Current State of the Art of the General Rank Decoding Problem

This talk gives an overview of the latest results in the general rank decoding problem. The main question is, how efficiently one can decode a given rank-metric code, without any known algebraic structure, from a random error. Answers to this question are of high interest, in particular in code-based cryptography, where rank-metric codes have extensively been studied to be used in a McEliece-type public key cryptosystem. During the last 5 years several algorithms have been proposed to solve (or at least improve) this problem – some deterministic, some probabilistic. We will introduce these algorithms, show the corresponding computational complexities, and state some open problems in this regard.