© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-Non Commercial-ShareAlike Licence. We study two-color lattice QCD with massless staggered fermions in the strong coupling limit using a new and efficient cluster algorithm. We focus on the phase diagram of the model as a function of temperature T and baryon chemical potential mby working on Lt × Ld lattices in both d = 2, 3. In d = 3 we find that at m = 0 the ground state of the system breaks the global U(2) symmetry present in the model to U(1), while the finite temperature phase transition (with Lt = 4) which restores the symmetry is a weak first order transition. In d = 2 we find evidence for a novel phase transition similar to the Berezinky-Kosterlitz-Thouless phenomena. On the other hand the quantum (T = 0) phase transition to a symmetric phase as a function of mis second order in both d = 2, 3 and belongs to the mean field universality class.