Shamir Secret Sharing Algorithm

In Shamir Secret Sharing Algorithm used to secure a secret in distributed way. In this algorithm a secret is divided into multiple parts called shares. Each unique shares is divided across multiple participants. These shares are used to reconstruct the original secret.

 

How to unlock a secret?

To unlock a secret, you need minimum number of shares. This minimum number is called the threshold.

 

How the algorithm works?

Divide the secret ‘S’ into ‘n’ pieces {S1, S2…Sn} such that

a.   We can compute the secret ‘S’ with the knowledge of any k or more pieces or shares .

b.   We can’t compute the secret ‘S’ with the knowledge of k-1 or fewer pieces.

 

This algorithm works based on the principle ‘to build a polynomial with the degree (K – 1) such that the constant term is the secret code and the remaining numbers are random and this constant term can be found by using any K points out of N points generated from this polynomial by using Legrange’s Basis Polynomial’.

 

 

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