Paper 2016/302

A Polynomial-Time Attack on the BBCRS Scheme

Alain Couvreur, Ayoub Otmani, Jean-Pierre Tillich, and Valérie Gauthier-Umana


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&#10878;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&#8730;) where R denotes the code rate. This attack has complexity O(n6) and breaks all the parameters suggested in the literature.

Available format(s)
Public-key cryptography
Publication info
Published by the IACR.Major revision. IACR-PKC--1
cryptanalysiscode-based cryptographyMcEliecedistinguisherfiltration attack
Contact author(s)
alain couvreur @ lix polytechnique fr
2016-03-17: received
Short URL
Creative Commons Attribution


      author = {Alain Couvreur and Ayoub Otmani and Jean-Pierre Tillich and Valérie Gauthier-Umana},
      title = {A Polynomial-Time Attack on the BBCRS Scheme},
      howpublished = {Cryptology ePrint Archive, Paper 2016/302},
      year = {2016},
      note = {\url{}},
      url = {}
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