Vulnerabilities of “McEliece in the World of Escher”

Abstract. Recently, Gligoroski et al. proposed code-based encryption and sig-nature schemes using list decoding, blockwise triangular private keys, and a nonuniform error pattern based on “generalized error sets. ” The general ap-proach was referred to as McEliece in the World of Escher. This paper demon-strates attacks which are significantly cheaper than the claimed security level of the parameters given by Gligoroski et al. We implemented an attack on the proposed 80-bit parameters which was able to recover private keys for both en-cryption and signatures in approximately 2 hours on a single laptop. We further find that increasing the parameters to avoid our attack will require parameters to grow by almost an order of magnitude for signatures, and (at least) two orders of magnitude for encryption