On the Security of Subspace Subcodes of Reed–Solomon Codes for Public Key Encryption

This article discusses the security of McEliece-like encryption schemes using subspace subcodes Reed–Solomon codes, i.e. codes over ${\mathbb {F}_{q^{m}}}$ whose entries lie in a fixed collection {F}_{q}}$ –subspaces . These appear to be natural generalisation Goppa and alternant provide broader flexibility designing code based schemes. For analysis, we introduce new operation on called xmlns:xlink="http://www.w3.org/1999/xlink">twisted product which yields polynomial time distinguisher such as soon chosen have dimension larger than notation="LaTeX">$m/2$ From this distinguisher, build an efficient attack particular breaks some parameters recent proposal due Khathuria, Rosenthal Weger.