A Code-Based Cryptosystem using GRS codes
Talk by Prof. Dr. Violetta Weger
Date: 07.12.16 Time: 16.00 - 17.00 Room: Y27H12
Code-based cryptography is a promising candidate for post-quantum cryptography. The original McEliece system using Goppa codes is not used in practice, due to his large key sizes. A solution towards this problem is to use another family of codes, like GRS codes. We present a variant of the McEliece system, proposed by Rosenthal et al. using GRS codes as secret code and a row weight two matrix instead of a permutation matrix. This variant is a special case of the BBCRS scheme, where they use instead of a permutation matrix, the sum T + R, where T is a sparse matrix of row weight m and R is a matrix of rank z. This alternative scrambling is meant to hide the algebraic structure of the secret code. Couvreur et al. presented for some parameters a distinguisher attack on the BBCRS scheme, using that the public code of the BBCRS scheme has a low square code dimension. This reveals a large subcode of the public code, which has as square code a GRS code. The main task of this master thesis was to show security of the new proposal against this distinguisher attack. We will give a lower bound for the probability that a random row weight two matrix satisfies, that the public matrix is of maximal square code dimension.