Secret Sharing: Difference between revisions
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== A Simple Approach == |
== A Simple Approach == |
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One simple approach to split a secret number <math>D</math> into <math>n</math> pieces <math>D_1, D_2, |
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. |
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When splitting the secret a random polynomial <math>f(x) = a_0 + a_1 |
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>. |
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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>. |
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>. |
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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 into pieces … such that any pieces are sufficient (and necessary) to reconstruct is using a polynomial.
When splitting the secret a random polynomial … with is generated. The are calculated as for ….
Given any it is possible to interpolate the polynomial and calculate which gives the original secret .
