Search results for PreparataSarwate Algorithm

Jules Maire, Damien VergnaudPublished 20240409 Show abstract PDF
We present new secure multiparty computation protocols for linear algebra over a finite field, which improve the stateoftheart in terms of security. We look at the case of unconditional security with perfect correctness, i.e., informationtheoretic security without errors. We notably propose an expected constantround protocol for solving systems of m linear equations in n variables over Fq with expected complexity O(k n^2.5 + k m) (where complexity is measured in terms of the number of secure multiplications required) with k > m(m+n)+1. The previous proposals were not errorfree: known protocols can indeed fail and thus reveal information with probability Omega(poly(m)/q). Our protocols are simple and rely on existing computeralgebra techniques, notably the PreparataSarwate algorithm, a simple but poorly known “babystep giantstep” method for computing the characteristic polynomial of a matrix, and techniques due to Mulmuley for errorfree linear algebra in positive characteristic.