Biography. Alex received a Ph.D. in Mathematics from Eindhoven University of Technology in the Netherlands. His research interests include cryptography, coding theory, algebraic geometry, and number theory.
Abstract. We explore new algebraic reductions of the Syndrome Decoding Problem (SDP) with bounded and exact weight to systems of quadratic equations. Over F2, we improve on a previous work and study the degree of regularity of the modeling of the exact weight SDP. Additionally, we introduce a novel technique that transforms SDP instances over Fq into systems of polynomial equations and thoroughly investigate the dimension of their varieties. We provide experimental results to evaluate the complexity of solving SDP instances using our models through Gröbner bases techniques.