Multiple-encoding retrieval for optical security John Fredy Barrera a , Rodrigo Henao a , Myrian Tebaldi b, * , Roberto Torroba b , Ne ´stor Bolognini c a Grupo de O ´ ptica y Fotonica, Instituto de Fı ´sica, Universidad de Antioquia, Medellin, Colombia b Centro de Investigaciones O ´ pticas (CONICET-CIC) and UID OPTIMO, Facultad Ingenierı ´a, Universidad Nacional de La Plata, P.O. Box 124, La Plata (1900), Argentina c Centro de Investigaciones O ´ pticas (CONICET-CIC), Facultad Ingenierı ´a and Ciencias Exactas, Universidad Nacional de La Plata, La Plata, Argentina Received 25 April 2007; accepted 25 April 2007 Abstract We propose a method for image encryption by multiple-step random phase encoding with an undercover multiplexing operation. The true image is stored in a multiple record we call encodegram; and then we can reconstruct it by the use of the appropriate random phase masks and a retrieval protocol. To increase the security of the true hidden image and confuse unauthorized receivers, we add to the encodegram an encoded fake image with different content. This fake image has only a small effect on the retrieval of the true hidden image, owing to the specific property of this protocol. In the decryption step, we can reveal the true image by applying the inverse protocol to two cyphertexts, one the encodegram containing the true image along with the fake image; and the other helping to get the random phase key to achieve the true image. Computer simulations verify the validity of this method for image encryption. Digital implementation of the method makes it particularly suitable for the remote transmission of information. Ó 2007 Elsevier B.V. All rights reserved. PACS: 42.30.d; 42.30.Va 1. Introduction The problem of unauthorized use and distribution of information has become increasingly more serious owing to the rapid development of modern communication tech- niques, because digital information such as image data delivered through the Internet can be easily hacked. Opti- cal encryption is a mean of providing confidentiality to a communication channel. Some data encryption methods use double random phase encoding [1,2], digital holography [3,4], multiplexing [5,6], virtual digital optics [7], and computer generated holograms [8]. At the same time, a related approach, infor- mation validation, has also been suggested [9–11]. Informa- tion encryption and validation are similar in both their principles and functions in terms of hiding and protecting messages from unauthorized distribution, except that, in the latter, as the original meaning of validation suggests, the content publicly delivered contains a hiding image that once recognized authenticates the message. There are some common criteria for evaluating the effec- tiveness of these methods in practice. The key functions should be difficult to find by chance, the images delivered openly should be intensity patterns for use in Internet com- munication, and decryption should be relatively easy for receivers with the keys. Much attention was paid to the first requirement in the methods reported so far. However, doubts were cast on the security optical tech- niques may offer, specifically on the double random phase encoding method [12,13]. A key decryption algorithm can be applied either to the encryption machine (the most 0030-4018/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.04.040 * Corresponding author. Tel.: +54 221 4840280; fax: +54 221 4712771. E-mail address: myrianc@ciop.unlp.edu.ar (M. Tebaldi). www.elsevier.com/locate/optcom Optics Communications 276 (2007) 231–236