Secret Sharing: Difference between revisions

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Revision as of 10:33, 1 December 2004

Secret Sharing is used to split a secret (usually a key) into several pieces which are then given to distinct persons so that some of these persons must cooperate to reconstruct the secret.

A Simple Approach

One simple approach to split a secret number $D$ into $n$ pieces $D_{1}, D_{2},$ … $, D_{n}$ such that any $k$ pieces are sufficient (and necessary) to reconstruct $D$ is using a $k - 1$ polynomial.

When splitting the secret a random polynomial $f (x) = a_{0} + a_{1} x + a_{2} x +$ … $+ a_{k - 1} x^{k - 1}$ with $a_{0} = D$ is generated. The $D_{i}$ are calculated as $D_{i} = f (i)$ for $i = 1,$ … $, n$ .

Given any $k$ $D_{i}$ it is possible to interpolate the polynomial and calculate $f (0)$ which gives the original secret $D$ .

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 == A Simple Approach ==
-One simple approach to split a secret number <math>D</math> into <math>n</math> pieces <math>D_1, D_2, \ldots, D_n</math> such that any <math>k</math> pieces are sufficient (and necessary) to reconstruct <math>D</math> is using a <math>k-1</math> polynomial.
+One simple approach to split a secret number <math>D</math> into <math>n</math> pieces <math>D_1, D_2, </math>…<math>, D_n</math> such that any <math>k</math> pieces are sufficient (and necessary) to reconstruct <math>D</math> is using a <math>k-1</math> polynomial.
-When splitting the secret a random polynomial <math>f(x) = a_0 + a_1 \cdot x + a_2 \cdot x + \ldots a_{k-1} x^{k-1}</math> with <math>a_0 = D</math> is generated. The <math>D_i</math> are calculated as <math>D_i = f(i) \mbox{ for } i = 1, \ldots, n</math>.
+When splitting the secret a random polynomial <math>f(x) = a_0 + a_1 x + a_2 x + </math>…<math> + a_{k-1} x^{k-1}</math> with <math>a_0 = D</math> is generated. The <math>D_i</math> are calculated as <math>D_i = f(i)</math> for <math>i = 1, </math>…<math>, n</math>.
 Given any <math>k</math> <math>D_i</math> it is possible to interpolate the polynomial and calculate <math>f(0)</math> which gives the original secret <math>D</math>.

Secret Sharing: Difference between revisions

Revision as of 10:33, 1 December 2004

A Simple Approach

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