This invention discloses new methods and security devices for authenticating documents and valuable products which may be applied to any support, including transparent synthetic materials and traditional opaque materials such as paper. The invention relates to parallax moire shapes which occur in a compound layer consisting of the superposition of specially designed and possibly geometrically transformed s-random base layer and s-random revealing layer with a small gap between them. The base and revealing layers are formed respectively by base layer element shapes and revealing layer sampling elements positioned at s-random locations, where the base layer locations and the revealing layer locations are strongly correlated. When tilting the compound layer or changing the viewing angle, a parallax moire intensity profile of a chosen shape is seen moving in the superposition, thereby allowing the authentication of the document. A major advantage of the present invention is in its intrinsically incorporated encryption system due to the arbitrary choice of the s-random number sequences used for defining the positions of the specially designed base layer element shapes and revealing layer sampling elements that are used in this invention.