Fractal cryptography
There have been some discussions on sci.crypt within the past few months on nonlinear/chaotic algorithms and their use in cryptography. Fractal cryptography sounds like it might be related. The problem is that unless an algorithm was SPECIFICALLY DESIGNED to prevent an intelligent adversary from defeating it, the chances of it being an effective cryptosystem are limited. Just because nonlinear systems produce complex-looking results does not mean that these results are unpredictable given enough data. Now, maybe this particular fractal cryptosystem idea will actually work well. I don't know; I haven't seen it. But the point is that these complex types of systems have not provided a good foundation for crypto- graphy in the past. sci.crypt messages are available on (at least) ripem.msu.edu, in /pub/crypt/sci.crypt. In that directory there is a file "subjects", which lists all the subject lines by message number, as well as a collection of files each of which holds a couple of months' worth of messages. You can grep the subjects file to find those messages which might be i{terested. The archives appear to go back a couple of years. Hal
hfinney@shell.portal.com (Hal Finney) wrote:
There have been some discussions on sci.crypt within the past few months on nonlinear/chaotic algorithms and their use in cryptography. Fractal cryptography sounds like it might be related. The problem is that unless an algorithm was SPECIFICALLY DESIGNED to prevent an intelligent adversary from defeating it, the chances of it being an effective cryptosystem are limited. Just because nonlinear systems produce complex-looking results does not mean that these results are unpredictable given enough data.
Yeah, but how much data? Just because something can be solved given enough data doesn't help me break it if I need 10^37643254 bytes of data to do it.
Now, maybe this particular fractal cryptosystem idea will actually work well. I don't know; I haven't seen it. But the point is that these complex types of systems have not provided a good foundation for crypto- graphy in the past.
Well, here's a little test. The following numbers were generated using a chaotic function: 568139551155097445567935056793172821494566808655678121156334445567812121480659 Do you see a pattern? What function did I use to generate it? :) (Actually, assuming you knew what function I used, you could probably solve for the key if you had enuf raw output from the PRNG, so it's probably not completely impossible to solve the above, but that wouldn't necessarily help you decrypt a file which had been encoded with such a pad, unless you knew a lot about the format of the file.)
Matthew J Ghio says:
hfinney@shell.portal.com (Hal Finney) wrote:
There have been some discussions on sci.crypt within the past few months on nonlinear/chaotic algorithms and their use in cryptography. Fractal cryptography sounds like it might be related. The problem is that unless an algorithm was SPECIFICALLY DESIGNED to prevent an intelligent adversary from defeating it, the chances of it being an effective cryptosystem are limited. Just because nonlinear systems produce complex-looking results does not mean that these results are unpredictable given enough data.
Yeah, but how much data? Just because something can be solved given enough data doesn't help me break it if I need 10^37643254 bytes of data to do it.
Amateurs regularly develop systems and claim fantastic things for them. They then turn out to be trivial to break. This has made people who are even semi-pro like some of the folks on this list shake their heads and say "oh no, not another one" every time someone who hasn't read the literature claims to have come up with "the new great cryptosystem". This is the reason that people tend to be so skeptical of the constant stream of new proposals from such individuals. Its nothing personal -- its just the sort of jaded attitude you get when this sort of thing happens repeatedly. Perry
"Perry E. Metzger" <pmetzger@lehman.com> wrote:
Amateurs regularly develop systems and claim fantastic things for them. They then turn out to be trivial to break. This has made people who are even semi-pro like some of the folks on this list shake their heads and say "oh no, not another one" every time someone who hasn't read the literature claims to have come up with "the new great cryptosystem". This is the reason that people tend to be so skeptical of the constant stream of new proposals from such individuals. Its nothing personal -- its just the sort of jaded attitude you get when this sort of thing happens repeatedly.
This is true. If you were specifically referring to the example I posted, it could probably be broken from the data presented if you really put your mind to it. However it is a fairly clever PRNG, and it takes quite a bit of data to get the exact pattern. It might not be feasible to create a cryptosystem using fractals and chaos functions, but I think the possibility could be explored a bit further...
-----BEGIN PGP SIGNED MESSAGE----- writes Hal Finney:
Now, maybe this particular fractal cryptosystem idea will actually work well. I don't know; I haven't seen it. But the point is that these complex types of systems have not provided a good foundation for crypto- graphy in the past.
(First, sorry for bringing up an old subject, I was at SC93, and now have 500 messages to surf through) I read an article in Electronic Engineering Times a while back (summer, I think), about some researchers doing encryption with chaos... they had two decryption chips (I think they used DSPs) that had a synchronized chaotic stream going between them, which they both used to [en,de]crypt the data... This seems kind of silly, since (assuming an intelligent adversary), they could just tap the chaotic flow, and start listening... Am I missing something? - -nate - -- +-----------------------------------------------------------------------+ | Nate Sammons nate@VIS.ColoState.Edu (303) 491-1578 | | Colorado State University -- Computer Visualization Laboratory | +-----------------------------------------------------------------------+
participants (4)
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hfinney＠shell.portal.com -
Matthew J Ghio -
nate＠VIS.ColoState.EDU -
Perry E. Metzger