On Sat, Jan 09, 2010 at 11:52:40PM +0100, Frank A. Stevenson wrote:
> On Sat, 2010-01-09 at 23:39 +0100, sascha wrote:
> > Another question is whether it is possible to convert an illegal state
> > that produces the correct keystream to a legal state
> > that produces the same keystream. When i generated some chains with
> > a simple increment function generating the start values i got 92% chain
> > merges in a 10M chains table which suggests that those states that
> > produce the same keystream are only a few bit flips apart.
> 
> I am not sure if a simple bit flip will do it, but perhaps it is
> possible by applying  single or few clockings of some direction to some
> of the LFSRs, so you get a "legal" state, but yet produce the same
> output.

Maybe clock the illegal state forward N ticks and check each of the ancestors
less than N + 5 clocks away from that new forward state whether there is
one that produces the same keystream. If i am correct and the 2 compatible
states are "close together" then they could very well be found that way.

> 
> Unfortunately when I found my false positives, I had thrown away the
> original keys, and had no basis to compare the false positive with the
> correct state. We should keep this in mind when we start testing the
> lookup code at a bigger scale: to keep the correct keys for reference
> and helping us understand better what the situation is with the false
> positives.
> 
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