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Cryptanalysis of McEliece cryptosystems based on Generalised Reed–Solomon codes

The McEliece encryption scheme based on binary Goppa codes was one of the first public-key encryption schemes  [24] . Niederreiter [25] dramatically reduced the (huge) key size—a major problem with McEliece's original proposal—using Generalised Reed–Solomon (GRS) codes, but his modified scheme was broken by Sidelnikov and Shestakov [26] in 1992. There have been several attempts at repairing these smaller-key McEliece schemes. In collaboration with P. Gaborit, V. Gautier, A. Otmani and J.-P. Tillich, Alain Couvreur found polynomial time attacks on these schemes using the distinguishability of GRS codes from random codes.