This invention discloses new methods, security devices and apparatuses for authenticating documents and valuable articles which may be applied to any support, including transparent synthetic materials and traditional opaque materials such as paper. The invention relates to moire intensity profiles which occur in the superposition of specially designed random structures. By using specially designed random basic screen and random master screen, where at least the basic screen is comprised in the document, a moire intensity profile of a chosen shape becomes visible in their superposition, thereby allowing the authentication of the document. An important advantage of the present invention is that it can be incorporated into the standard document printing process, so that it offers high security at the same cost as standard state of the art document production. Another major advantage of the present invention is in its intrinsically incorporated encryption system due to the arbitrary choice of the random number sequences for the generation of the specially designed random dot screens that are used in this invention.