Fraunhofer Institute for Industrial Engineering

In cryptography, techniques and tools developed in the subfield of linear cryptanalysis have previously successfully been used to allow attackers to break many sophisticated cryptographic ciphers. Since these linear cryptanalytic techniques require exploitable linear approximations to relate the input and output of vectorial Boolean functions, e.g., the plaintext, ciphertext, and key of the cryptographic function, finding these approximations is essential. For this purpose, the Correlation Extraction Algorithm (CEA), which leverages the emerging field of quantum computing, appears promising. However, there has been no comprehensive analysis of the CEA regarding finding an exploitable linear approximation for linear cryptanalysis. In this paper, we conduct a thorough theoretical analysis of the CEA. We aim to investigate its potential in finding a linear approximation with prescribed statistical characteristics. To support our theoretical work, we also present the results of a small empirical study based on a computer simulation. The analysis in this paper shows that an approach that uses the CEA to find exploitable linear approximations has an asymptotic advantage, reducing a linear factor to a logarithmic one in terms of time complexity, and an exponential advantage in terms of space complexity compared to a classical approach that uses the fast Walsh transform. Furthermore, we show that in specific scenarios, CEA can exponentially reduce the search space for exploitable linear approximations in terms of the number of input bits of the cipher. Neglecting the unresolved issue of efficiently checking the property of linear approximations measured by the CEA, our results indicate that the CEA can support the linear cryptanalysis of vectorial Boolean functions with relatively few (e.g., n≤32) output bits.

This article describes advancements in the ongoing digital transformation in materials science and engineering. It is driven by domain‐specific successes and the development of specialized digital data spaces. There is an evident and increasing need for standardization across various subdomains to support science data exchange across entities. The MaterialDigital Initiative, funded by the German Federal Ministry of Education and Research, takes on a key role in this context, fostering collaborative efforts to establish a unified materials data space. The implementation of digital workflows and Semantic Web technologies, such as ontologies and knowledge graphs, facilitates the semantic integration of heterogeneous data and tools at multiple scales. Central to this effort is the prototyping of a knowledge graph that employs application ontologies tailored to specific data domains, thereby enhancing semantic interoperability. The collaborative approach of the Initiative's community provides significant support infrastructure for understanding and implementing standardized data structures, enhancing the efficiency of data‐driven processes in materials development and discovery. Insights and methodologies developed via the MaterialDigital Initiative emphasize the transformative potential of ontology‐based approaches in materials science, paving the way toward simplified integration into a unified, consolidated data space of high value.