Distributed and secure linear algebra -- Master Thesis

TL;DR

This thesis explores adapting secure linear algebra protocols for matrices with polynomial coefficients and analyzes their computational complexities in networked cryptographic settings.

Contribution

It introduces adaptations of existing protocols for polynomial coefficient matrices and provides a comprehensive complexity analysis.

Findings

Protocols successfully adapted for polynomial matrices

Complexity analysis of the adapted protocols completed

Framework established for secure polynomial matrix algebra

Abstract

Cryptography is the discipline that allows securing of the exchange of information. In this internship, we will focus on a certain branch of this discipline, secure computation in a network. The main goal of this internship, illustrated in this report, is to adapt a roster of protocols intended to do linear algebra. We want to adapt them to do algebra for matrices with polynomial coefficients. We then wish to make a complete analysis of the different complexities of these protocols.