Deciding Orthogonality in Construction-A Lattices

Lattices are discrete mathematical objects with widespread applications to integer programs as well as modern cryptography. A fundamental problem in both domains is the Closest Vector Problem (popularly known as CVP). It is well-known that CVP can be easily solved in lattices that have an orthogonal basis \emph{if} the orthogonal basis is specified. This motivates the orthogonality decision problem: verify whether a given lattice has an orthogonal basis. Surprisingly, the orthogonality decision problem is not known to be either NP-complete or in P. In this paper, we focus on the orthogonality decision problem for a well-known family of lattices, namely Construction-A lattices. These are lattices of the form $C+q\mathbb{Z}^n$, where $C$ is an error-correcting $q$-ary code, and are studied in communication settings. We provide a complete characterization of lattices obtained from binary and ternary codes using Construction-A that have an orthogonal basis. We use this characterization to give an efficient algorithm to solve the orthogonality decision problem. Our algorithm also finds an orthogonal basis if one exists for this family of lattices. We believe that these results could provide a better understanding of the complexity of the orthogonality decision problem for general lattices

Tech Imaginations

Prof. Dr. Jens Schröter, Christoph Borbach, Max Kanderske und Prof. Dr. Benjamin Beil sind Herausgeber der Reihe. Die Herausgeber*innen der einzelnen Hefte sind renommierte Wissenschaftler*innen aus dem In- und Ausland.Technologies and especially media technologies are pervasive in modern societies. But even more omnipresent are the imaginaries of modern technologies – what technologies are thought to be capable of or what effects they are supposed to have. These imaginations reveal a lot of the political and ideological self-descriptions of societies, hence the (techno-)imaginary also functions as a kind of epistemic tool. Concepts of the imaginary therefore have experienced an increasing attention in cultural theory and the social sciences in recent years. In particular, work from political philosophy, but also approaches from science and technology studies (STS) or communication and media studies are worth mentioning here. The term "techno-imagination", coined by Vilém Flusser in the early 1990s, refers to the close interconnection of (digital) media and imaginations, whose coupling can not only be understood as a driver of future technology via fictional discourses (e.g. science fiction), but much more fundamentally also as a constitutive element of society and sociality itself, as Castoriadis has argued. In the first part of the issue several theoretical contributions add new aspects to the discussion of socio-technical imaginaries, while in the second part a workshop held in January 2022 at the CAIS in Bochum is documented, in which the case of the imaginaries of “Future Internets” was discussed

Provable and Practical Security for Database Outsourcing

In this work, we provide formal notions for different privacy goals of data outsourcing and establish their relations. Furthermore, as a main contribution, we provide a meaningful security notion for database outsourcing and a practical scheme fulfilling this notion as well as implementations that demonstrate the viability. We prove the security of our scheme in a formal model and provide extensions an optimisations for performance as well as for security