Abstract. The BBCRS scheme is a variant of the McEliece public-key encryption scheme where the hiding phase is performed by taking the inverse of a matrix which is of the form T +R where T is a sparse matrix with average row/column weight equal to a very small quantity m, usually m < 2, and R is a matrix of small rank z 1. The rationale of this new transformation is the reintroduction of families of codes, like generalized Reed-Solomon codes, that are famously known for representing insecure choices. We present a key-recovery attack when z = 1 and m is chosen between 1 and 1 + R + O() where R denotes the code rate. This attack has complexity O(n 6 ) and breaks all the parameters suggested in the literature.

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