic particles leaving these acceleration sites, it is necessary to study the whole system with a multi-frequency and multi-instrument perspective that combines both in-situ and remote observations with detailed modelling of phenomena. This article demonstrates this comprehensive approach, and shows its necessity, by analysing a trio of unusual and striking solar eruptions, radio and X-ray bursts, and SEP events that occurred on 4 November 2015. These events show both strong similarities and differences from standard events and each other, despite having very similar interplanetary conditions and only two are sites and CME genesis regions. They are therefore major targets for further in-depth observational studies, and for testing both existing and new theories and models. Based on the very limited modelling available we identify the aspects that are and are not understood, and we discuss ideas that may lead to improved understanding of the SEP, radio, and space-weather events., Comment: 56 pages, 25 figures; Accepted for publication in Solar Physics

Today, the near-Earth space is facing a paradigm change as the number of new spacecraft is literally sky-rocketing. Increasing numbers of small satellites threaten the sustainable use of space, as without removal, space debris will eventually make certain critical orbits unusable. A central factor affecting small spacecraft health and leading to debris is the radiation environment, which is unpredictable due to an incomplete understanding of the near-Earth radiation environment itself and its variability driven by the solar wind and outer magnetosphere. This paper presents the FORESAIL-1 nanosatellite mission, having two scientific and one technological objectives. The first scientific objective is to measure the energy and flux of energetic particle loss to the atmosphere with a representative energy and pitch angle resolution over a wide range of magnetic local times. To pave the way to novel model - in situ data comparisons, we also show preliminary results on precipitating electron fluxes obtained with the new global hybrid-Vlasov simulation Vlasiator. The second scientific objective of the FORESAIL-1 mission is to measure energetic neutral atoms (ENAs) of solar origin. The solar ENA flux has the potential to contribute importantly to the knowledge of solar eruption energy budget estimations. The technological objective is to demonstrate a satellite de-orbiting technology, and for the first time, make an orbit manoeuvre with a propellantless nanosatellite. FORESAIL-1 will demonstrate the potential for nanosatellites to make important scientific contributions as well as promote the sustainable utilisation of space by using a cost-efficient de-orbiting technology., Comment: 26 pages, 7 figures, 5 tables Published online in JGR: Space Physics on 21 May 2019

This paper reviews Vlasov-based numerical methods used to model plasma in space physics and astrophysics. Plasma consists of collectively behaving charged particles that form the major part of baryonic matter in the Universe. Many concepts ranging from our own planetary environment to the Solar system and beyond can be understood in terms of kinetic plasma physics, represented by the Vlasov equation. We introduce the physical basis for the Vlasov system, and then outline the associated numerical methods that are typically used. A particular application of the Vlasov system is Vlasiator, the world's first global hybrid-Vlasov simulation for the Earth's magnetic domain, the magnetosphere. We introduce the design strategies for Vlasiator and outline its numerical concepts ranging from solvers to coupling schemes. We review Vlasiator's parallelisation methods and introduce the used high-performance computing (HPC) techniques. A short review of verification, validation and physical results is included. The purpose of the paper is to present the Vlasov system and introduce an example implementation, and to illustrate that even with massive computational challenges, an accurate description of physics can be rewarding in itself and significantly advance our understanding. Upcoming supercomputing resources are making similar efforts feasible in other fields as well, making our design options relevant for others facing similar challenges., Comment: Invited review for Living Reviews in Computational Astrophysics

The source of high-energy protons (>500 MeV) responsible for the so-called ground level enhancements (GLEs) remains an open question in solar physics. One of the candidates is a shock wave driven by a coronal mass ejection, which is thought to accelerate particles via diffusive-shock acceleration. We perform physics-based simulations of proton acceleration using information on the shock and ambient plasma parameters derived from the observation of a real GLE event. We analyse the simulation results with the aim to find out which of the parameters are significant in controlling the acceleration efficiency and to get a better understanding of the conditions under which the shock can produce relativistic protons. We use results of the recently developed technique to determine the shock and ambient plasma parameters, applied to the 17 May 2012 GLE event, and carry out proton acceleration simulations with the Coronal Shock Acceleration model. We have performed proton acceleration simulations for nine individual magnetic field lines characterised by various plasma conditions. Analysis of the simulation results shows that the acceleration efficiency of the shock, i.e., its ability to accelerate particles to high energies, tends to be higher for those shock portions that are characterised by larger values of the scattering-centre compression ratio and/or the fast-mode Mach number. At the same time, the acceleration efficiency can be strengthened due to enhanced plasma density in the flux tube. Analysis of the delays between the flare onset and the production times of protons of 1 GV rigidity for different field lines in our simulations, and a subsequent comparison of those with the observed values indicate a possibility that quasi-perpendicular portions of the shock play the main role in producing relativistic protons., Comment: 11 pages, 9 figures

Forecasting Solar Energetic Particle (SEP) fluence, as integrated over an SEP event, is an important element when estimating the effect of solar eruptions on humans and technology in space. Current real-time estimates are based on SEP measurements at a single location in space. However, the interplanetary magnetic field corotates with the Sun approximately 13$^\circ$ each day with respect to Earth, thus in 4 days a near-Earth spacecraft will have changed their connection about 60$^\circ$ from the original SEP source. We estimate the effect of the corotation on particle fluence using a simple particle transport model, and show that ignoring corotation can cause up to an order of magnitude error in fluence estimations, depending on the interplanetary particle transport conditions. We compare the model predictions with STEREO observations of SEP events., Comment: 3 pages, 3 figures. Accepted for publication in Proceedings of IAU Symposium 335: Space Weather of the Heliosphere: Processes and Forecasts

Understanding the transport of Solar Energetic Particles (SEPs) from acceleration sites at the Sun into interplanetary space and to the Earth is an important question for forecasting space weather. The Interplanetary Magnetic Field (IMF), with two distinct polarities and a complex structure, governs energetic particle transport and drifts. We analyse for the first time the effect of a wavy Heliospheric Current Sheet (HCS) on the propagation of SEPs. We inject protons close to the Sun and propagate them by integrating fully 3D trajectories within the inner heliosphere in the presence of weak scattering. We model the HCS position using fits based on neutral lines of magnetic field source surface maps (SSMs). We map 1 au proton crossings, which show efficient transport in longitude via HCS, depending on the location of the injection region with respect to the HCS. For HCS tilt angles around $30^\circ-40^\circ$, we find significant qualitative differences between A+ and A$-$ configurations of the IMF, with stronger fluences along the HCS in the former case but with a distribution of particles across a wider range of longitudes and latitudes in the latter. We show how a wavy current sheet leads to longitudinally periodic enhancements in particle fluence. We show that for an A+ IMF configuration, a wavy HCS allows for more proton deceleration than a flat HCS. We find that A$-$ IMF configurations result in larger average fluences than A+ IMF configurations, due to a radial drift component at the current sheet., Comment: 16 pages, 8 figures and 1 table, plus appendix of 2 pages, 1 figure and 1 table