This talk was about some extensions of recent results on the complexity of computing Gröbner bases of comaximal determinantal systems and the implications of these results for some multivariate post-quantum cryptography schemes.
This talk was about applications of my work to the analysis of multivariate post-quantum cryptography schemes which rely on the hardness of the MinRank problem.
This paper gives new criteria for the detection and avoidance of reductions to zero when computing Gröbner bases of determinantal ideals of square matrices of polynomials. In the comaximal case and under certain genericity assumptions, all reductions to zero are avoided and a complexity analysis of the resulting algorithm is provided.