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A polynomial-time attack on the BBCRS scheme

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Couvreur, Alain
Otmani, Ayoub
Tillich, Jean-Pierre
Gauthier-Umaña, Valérie

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2015

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Springer Verlag

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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 and lt; 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 representin insecure choices. We present a key-recovery attack when z = 1 and m is chosen between 1 and 1+R+O(1/?n) where R denotes the code rate. This attack has complexity O(n6) and breaks all the parameters suggested in the literature. © International Association for Cryptologic Research 2015.
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Codes (symbols) , Cryptography , Matrix algebra , Polynomial approximation , Reed-Solomon codes , Code-based cryptography , Component wise , Distinguishers , Generalized reed-solomon codes , Key recovery , Public key cryptography , Code-based cryptography , Component-wise product of codes , Distinguisher , Generalized Reed-Solomon codes , Key-recovery
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