Let <img src=image/13427481_01.gif> be a simple, finite, connected, plane graph with the vertex set <img src=image/13427481_02.gif>, the edge set <img src=image/13427481_03.gif> and the face set <img src=image/13427481_04.gif>). Martin Baca [1] defined, a connected plane graph <img src=image/13427481_01.gif> with vertex set <img src=image/13427481_02.gif>, edge set <img src=image/13427481_03.gif> and face set <img src=image/13427481_04.gif> to be <img src=image/13427481_05.gif> face antimagic if there exists positive integers <img src=image/13427481_06.gif> and <img src=image/13427481_07.gif> and a bijection <img src=image/13427481_08.gif>: <img src=image/13427481_09.gif> such that the induced mapping <img src=image/13427481_10.gif>: <img src=image/13427481_11.gif>, where for a face <img src=image/13427481_12.gif>, <img src=image/13427481_13.gif> is the sum of all <img src=image/13427481_14.gif> for all edges <img src=image/13427481_15.gif> surrounding <img src=image/13427481_12.gif> is also a bijection. This paper proves the existence of face antimagic labeling for the double duplication of all vertices by edges of gear graph <img src=image/13427481_16.gif> for <img src=image/13427481_17.gif>, grid graph <img src=image/13427481_18.gif> for <img src=image/13427481_19.gif>, where <img src=image/13427481_20.gif> even, prism graph <img src=image/13427481_21.gif> for <img src=image/13427481_22.gif> and the double duplication of all vertices by edges of strong face of triangular snake graph <img src=image/13427481_23.gif> for <img src=image/13427481_17.gif>. The <img src=image/13427481_05.gif> face antimagic labeling for double duplication of special graphs can be used to encrypt and decrypt the messages, which is used as a real time application. In [3], we used <img src=image/13427481_05.gif> face antimagic labeling of strong face of duplication of all vertices by edges of a tree <img src=image/13427481_23.gif> for <img src=image/13427481_24.gif> to encrypt and decrypt thirteen secret numbers which can be extended to double duplication of graphs to encode and decode the numbers, which in turn can be used in military base, ATM and so on.