Direct solution of the (11, 9, 8)-MinRank problem by the block Wiedemann algorithm in magma with a tesla GPU

@inproceedings{Steel2015DirectSO,
  title={Direct solution of the (11, 9, 8)-MinRank problem by the block Wiedemann algorithm in magma with a tesla GPU},
  author={Allan K. Steel},
  booktitle={PASCO},
  year={2015}
}
We show how some very large multivariate polynomial systems over finite fields can be solved by Gröbner basis techniques coupled with the Block Wiedemann algorithm, thus extending the Wiedemann-based 'Sparse FGLM' approach of Faugère and Mou. The main components of our approach are a dense variant of the Faugère F4 Gröbner basis algorithm and the Block Wiedemann algorithm, which have been implemented within the Magma Computer Algebra System (released in version V2.20 in late 2014). A major… CONTINUE READING
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Spaenlehauer. Computing Loci of Rank Defects of Linear Matrices using Grobner Bases and Applications to Cryptology

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