Re: two of three

From: Volker Hetzer (volker.hetzer_at_ieee.org)
Date: 01/28/05 

Date: Fri, 28 Jan 2005 16:29:27 +0100

"Bob Harris" <plasticnitlion@wrappermindspring.com> schrieb im Newsbeitrag
news:BE1FAA10.47B10%plasticnitlion@wrappermindspring.com...
> Howdy,
>
> Suppose I have a value x (chosen from some range) and I want to encrypt it
> with three value a, b, and c (each from the same range as x) such that x can
> be recovered from any two of those values. In other words, we have
> functions f, g, and h such that f(a,b) = g(b,c) = h(c,a) = x.
>
> Do such schemes exist? (I think probably the answer is yes). Please
> enlighten me.
Ok, first you encrypt it, using a key.
Then you have two methods:
a) you treat the key as the y-value at point 0 on the x-axis of a two dimensional diagram.
   Create a polynom of degree 1 (i.e. a straight line with m!=1). Find three points of that
   line and give each one the coordinates of one point. Now any two can get together, figure
   out the y=mx+n equation, with n being the key to the encrypted text
b) you treat the key as a point in 2 dimensional space. Like you've got a 128bit key, you treat
    the first 64bit as x and the other 64bit as y. Find three different straight lines
    that pass through that point. Be careful that none is parallel to an axis. Hand each one a line
    equation. Now, any two can get together and find out where their lines cross.

Lots of Greetings!
Volker