Dr. Dobb's Journal - October 2007 - (Page 24)

Core Technology BIT-PLANE COMPLEXITY SEGMENTATION AND VISUAL CRYPTOGRAPHY Figure 1: (a) Secret message; (b) recomposed message; (c) first share; (d) second share. continued from page 22 above a certain threshold can be replaced with embedded data. This technique works on 24-bit true-color or 8-bit grayscale images. It doesn’t work on paletted images; small changes in a pixel value might have drastic effects on the color of the pixel in the paletted image. Kawaguchy and Eason (citeseer.ist.psu .edu/kawaguchi98principle.html) suggest that the bit-planes of natural images display monotonic increasing complexity from the Most Significant Bit-plane (MSB) to the Least Significant Bit-plane (LSB). Most of the LSBs just look like random noise (Figure 2). Following the separation of the image in bit-planes, every bit-plane is decomposed in 8✕8 square regions and the complexity of the regions is calculated. There is no general definition for the complexity of a binary image. Nevertheless, there’s a simple way to calculate the complexity of a region in the bit-plane—just count the number of color changes in every row and column of the region. To define a coherent scale of complexities, you normalize this figure such that one plain color has a complexity of 0 and the checkerboard pattern (the most complex possible region) has a complexity of 1. Any region in any bit-plane with a complexity above a chosen threshold is considered random noise and replaced by 8 bytes of data. Modified BPCS Steganography It is still possible that an embedded block will not have a complexity above the threshold value. In this case, the conjugate of the block must be taken. The conjugate of a binary image is obtained by XORing the image with the checkerboard pattern. Obviously, the original data can be remade by XORing the new image with the checkerboard pattern again. If necessary, the conjugate is calculated,and you need a “flag pixel” to mark the region as “conjugated.” In the decryption process (as in a puzzle), you have to detect any piece of embedded data and put it back in place. To properly identify every square, I mark each with a sequence number. The sequence number is an integer number binary representation. Because the proposed embedding scheme is “blind” (that is, no prior knowledge of the image or other information is needed to extract the embedded message), the additional information consisting of the conjugate flag and sequence number has to be written back into the image, together with the embedding data. 24 Dr. Dobb’s Journal l www.ddj.com l October 2007 http://citeseer.ist.psu.edu/kawaguchi98principle.html http://citeseer.ist.psu.edu/kawaguchi98principle.html http://www.sparxsystems.com http://www.sparxsystems.com http://www.ddj.com

Table of Contents Feed for the Digital Edition of Dr. Dobb's Journal - October 2007

Cover Contents Hmmmm Alia Vox Developer Diaries Developer’s Notebook AI: It’s OK Again! Conversations Visual Cryptography and Bit-Plane Complexity Segmentation Inside the Windows Vista Disk Encryption Algorithm Memory-Aware Components Software and the Core Description Process Logging In C++ Effective Concurrency The Agile Edge Swaine’s Flames

Dr. Dobb's Journal - October 2007

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