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Title:
A Polynomial-Time Attack on the BBCRS Scheme
Authors: Alain Couvreur, Ayoub Otmani, Jean-Pierre Tillich, Valérie Gauthier-Umana
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(1n√) where R denotes the code rate. This attack has complexity O(n6) and breaks all the parameters suggested in the literature.
ePrint: https://eprint.iacr.org/2016/302
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