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This article discusses the security of McEliece-like encryption schemes usingsubspace subcodes of Reed-Solomon codes, i.e. subcodes of Reed-Solomon codesover $\mathbb{F}_{q^m}$ whose entries lie in a fixed collection of$\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}$. These codes appear to be anatural generalisation of Goppa and alternant codes and provide a broaderflexibility in designing code based encryption schemes. For the securityanalysis, we introduce a new operation on codes called the twisted productwhich yields a polynomial time distinguisher on such subspace subcodes as soonas the chosen $\mathbb{F}_q$-subspaces have dimension larger than $m/2$. Fromthis distinguisher, we build an efficient attack which in particular breakssome parameters of a recent proposal due to Khathuria, Rosenthal and Weger.

On the security of subspace subcodes of Reed-Solomon codes for public key encryption