Koopman interpretation and analysis of a public-key cryptosystem: Diffie-Hellman key exchange

The security of public-key cryptosystems relies on computationally hard problems, that are classically analyzed by number theoretic methods. In this paper, we introduce a new perspective on cryptosystems by interpreting the Diffie-Hellman key exchange as a nonlinear dynamical system. Employing Koopman theory, we transfer this dynamical system into a higher-dimensional space to analytically derive a purely linear system that equivalently describes the underlying cryptosystem. In this form, analytic tools for linear systems allow us to reconstruct the secret integers of the key exchange by simple manipulations. Moreover, we provide an upper bound on the minimal required lifting dimension to obtain perfect accuracy. To demonstrate the potential of our method, we relate our findings to existing results on algorithmic complexity. Finally, we transfer this approach to a data-driven setting where the Koopman representation is learned from data samples of the cryptosystem.Comment: 8 pages. This work has been submitted to IFAC for possible publicatio

Towards a European military culture?

Recent discussion of the Common Security and Foreign Policy has focussed on the international relations between European member states. Such a focus is entirely valid since the project is being driven forward by nation states. However, the success of the Common Security and Foreign Policy and especially the development of a specifically European military capability under the European Security and Defence Policy will depend not merely on the will of the participating nation-states. Above all, it will depend on the development of a common military culture at the level of weapons development and procurement and at the level of doctrine. The problem is that at neither level is the development of a European culture remotely in sight

Heat-Labile Enterotoxin: Beyond GM1 Binding

Enterotoxigenic Escherichia coli (ETEC) is a significant source of morbidity and mortality worldwide. One major virulence factor released by ETEC is the heat-labile enterotoxin LT, which is structurally and functionally similar to cholera toxin. LT consists of five B subunits carrying a single catalytically active A subunit. LTB binds the monosialoganglioside GM1, the toxin’s host receptor, but interactions with A-type blood sugars and E. coli lipopolysaccharide have also been identified within the past decade. Here, we review the regulation, assembly, and binding properties of the LT B-subunit pentamer and discuss the possible roles of its numerous molecular interactions

Holography in the short-wave infrared range

This master's thesis focuses on digital holography in the near-infrared region. Digital holography is a method that allows for the reconstruction of phase changes and is therefore suitable for studying optical metasurfaces and their properties beyond the capabilities of traditional intensity measurements. The initial research part of the thesis discusses the theory of optical metasurfaces and the principles of digital holography. The acquired knowledge is utilized in the subsequent section of the thesis, which deals with the design of a holographic module that, when connected to a suitable imaging system, enables the implementation of digital holographic microscopy methods. The holographic module is based on a geometric-phase metasurface made of silicon, which allows for operation at a central wavelength of 1550\,nm. The thesis provides a theoretical design of the metasurface and the entire holographic module. The obtained parameters are verified through numerical simulations of holographic imaging. The practical part describes the experimental procedure for testing samples of the geometric-phase metasurface and demonstrates its integration into the assembled holographic module. In the conclusion of the thesis, the holographic module is connected to a microscope and tested under holographic microscopy conditions. The results of the master's thesis can be applicable for investigating phase changes induced by tunable metasurfaces made of vanadium oxide

Holography in the short-wave infrared range

This master's thesis focuses on digital holography in the near-infrared region. Digital holography is a method that allows for the reconstruction of phase changes and is therefore suitable for studying optical metasurfaces and their properties beyond the capabilities of traditional intensity measurements. The initial research part of the thesis discusses the theory of optical metasurfaces and the principles of digital holography. The acquired knowledge is utilized in the subsequent section of the thesis, which deals with the design of a holographic module that, when connected to a suitable imaging system, enables the implementation of digital holographic microscopy methods. The holographic module is based on a geometric-phase metasurface made of silicon, which allows for operation at a central wavelength of 1550\,nm. The thesis provides a theoretical design of the metasurface and the entire holographic module. The obtained parameters are verified through numerical simulations of holographic imaging. The practical part describes the experimental procedure for testing samples of the geometric-phase metasurface and demonstrates its integration into the assembled holographic module. In the conclusion of the thesis, the holographic module is connected to a microscope and tested under holographic microscopy conditions. The results of the master's thesis can be applicable for investigating phase changes induced by tunable metasurfaces made of vanadium oxide