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Stefan Rosemann

Publications and source records attributed to Stefan Rosemann.

11 recordsLinked to original sources
arXiv2026

Simon's Algorithm for the Even-Mansour Cipher on Quantum Hardware

Simon's algorithm is a polynomial period-finding algorithm that has been used to exploit the algebraic structure of specific symmetric ciphers, showing that exponential speedups in their cryptanalysis are theoretically possible. While the theoretical framework for an attack using Simon's algorithm on the Even-Mansour cipher is well-established, practical implementations on noisy intermediate-scale quantum (NISQ) hardware remain limited. This paper presents a proof of concept quantum cryptanalysis of the Even-Mansour cipher using Simon's period-finding algorithm on NISQ hardware. For N = 3 and N = 4, we successfully demonstrate secret key recovery for N-bit constructions on the ibm_miami processor. Our experiments also identify a scaling limitation in the classical pre-processing stage: The DORCIS circuit optimization tool encountered a memory bottleneck at N = 5, preventing the generation of optimized circuits for larger key lengths. Our results suggest firstly that Simon's algorithm is effective for the Even-Mansour cipher for short bit lengths on current quantum hardware. Secondly, while DORCIS is effective for the small-scale S-boxes for which it was designed, there remains a need for the investigation of more scalable and efficient synthesis tools capable of handling larger and more general permutations in the context of Even-Mansour ciphers.

quant-ph↗
arXiv2018

Slodowy slices and the complete integrability of Mishchenko-Fomenko subalgebras on regular adjoint orbits

This work is concerned with Mishchenko-Fomenko subalgebras and their restrictions to the adjoint orbits in a finite-dimensional complex semisimple Lie algebra. In this setting, it is known that each Mishchenko-Fomenko subalgebra restricts to a completely integrable system on every orbit in general position. We improve upon this result, showing that each Mishchenko-Fomenko subalgebra yields a completely integrable system on all regular orbits (i.e. orbits of maximal dimension). Our approach incorporates the theory of regular $\mathfrak{sl}_2$-triples and associated Slodowy slices, as developed by Kostant.

math.SG↗
arXiv2017

Local description of Bochner-flat (pseudo-)Kähler metrics

The Bochner tensor is the Kähler analogue of the conformal Weyl tensor. In this article, we derive local (i.e., in a neighbourhood of almost every point) normal forms for a (pseudo-)Kähler manifold with vanishing Bochner tensor. The description is pined down to a new class of symmetric spaces which we describe in terms of their curvature operators. We also give a local description of weakly Bochner-flat metrics defined by the property that the Bochner tensor has vanishing divergence. Our results are based on the local normal forms for c-projectively equivalent metrics. As a by-product, we also describe all Kähler-Einstein metrics admitting a c-projectively equivalent one.

math.DG↗
arXiv2015

Curvature and the c-projective mobility of Kaehler metrics with hamiltonian 2-forms

The mobility of a Kaehler metric is the dimension of the space of metrics with which it is c-projectively equivalent. The mobility is at least two if and only if the Kaehler metric admits a nontrivial hamiltonian 2-form. After summarizing this relationship, we present necessary conditions for a Kaehler metric to have mobility at least three: its curvature must have nontrivial nullity at every point. Using the local classification of Kaehler metrics with hamiltonian 2-forms, we describe explicitly the Kaehler metrics with mobility at least three and hence show that the nullity condition on the curvature is also sufficient, up to some degenerate exceptions. In an Appendix, we explain how the classification may be related, generically, to the holonomy of a complex cone metric.

math.DG↗
arXiv2015

Local normal forms for c-projectively equivalent metrics and proof of the Yano-Obata conjecture in arbitrary signature. Proof of the projective Lichnerowicz conjecture for Lorentzian metrics

Two Kähler metrics on a complex manifold are called c-projectively equivalent if their $J$-planar curves coincide. These curves are defined by the property that the acceleration is complex proportional to the velocity. We give an explicit local description of all pairs of c-projectively equivalent Kähler metrics of arbitrary signature and use this description to prove the classical Yano-Obata conjecture: we show that on a closed connected Kähler manifold of arbitrary signature, any c-projective vector field is an affine vector field unless the manifold is $CP^n$ with (a multiple of) the Fubini-Study metric. As a by-product, we prove the projective Lichnerowicz conjecture for metrics of Lorentzian signature: we show that on a closed connected Lorentzian manifold, any projective vector field is an affine vector field.

math.DG↗
arXiv2015

The degree of mobility of Einstein metrics

Two pseudo-Riemannian metrics are called projectively equivalent if their unparametrized geodesics coincide. The degree of mobility of a metric is the dimension of the space of metrics that are projectively equivalent to it. We give a complete list of possible values for the degree of mobility of Riemannian and Lorentzian Einstein metrics on simply connected manifolds, and describe all possible dimensions of the space of essential projective vector fields.

math.DG↗
arXiv2013

Four-dimensional Kähler metrics admitting c-projective vector fields

A vector field on a Kähler manifold is called c-projective if its flow preserves the J-planar curves. We give a complete local classification of Kähler real 4-dimensional manifolds that admit an essential c-projective vector field. An important technical step is a local description of 4-dimensional c-projectively equivalent metrics of arbitrary signature. As an application of our results we prove the natural analog of the classical Yano-Obata conjecture in the pseudo-Riemannian 4-dimensional case.

math.DG↗
arXiv2013

Conification construction for Kaehler manifolds and its application in c-projective geometry

Two Kaehler metrics on one complex manifold are said to be c-projectively equivalent if their J-planar curves, i.e., curves defined by the property that their acceleration is complex proportional to their velocity, coincide. The degree of mobility of a Kaehler metric is the dimension of the space of metrics that are c-projectively equivalent to it. We give the list of all possible values of the degree of mobility of simply connected 2n-dimensional Riemannian Kaehler manifolds. We also describe all such values under the additional assumption that the metric is Einstein. As an application, we describe all possible dimensions of the space of essential c-projective vector fields of Kaehler and Kaehler-Einstein Riemannian metrics. We also show that two c-projectively equivalent Kaehler Einstein metrics (of arbitrary signature) on a closed manifold have constant holomorphic curvature or are affinely equivalent.

math.DG↗
arXiv2011

Two remarks on $PQ^ε$-projectivity of Riemannian metrics

We show that $PQ^ε$-projectivity of two Riemannian metrics introduced in \cite{Top2003} implies affine equivalence of the metrics unless $ε\in\{0,-1,-3,-5,-7,...\}$. Moreover, we show that for $ε=0$, $PQ^ε$-projectivity implies projective equivalence.

math.DG↗
arXiv2010

The Tanno-Theorem for Kählerian metrics with arbitrary signature

Considering a non-constant smooth solution $f$ of the Tanno equation on a closed, connected Kähler manifold $(M,g,J)$ with positively definite metric $g$, Tanno showed that the manifold can be finitely covered by $(\mathbb{C}P(n),\mbox{const}\cdot g_{FS})$, where $g_{FS}$ denotes the Fubini-Study metric of constant holomorphic sectional curvature equal to $1$. The goal of this paper is to give a proof of Tannos Theorem for Kähler metrics with arbitrary signature.

math.DG↗