Based on the rings of integers modulo k, Chen-Pan-Tseng (2000) has given a block-based scheme (CPT scheme) which permits in each block F of size m x n of a given binary image B to embed r =log2(q+1) secret bits by changing at most two entries of F, q=m.n. In this paper, the authors propose two new hiding schemes 1-M3 and 2-M3 based on modules over rings of characteristic 3, which can be applied for binary and color images with high hiding ratios. From 1-M3 scheme, and can embed 3 secrete bits in each block F of 8 pixels of any binary image by changing at most 2 pixels of F or in each block of 4 pixels of any color image by changing at most 1 pixel. From 2-M3, can embed 6= log2 of 81 secrete bits in each block F of 8 pixels by changing at most 2 pixel of F. The changing in color images was carried out only on 2 bits LSB so the schemes will have high quality hiding images.