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> The way it works is the key is split into M parts in such a way that
> so long as you have N of the parts it can be reconstructed.
The key is not split. Calling it a "split key" is a misnomer at best,
and is a further example of how PGP.com deliberately uses the wrong
terminology.
> The reconstructed key is the original key and is used as normal.
The key is derived, not reconstructed.
>; The system is a LITTLE <g> more complex than this but basically works
>; the same way (ie: The data is distributed in such a way that each
> piece occurs at least once so long as you have access to N parts and
> you can tell how to recombine them).
This, too, is incorrect.
The Shamir Secret-Sharing Protocol, which is what PGP uses last I
checked some years ago, works on principles that are absolutely obvious
once you think about it.
Imagine a graph where (0,0) is at the origin. You're looking for a line
that crosses the vertical line at 0--the "y-intercept" of the line, if
you remember your high school geometry. The y-intercept of this line is
your key.
Now give one person a coordinate in the plane. Can they derive a line
from that point? Of course not: you need two points to draw a line.
Now give three people each a different coordinate in the plane. Can
they derive a line? Sure: they have enough points. In fact, any _two_
of them can derive a line. They just plot their points on the graph and
draw a line between them. And where that line crosses the y-axis?
That's the shared key.
This is a simple example of a scheme where you're breaking up a key
among N people, where any two people working together can derive the
original key. But at no point is any of the N people actually given a
part of the key, and it's mathematically impossible to derive the key
without two or more people sharing their information.
Want to share a key among three people? Well, three points define a
parabola... so instead of using a line, say "where a certain parabola
crosses the Y-axis, that's the secret key". Give each of N people a
point on the graph. If three of them share their data they can recreate
the parabola and derive the secret key.
Want to share a key among four people? Four points define a cubic
equasion. Among five? Quartic equasion. Six? Quintic.
It scales quite well.
Real world implementations of the Shamir protocol typically add
additional layers of complexity, but this should be a reasonably
accurate introduction to it.
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