On Wed, 19 Jul 1995, Timothy C. May wrote:
At 7:57 AM 7/19/95, Douglas B. Renner wrote: [snip]
I'd conjecture that it's possible. Imagine fractal compression of a text file, with the decompression routine adding some "randomness" which would be your message, obscured at a very abstract level. Depending on how much "randomness" was added, I'm wondering if the resulting text might possibly retain some of its original legibility (?) ... [snip] (I am looking at an ad for a graphics program, "Images Incorporated" by Iterated Systems which with fractal techniques can achieve 100:1 compression -- and then -- decompress to 8 times the original bitmap size with minimal added distortion.)
But fractal compression schemes are usually _lossy_, that is, some of the original bits are irretrievably lost. (This should be clear also from the amount of compression achieved....multiple files/images compress to the "same" smaller file--by the "pigeonhold principle.")
Lossy compression is often OK for visual images and audible files, a la music, but would be pretty bad for any scheme dependent on encryption.
Yes; however It's not so much the compression ratio I was concerned with other than that it demonstrates the level of abstraction achieved in the analysis. For crypto we wouldn't really mind if the intermediate fractal file were actually larger than the original and I assume that these techniques can be lossless if we are willing to accept this tradeoff. What I think is remarkable about the example of compression and enlargement is that with the process of enlargement, image *detail* is added in a manner consistent with the original. (!!!) By altering the decompression with a hidden message one would of course be, replacing or adding information, and if the goal were to have this new information "blend in" with its container, then perhaps we could learn from fractal compression. Doug