Efficient multiplication of a vector by a matrix MDS
DOI:
https://doi.org/10.54654/isj.v3i17.888Keywords:
MDS matrices, multiplication of polynomialsTóm tắt
Abstract— An algorithm is proposed for the efficient multiplication of a vector by an n x n MDS matrix defined on Fq or by its inverse. The algorithm is based on the multiplication of two polynomials modulo a polynomial of degree n Reed-Solomon code generator and has complexity O(nlog2log2(nlog2q)).
The algorithm only needs to store n values of the Fq field for the multiplication of a vector by an n x n MDS matrix and 2n values for the multiplication of the vector by the inverse matrix.
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