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.
