Visual cryptography schemes (VCSs) generate random and meaningless shares to share and protect secret images. Conventional VCSs suffer from a transmission risk problem because the noise-like shares will raise the suspicion of attackers and the attackers might intercept the transmission. Previous research has involved in hiding shared content in halftone shares to reduce these risks, but this method exacerbates the pixel expansion problem and visual quality degradation problem for recovered images. In this paper, a binocular VCS (BVCS), called the (2,n)-BVCS, and an encryption algorithm are proposed to hide the shared pixels in the single image random dot stereograms (SIRDSs). Because the SIRDSs have the same 2D appearance as the conventional shares of a VCS, this paper tries to use SIRDSs as cover images of the shares of VCSs to reduce the transmission risk of the shares. The encryption algorithm alters the random dots in the SIRDSs according to the construction rule of the (2,n)-BVCS to produce nonpixel-expansion shares of the BVCS. Altering the dots in a SIRDS will degrade the visual quality of the reconstructed 3D objects. Hence, we propose an optimization model that is based on the visual quality requirement of SIRDSs to develop construction rules for a (2,n)-BVCS that maximize the contrast of the recovered image in the BVCS.