Cryptography with Skew Codes

• Applicants: Professorin Dr. Juliane Krämer; Professorin Dr.-Ing. Antonia Wachter-Zeh
• Subject Area: Security and Dependability, Operating-, Communication- and Distributed Systems ; Communication Technology and Networks, High-Frequency Technology and Photonic Systems, Signal Processing and Machine Learning for Information Technology
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 505500359

The goal of our project is to study skew metrics and their potential cryptographic applications. These metrics generalise the so-called rank metric which has important applications in the fields of algebraic coding theory, in cryptography, data storage, and network coding. The common ground of these metrics is the property of non-commutativity of Euclidean rings called Ore rings, extending the classical notion of commutative polynomial rings by skewing the multiplication with an endomorphism and/or a derivation operator. These operations enrich considerably the possibilities for designing new metrics and new codes endowed with efficient arithmetical operations. This is promising for efficient and secure concepts and implementations in cryptography. The project consists of three complementary parts which are strongly connected and will be realized in a close collaboration of the research groups.(1) A theoretical part dealing with linear codes endowed with skew metrics. In this project, we aim at studying new metrics as well as evaluation codes using, e.g., tools such as Gröbner bases. We will investigate combinatorial bounds and search for the existence of optimal codes regarding these bounds. (2) An algorithmic part dedicated to efficient decoding algorithms and the analysis of the security of cryptographic primitives based on codes endowed with skew metrics. This part implies the design of new decoding algorithms, as well as a thorough analysis of the new codes from (1) for the design of new efficient and secure encryption and signature schemes. We will study the security of the schemes against classical algorithmic attacks as well as attacks related to the use of hints obtained by side-channel analysis or faults on implementations.(3) A part on the implementation of rank-metric based encryption schemes. The goal is to study their practical security including side-channel and fault attacks. The considered systems will be in particular outputs from (2) as well as rank-metric based proposals which were submitted to the NIST standardisation process for post-quantum cryptography and promising signature schemes. The study of leaks and the impact of faults on specific implementations will in turn be fed back to (2) in order to obtain fault-tolerant and side-channel-resilient implementations. One of the main characteristics of this project is its large interdisciplinarity. It incorporates French and German researchers with a strong complementary interdisciplinary expertise from mathematical coding theory to algorithmics and hardware implementations. The project will develop strong links and future collaborations between these teams with the common objective to develop post-quantum cryptography based on skew codes and skew metrics.One goal of this proposal is to participate with at least to the submission of a rank-metric based cryptographic signature scheme in the planned NIST post-quantum secure signature competition.

• DFG Programme: Research Grants
• International Connection: France
• Partner Organisation: Agence Nationale de la Recherche / The French National Research Agency
• Cooperation Partners: Professorin Dr. Delphine Boucher; Professorin Dr. Annelie Heuser; Professor Dr. Pierre Loidreau; Professor Dr. Felix Ulmer