Tradition reference table based (RTB) methods employ two pixels to conceal a secret digit according to a two-dimensional reference table. In this paper, x-dimensional reference table framework is defined, which can be regarded as generalization of the prior works. The available pixels to be embedded are limited in two-dimensional space, so the proposed methods extend the dimensional space of reference table. Theoretical analyses are given to justify the effectiveness of the proposed construction. Two novel RTB methods named CRT (cubic reference table) and CRT-PVD (cubic reference table and pixel value differencing) are presented. The former is independent of image contents while embedding, and the latter is depended on the discriminated image smoothness. Experimental results show that two proposed methods can achieve better performance compared with the prior works. © 2017, Springer Science+Business Media, LLC.