Security assessment of the LG cryptosystem

The LG cryptosystem is a public-key encryption scheme in the rank metric using the recent family of \(\mathbf{\mathrm {\lambda }}-\) $\lambda -$ Gabidulin codes and introduced in 2019 by Lau and Tan. In this paper, we present a cryptanalysis showing that the security of several parameters of the scheme have been overestimated. We also show the existence of some weak keys allowing an attacker to find in polynomial time an alternative private key.