Section: New Results

Linear Time Interactive Certificates for the Minimal Polynomial and the Determinant of a Sparse Matrix

Participant : Emmanuel Thomé [contact] .

Following discussion with Jean-Guillaume Dumas which began in March 2015 on the topic of computing checkpoints for the krylov step of the block Wiedemann algorithm, we determined that a scheme very similar to this checkpointing technique (originally designed to spot data corruption errors) was able to provide a proving algorithm —in the cryptographic sense— for the computation of the minimal polynomial of a sparse matrix, or for its determinant. This led to a joint paper with Jean-Guillaume Dumas, Erich Kaltofen and Gilles Villard, published at ISSAC 2016 [8].