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Unformatted text preview: Massachusetts Institute of Technology Handout 19 6.857: Network and Computer Security November 13, 2003 Professor Ronald L. Rivest Problem Set 5 Solutions Problem 5-1. Watermarking Problem 5-1 was not supposed to be a dicult problem. Nevertheless, most of the groups did not do well on it. Your TAs were generally dissappointed by the lack of critical thinking that was evidenced on this problem. Many groups gave estimates for the items in part (a) that were nothing more than wild guesses. Many groups suggested approaches in part (b) which had been specifically discussed in class as being technically poor. Grading: Part (a) was worth 5 points. Our plan was to remove one point for each significant technical error, sloppiness, and other problems. But some groups made so many errors that we couldnt hold them to this, otherwise they would have received no credit at all. Common errors that were seen in part (a) include: Watermarking Shakespeare with Spaces. Many students didnt bother to survey Shakespeares plays to find out how many lines there actually are! Some students assumed that the average line length was 80 characters (it isnt) and calculated the number of lines by dividing the size of the play by 80. Other groups guessed wildly. One group Googled for a reference which they then misinterperted they were off by two orders of magnitude. In fact, depending on the play and how it is formatted, there are between 2000 and 5000 lines in the typical play. You could determine this by using the Unix wc command or the Word Count feature built in to Microsoft Word (which also reports lines). Watermarking photos by adding 1 to pixel values. Many groups erroneously asserted that the mark is detectable, because adding 1 to a pixel with a 255 value would cause the pixel to wrap to 0. But this can easily be avoided because you have the original, you can decrease the color value to 254 in this special case (this is what we did in Problem 5-3). In any case, the watermark is easily removed: use a lossy compression scheme (like JPEG) to smooth out these small jumps, or re-encode the picture with a slightly smaller color palette. Either way, the picture will retain almost all of its quality, but the mark will disappear. Watermarking movies by dropping frames. There were wildly divergent opinions as to how many continious shots are in a typical movie. One group actually watched the first 10 minutes of The Matrix Reloaded and counted. Another group correctly noted that different directors would have different averages. Most other groups just guessed. Many groups asserted that this watermark could not be removed. In fact, it could be removed by randomly dropping 1 or 2 frames at the beginning and end of every sequence. This would slightly affect the quality of the film (the sound would have to be dropped too), but it wouldnt be terrible....
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- Spring '03
- Computer Security