CROWD

The goal of our project is to study skew metrics and their potential cryptographic applications. These metrics in some sense 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. These parts are connected and a close collaboration will strengthen the research results. (1) A theoretical part dealing with linear codes endowed with skew metrics. These metrics and these codes are intrinsically related to skew polynomial rings or Ore rings. These rings generalise the notion of classical polynomial rings by skewing the multiplication with an endomorphism and introducing a derivation operator. In this project, we aim at studying new metrics and evaluation codes derived from these rings. We will investigate combinatorial bounds and search for the existence of optimal codes regarding those bounds. (2) An algorithmic part dedicated to the search for 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 error-correcting codes, searching for new decoding algorithms as well as their analysis for the design of new efficient and secure encryption and signature schemes from these codes. We will also study the security against classical algorithmic attacks as well as attacks related to the use of hints obtained by side-channel analysis (see (3)) or faults on implementations, that we will realise. (3) A part on implementation of rank-metric based encryption schemes. The goal is to study their practical security including side-channel and fault attacks. As an input we will take in particular outputs from (2) as well as rank-metric based proposals which were submitted to the NIST standardisation process for post-quantum cryptography, or other signature schemes who could be candidates to the reopening process. The study of leaks and the impact of faults on specific implementations will feed (2) concerning the search for fault-tolerant and side-channel proof implementations. One of the main characteristics of this project is its large interdisciplinarity. It regroups French and German researchers coming from various fields from algebraic coding theory to algorithmics and implementation. It aims at developing strong links and future collaborations between these teams with a common objective to improve knowledge in the field of post-quantum cryptography based on skew codes and skew metrics, with practical implications. If the time schedule is coherent, one of our goal would be to participate to at least to the submission of a rank metric based cryptographic scheme.