892 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 14, NO. 6, JUNE 2004 Image Scrambling Without Bandwidth Expansion Dimitri Van De Ville, Member, IEEE, Wilfried Philips, Member, IEEE, Rik Van de Walle, Member, IEEE, and Ignace Lemahieu, Senior Member, IEEE Abstract—Image-scrambling schemes are designed to render the image content unintelligible. Wyner has proposed an elegant one-dimensional (1-D) scrambling scheme without bandwidth ex- pansion, making use of the discrete prolate spheroidal sequences (DPSS). The DPSS are optimal regarding their energy concentra- tion in a given frequency subband. In this paper, we propose the two-dimensional (2-D) extension and application of this algorithm. We discuss new possibilities introduced by the 2-D approach. We also include experimental results. Index Terms—Conditional access, content protection, discrete prolate spheroidal sequences (DPSS), Hadamard matrix, image scrambling, orthogonal transforms. I. INTRODUCTION S ECURITY of image and video data becomes increasingly important for many applications, e.g., pay-TV, confidential transmission of video conferencing, video surveillance, secure facsimile, medical, and military applications. Two main groups of technologies have been developed for this purpose. The first one is content protection through encryption. Proper decryption of the data requires a key [1]–[4]. The second one is digital wa- termarking, which aims at embedding a message into the multi- media data [5]–[8]. These two technologies could be used com- plementary to each other. This paper will focus on the first type of technique. A scrambling scheme, which renders content unintelligible, can be part of a secure multimedia system [9]. In particular, an image-scrambling scheme transforms an image into another unintelligible image, based on keys only known to the senders and the receivers. Initially, video scrambling schemes were fairly simple because they needed to be implemented in analog electronics. The advent of fast and affordable VLSI electronics made it possible to store images into a frame buffer and perform (de)scrambling operations digitally. The early digital scrambling techniques include methods such as line reversal, line dispersal, and line segment swapping. A commercially deployed algorithm permutes lines [10]. These simple tech- niques are prone to “correlation attacks;” i.e., the correlation Manuscript received May 2, 2001; revised February 20, 2003. This work was supported in part by the Fund for Scientific Research (FWO), Flanders, Bel- gium, through a mandate of Research Assistant D. Van De Ville. This paper was recommended by Associate Editor C.-W. Chen. D. Van De Ville is with the Biomedical Imaging Group, Swiss Federal Insti- tute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland (e-mail: dimitri.vandeville@epfl.ch). W. Philips is with the Department for Telecommunication and Information Processing (TELIN), Ghent University, B-9000 Ghent, Belgium (e-mail: wil- fried.philips@ugent.be). R. Van de Walle and I. Lemahieu are with the Department of Electronics and Information Systems, B-9000 Ghent, Belgium (e-mail: rik.vande- walle@ugent.be; ignace.lemahieu@ugent.be). Digital Object Identifier 10.1109/TCSVT.2004.828325 properties available in typical images could be employed to restore the image [11]. Matias et al. [12] presented a more advanced way to reorder the pixel data: they change the scan order according to a space-filling curve. Essentially, all these techniques change the scan order of the images. Another possibility is to scramble the image in a transformed domain. Zeng et al. [13] presented a technique to scramble an MPEG video sequence in the DCT domain. Their main concern is to have a minimum impact on the compression efficiency after scrambling DCT coefficients. Digital encryption could also be applied after (MPEG) compression, resulting in high security. Wyner presented an interesting technique designed for speech scrambling [14], [15]. Making use of an optimal set of basis functions, he proposed a scrambling scheme based on an or- thonormal linear transform which results in a negligible ex- pansion of bandwidth. In this paper, we extend the transform to two-dimensional (2-D), which makes it suitable for image scrambling. This opens up a new class of image-scrambling schemes. We also show that the 2-D scrambling scheme offers a wider scrambling potential compared to the one-dimensional (1-D) scheme. The scrambling operation itself needs a key. We will only briefly engage into the key management—the selec- tion and the update of this key—using Hadamard matrices. The paper is organized as follows. In Section II, we briefly review the original 1-D scrambling method presented by Wyner [14]. Next, in Section III, we show the 2-D extension and apply it to image scrambling. Next, we add a note on the encryption; i.e., the selection of the key. In Section V we present some ex- perimental results of the scrambling method, followed by a dis- cussion in Section VI. II. BRIEF REVIEW OF THE 1-D SCRAMBLING PROBLEM Consider a discrete sequence of real numbers . The Fourier transform or spectrum of equals (1) Note that the spectrum is periodic with period 1, and we will consider it only for . The inner product of two sequences and is defined by (2) and the -norm of is . All sequences that we consider are part of the vector space of square-summable sequences. The sequence is said band-limited to , if the spectrum , for . We 1051-8215/04$20.00 © 2004 IEEE