User talk:Malathi524

Welcome
 Hello Malathi524, and Welcome to Wikipedia!  Welcome to Wikipedia! I hope you enjoy the encyclopedia and want to stay. As a first step, you may wish to read the Introduction.

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---Mr. Stradivarius Malathi524, good luck, and have fun. -- — Mr. Stradivarius  ♫ 07:02, 4 June 2011 (UTC)

Cloud computing
Hi there Malathi524! About this edit - just for your info, questions about content should be asked at the reference desk, not on user talk pages or on help page talk pages. And you can find your answer at our article cloud computing. All the best.  — Mr. Stradivarius  ♫ 07:05, 4 June 2011 (UTC)

Shamir's Secret Sharing
Example

The following example illustrates the basic idea. Note, however, that calculations in the example are done using integer arithmetic rather than using finite field arithmetic. Therefore the example below does not provide perfect secrecy, and is not a true example of Shamir's scheme. Preparation

Suppose that our secret is 1234 (S=1234)\,\!.

We wish to divide the secret into 6 parts (n=6)\,\!, where any subset of 3 parts (k=3)\,\! is sufficient to reconstruct the secret. At random we obtain 2 numbers: 166, 94.

(a_1=166;a_2=94)\,\!

Our polynomial to produce secret shares (points) is therefore:

f\left(x\right)=1234+166x+94x^2\,\!

We construct 6 points from the polynomial:

\left(1,1494\right);\left(2,1942\right);\left(3,2578\right);\left(4,3402\right);\left(5,4414\right);\left(6,5614\right)\,\!

We give each participant a different single point (both x\,\! and f\left(x\right)\,\!). Reconstruction

In order to reconstruct the secret any 3 points will be enough.

Let us consider \left(x_0,y_0\right)=\left(2,1942\right);\left(x_1,y_1\right)=\left(4,3402\right);\left(x_2,y_2\right)=\left(5,4414\right)\,\!.

We will compute Lagrange basis polynomials:

\ell_0=\frac{x-x_1}{x_0-x_1}\cdot\frac{x-x_2}{x_0-x_2}=\frac{x-4}{2-4}\cdot\frac{x-5}{2-5}=\frac{1}{6}x^2-\frac{3}{2}x+\frac{10}{3}\,\!

\ell_1=\frac{x-x_0}{x_1-x_0}\cdot\frac{x-x_2}{x_1-x_2}=\frac{x-2}{4-2}\cdot\frac{x-5}{4-5}=-\frac{1}{2}x^2+\frac{7}{2}x-5\,\!

\ell_2=\frac{x-x_0}{x_2-x_0}\cdot\frac{x-x_1}{x_2-x_1}=\frac{x-2}{5-2}\cdot\frac{x-4}{5-4}=\frac{1}{3}x^2-2x+\frac{8}{3}\,\!

Therefore

f(x)=\sum_{j=0}^2 y_j\cdot\ell_j(x)\,\!

=1942\cdot\left(\frac{1}{6}x^2-\frac{3}{2}x+\frac{10}{3}\right)+3402\cdot\left(-\frac{1}{2}x^2+\frac{7}{2}x-5\right)+4414\cdot\left(\frac{1}{3}x^2-2x+\frac{8}{3}\right)\,\!

=1234+166x+94x^2\,\!

Recall that the secret is the free coefficient, which means that S=1234\,\!, and we are done.

HELP--why they pick 166 and 94 randomly in this secret sharing alg.....?can anybody explain this?