Described is paper or cardboard packaging produced from mineral oil contaminated, (e.g., recycled) paper, wherein the packaging includes a barrier layer obtainable by applying an aqueous polymer dispersion comprising a copolymer obtainable by emulsion polymerization of C1-C4 alkyl (meth)acrylates, acid monomers, e.g., acrylic acid or methacrylic acid, 0-20 wt % of acrylonitrile and 0 to 10 wt % of further monomers in an aqueous medium in the presence of a carbohydrate compound, preferably in the form of a degraded starch, wherein the glass transition temperature of the copolymer is in the range from +10 to +45° C. The barrier layer may be situated on one of the surfaces of the packaging or form one of multiple layers of a multilayered packaging coating or be situated as a coating on one side of an inner bag situated within the packaging.