arXiv subjects

Tobias Damm

Publications and source records attributed to Tobias Damm.

At least 19 recordsLinked to original sources

arXiv2026

Breaking ECDSA with Electromagnetic Side-Channel Attacks: Challenges and Practicality on Modern Smartphones

Smartphones handle sensitive tasks such as messaging and payment and may soon support critical electronic identification through initiatives such as the European Digital Identity (EUDI) wallet, currently under development. Yet the susceptibility of modern smartphones to physical side-channel analysis (SCA) is underexplored, with recent work limited to pre-2019 hardware. Since then, smartphone system on chip (SoC) platforms have grown more complex, with heterogeneous processor clusters, sub 10 nm nodes, and frequencies over 2 GHz, potentially complicating SCA. In this paper, we assess the feasibility of electromagnetic (EM) SCA on a Raspberry Pi 4, featuring a Broadcom BCM2711 SoC and a Fairphone 4 featuring a Snapdragon 750G 5G SoC. Using new attack methodologies tailored to modern SoCs, we recover ECDSA secrets from OpenSSL by mounting the Nonce@Once attack of Alam et al. (Euro S&P 2021) and show that the libgcrypt countermeasure does not fully mitigate it. We present case studies illustrating how hardware and software stacks impact EM SCA feasibility. Motivated by use cases such as the EUDI wallet, we survey Android cryptographic implementations and define representative threat models to assess the attack. Our findings show weaknesses in ECDSA software implementations and underscore the need for independently certified secure elements (SEs) in all smartphones.

cs.CR↗

arXiv2026

Impact of Markov Decision Process Design on Sim-to-Real Reinforcement Learning

Reinforcement Learning (RL) has demonstrated strong potential for industrial process control, yet policies trained in simulation often suffer from a significant sim-to-real gap when deployed on physical hardware. This work systematically analyzes how core Markov Decision Process (MDP) design choices -- state composition, target inclusion, reward formulation, termination criteria, and environment dynamics models -- affect this transfer. Using a color mixing task, we evaluate different MDP configurations and mixing dynamics across simulation and real-world experiments. We validate our findings on physical hardware, demonstrating that physics-based dynamics models achieve up to 50% real-world success under strict precision constraints where simplified models fail entirely. Our results provide practical MDP design guidelines for deploying RL in industrial process control.

cs.LG↗

arXiv2026

A spectral approach to interface layers on networks for the linearized BGK equation and its acoustic limit

We consider in this paper a velocity discretized version of the full linear kinetic BGK model and the corresponding limit for small Knudsen number, the linearised Euler or acoustic system. Considering these equations on networks, coupling conditions for the macroscopic equations are derived from the kinetic conditions via an asymptotic analysis near the nodes of the network. Here, a degeneracy in the limit equations requires not only the investigation of kinetic layers, but also the discussion of viscous layers. Using the kinetic coupling conditions at the junction and coupling kinetic and viscous layers to the outer problems on the edges one obtains a coupled kinetic half-space problem at each node. A spectral method is developed to solve this coupled kinetic half-space problems. This allows to obtain a detailed picture of the various interface layers near the nodes and to determine the relevant coefficients in the kinetic derived coupling conditions for the macroscopic equations.Numerical results show the accuracy and efficiency of the approach.

math.AP↗

arXiv2026

Efficient $k$-Sign Consistency Verification of Hankel Matrices via Schur Polynomials

We consider the problem of certifying (strict) $k$-sign consistency of a matrix, that is, whether all of its $k$-th order minors share the same (strict) sign. Although this problem is generally of combinatorial complexity, we show that for Hankel matrices it can be significantly simplified: our sufficient condition requires checking only the $k$-th order minors of a reshaped Hankel matrix with $k$ rows. Remarkably, when applied to the Hankel operator, this sufficient condition is also necessary. Comparable results were known only in the setting of (strictly) $k$-positive Hankel matrices and operators, in which all minors of order up to $k$ have the same (strict) sign. More concretely, we derive a formula expressing the $k$-th order minors of Hankel matrices as nonnegative integer linear combinations of $k$-th order minors with consecutive row indices. Our derivation uses Schur polynomial theory to show that the $k$-th order minors of any matrix are nonnegative integer linear combinations of row-consecutive $k$-th order minors, meaning minors formed from distinct columns whose consecutive row indices need not coincide across columns. For Hankel matrices, these minors coincide -- up to sign changes arising from column swaps -- with the usual $k$-th order minors with consecutive row indices. Our main result then follows by showing that the sum of certain signed nonnegative integer coefficients equals the corresponding Littlewood--Richardson coefficients. In our problem, the nonnegativity of these coefficients ensures that negatively signed column permutations are cancelled by positively signed ones. Our results also extend naturally to Toeplitz matrices and operators, and we present a partial analogue for circulant matrices.

math.CO↗

arXiv2025

Interface layers and coupling conditions for discrete kinetic models on networks: a spectral approac

We consider kinetic and related macroscopic equations on networks. A class of linear kinetic BGK models is considered, where the limit equation for small Knudsen numbers is given by the wave equation. Coupling conditions for the macroscopic equations are obtained from the kinetic coupling conditions via an asymptotic analysis near the nodes of the network and the consideration of coupled solutions of kinetic half-space problems. Analytical results are obtained for a discrete velocity version of the coupled half-space problems. Moreover, an efficient spectral method is developed to solve the coupled discrete velocity half-space problems. In particular, this allows to determine the relevant coefficients in the coupling conditions for the macroscopic equations from the underlying kinetic network problem. These coefficients correspond to the so-called extrapolation length for kinetic boundary value problems. Numerical results show the accuracy and fast convergence of the approach. Moreover, a comparison of the kinetic solution on the network with the macroscopic solution is presented.

math.NA↗

arXiv2025

On Model Predictive Funnel Control with Equilibrium Endpoint Constraints

We propose model predictive funnel control, a novel model predictive control (MPC) scheme building upon recent results in funnel control. The latter is a high-gain feedback methodology that achieves evolution of the measured output within predefined error margins. The proposed method dynamically optimizes a parameter-dependent error boundary in a receding-horizon manner, thereby combining prescribed error guarantees from funnel control with the predictive advantages of MPC. On the one hand, this approach promises faster optimization times due to a reduced number of decision variables, whose number does not depend on the horizon length. On the other hand, the continuous feedback law improves the robustness and also explicitly takes care of the inter-sampling behavior. We focus on proving stability by leveraging results from MPC stability theory with terminal equality constraints. Moreover, we rigorously show initial and recursive feasibility.

math.OC↗

arXiv2024

On the balanced truncation error bound and sign parameters from arrowhead realizations

Balanced truncation and singular perturbation approximation for linear dynamical systems yield reduced-order models that satisfy a well-known error bound involving the Hankel singular values. We show that this bound holds with equality for single-input, single-output systems, if the sign parameters corresponding to the truncated Hankel singular values are all equal. These signs are determined by a generalized state-space symmetry property of the corresponding linear model. For a special class of systems having arrowhead realizations, the signs can be determined directly from the off-diagonal entries of the corresponding arrowhead matrix. We describe how such arrowhead systems arise naturally in certain applications of network modeling, and illustrate these results with a power system model that motivated this study.

eess.SY↗

arXiv2023

Complexity reduction of large-scale stochastic systems using linear quadratic Gaussian balancing

In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic systems are identified exploiting these Gramians. An associated balancing related scheme is proposed that removes unimportant information from the stochastic dynamics in order to obtain a reduced system. We show that this reduced model preserves important features like stabilizability and detectability. Additionally, a comprehensive error analysis based on eigenvalues of the Gramian pair product is conducted. This provides an a-priori criterion for the reduction quality which we illustrate in numerical experiments.

math.OC↗

arXiv2023

Hadamard Powers and Kernel Perceptrons

We study a relation between Hadamard powers and polynomial kernel perceptrons. The rank of Hadamard powers for the special case of a Boolean matrix and for the generic case of a real matrix is computed explicitly. These results are interpreted in terms of the classification capacities of perceptrons.

math.RA↗

arXiv2022

On Coercivity and the Frequency Domain Condition in Indefinite LQ-Control

We introduce a coercivity condition as a time domain analogue of the frequency criterion provided by the famous Kalman-Yakubovich-Popov lemma. For a simple stochastic linear quadratic control problem we show how the coercivity condition characterizes the solvability of Riccati equations.

math.OC↗

arXiv2021

Balanced truncation of $k$-positive systems

This paper considers balanced truncation of discrete-time Hankel $k$-positive systems, characterized by Hankel matrices whose minors up to order $k$ are nonnegative. Our main result shows that if the truncated system has order $k$ or less, then it is Hankel totally positive ($\infty$-positive), meaning that it is a sum of first order lags. This result can be understood as a bridge between two known results: the property that the first-order truncation of a positive system is positive ($k=1$), and the property that balanced truncation preserves state-space symmetry. It provides a broad class of systems where balanced truncation is guaranteed to result in a minimal internally positive system.

math.OC↗

arXiv2020

Simultaneous hollowisation, joint numerical range, and stabilization by noise

We consider orthogonal transformations of arbitrary square matrices to a form where all diagonal entries are equal. In our main results we treat the simultaneous transformation of two matrices and the symplectic orthogonal transformation of one matrix. A relation to the joint real numerical range is worked out, efficient numerical algorithms are developped and applications to stabilization by rotation and by noise are presented.

math.NA↗

arXiv2019

Riemannian optimal identification method for linear systems with symmetric positive-definite matrix

This study develops identification methods for linear continuous-time symmetric systems, such as electrical network systems, multi-agent network systems, and temperature dynamics in buildings. To this end, we formulate three system identification problems for the corresponding discrete-time systems. The first is a least-squares problem in which we wish to minimize the sum of squared errors between the true and model outputs on the product manifold of the manifold of symmetric positive-definite matrices and two Euclidean spaces. In the second problem, to reduce the search dimensions, the product manifold is replaced with the quotient set under a specified group action by the orthogonal group. In the third problem, the manifold of symmetric positive-definite matrices in the first problem is replaced by the manifold of matrices with only positive diagonal elements. In particular, we examine the quotient geometry in the second problem. We propose Riemannian conjugate gradient methods for the three problems, and select initial points using a popular subspace method. The effectiveness of our proposed methods is demonstrated through numerical simulations and comparisons with the Gauss--Newton method, which is one of the most popular approach for solving least-squares problems.

math.OC↗

arXiv2019

Optimal control of district heating networks using a reduced order model

We study the optimal control of district heating networks using a reduced order model based on a system theoretic description close to the underlying Euler equations. In the presented scenarios, the central task is to limit the maximal feed-in power occurring as a product of control and state variables. The underlying dynamics of heating networks acting as optimization constraints pose the central computational complexity, prohibiting the determination of an optimal control online. The advection of the injected energy density on the network results in an index-1, quadratic in state differential algebraic equation, challenging to reduce. The suggested reduced model decreases the computation time of the optimization significantly. The effectiveness of the presented approach is demonstrated for an existing, large-scale heating network including changes of flux directions.

math.OC↗

arXiv2019

Model order reduction of hyperbolic systems at the example of district heating networks

In this article a framework for the generation of a computationally fast surrogate model for district heating networks is presented. An appropriate model results in an index-1 hyperbolic, differential algebraic equation quadratic in state, exhibiting several hundred of outputs to be approximated. We show the existence of a global energy matrix which fulfills the Lyapunov inequality ensuring stability of the reduced model. By considering algebraic variables as parameters to the dynamical transport, the reduction of a linear, time varying (LTV) problem results. We present a scheme to efficiently combine linear reductions to a global surrogate model using a greedy strategy in the frequency domain. The numerical effectiveness of the scheme is demonstrated at different, existing, large scale networks.

math.OC↗

arXiv2019

Levitated cavity optomechanics in high vacuum

We report dispersive coupling of an optically trapped silica nanoparticle ($143~$nm diameter) to the field of a driven Fabry-Perot cavity in high vacuum ($4.3\times 10^{-6}~$mbar). We demonstrate nanometer-level control in positioning the particle with respect to the intensity distribution of the cavity field, which allows access to linear, quadratic and tertiary optomechanical interactions in the resolved sideband regime. We determine all relevant coupling rates of the system, i.e. mechanical and optical losses as well as optomechanical interaction, and obtain a quantum cooperativity of $C_Q = 0.01$. Based on the presented performance the regime of strong cooperativity ($C_Q > 1$) is clearly within reach by further decreasing the mode volume of the cavity.

physics.optics↗

arXiv2017

Variable Potentials for Thermalized Light and Coupled Condensates

For over a decade, cold atoms in lattice potentials have been an attractive platform to simulate phenomena known from solid state theory, as the Mott-insulator transition. In contrast, the field of photonics usually deals with non-equilibrium physics. Recent advances towards photonic simulators of solid state equilibrium effects include polariton double-site and lattice experiments, as well as the demonstration of a photon condensate in a dye-filled microcavity. Here we demonstrate a technique to create variable micropotentials for light using thermo-optic imprinting within an ultrahigh-reflectivity mirror microcavity filled with a dye-polymer solution that is compatible with photon gas thermalization. By repeated absorption-emission cycles photons thermalize to the temperature of the dye solution, and in a single microsite we observe a photon Bose-Einstein microcondensate. Effective interactions between the otherwise nearly non-interacting photons are observed due to thermo-optic effects, and in a double-well system tunnel coupling between sites is demonstrated, as well as the hybridization of eigenstates. Prospects of the new experimental platform include photonic structures in which photons thermalize into entangled manybody states.

cond-mat.quant-gas↗

arXiv2017

First-order spatial coherence measurements in a thermalized two-dimensional photonic quantum gas

Phase transitions between different states of matter can profoundly modify the order in physical systems, with the emergence of ferromagnetic or topological order constituting important examples. Correlations allow to quantify the degree of order and classify different phases. Here we report measurements of first-order spatial correlations in a harmonically trapped two-dimensional photon gas below, at, and above the critical particle number for Bose-Einstein condensation, using interferometric measurements of the emission of a dye-filled optical microcavity. For the uncondensed gas, the transverse coherence decays on a length scale determined by the thermal de Broglie wavelength of the photons, which shows the expected scaling with temperature. At the onset of Bose-Einstein condensation true long-range order emerges, and we observe quantum statistical effects as the thermal wave packets overlap. The excellent agreement with equilibrium Bose gas theory prompts microcavity photons as promising candidates for studies of critical scaling and universality in optical quantum gases.

cond-mat.quant-gas↗