We give a witness-finding cryptanalysis of Stickel-type key exchange schemes, which involve two-sided multiplication of n×nn \times n matrices over Fp\mathbb{F}_p, where these matrices are drawn from public subspaces with a particular commuting structure. This analysis covers Stickel's original proposal, Shpilrain's polynomial extension of that scheme, Nager's algebraic extension of that scheme, and more generally all Stickel-type approaches using public subspaces over matrix algebra in finit