2018/05/22 by Tohaneanu, Stefan O., Vargas, Jesus
#05A05 (Primary) 94A60 #11T71 (Secondary) #94B05 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1805.08343
Given two k× n matrices A and B, we describe a couple of methods to solve the matrix equation XA=BY, where X is an invertible k× k matrix, and Y is an n× n permutation matrix, both of which we want to determine. We are interested in pursuing those techniques that have algebraic geometric flavor. An application to solving such a matrix equation comes from the cryptanalysis of McEliece cryptosystem. By using codewords of minimum weight of a linear code, in concordance with these methods of solving XA=BY, we present an efficient way to determine the entire encryption keys for the McEliece cryptosystems built on Reed-Solomon codes.