Question

Describe (t,n) Shamir secret sharing scheme

Answer 1

Shamir secret (t, n) sharing scheme:

It is a cryptographic procedure to share a secret message by dividing it into parts. The reconstruction of the secret that shared is not possible without a minimum number of shares. And that share number is known as the threshold (t) of the sharing schema.

For example if the shared secret is a key to be shared between the employees in a company, then the secret. Then the number “n” is the number of pieces in which the secret has divided. Now the recreation of the secret is possible only if at east “t” parts are available to a person, that “t” is known as the threshold of the algorithm. That is even if some parts are missing then also the secret can be generated if still there are “t” parts are available.

n: Number of parts in which the secret that to be shared is divided into.

t: Number of minimum parts among “n” is required to reconstruct the divided secret.

The procedure used in Shamir secret (t, n) sharing scheme is provided below:

• Let the secret to be shared is “S”, then the secret is divided into “n” parts:
  • S1, S2, S3,.., Sn
• If any “t” or more “Si” are available, then S can be recreated.
• If any number of parts available that is less than “t” can’t produce even a part of “S”, and it is like zero knowledge. It is the main highlight of the algorithm.

Note: Please comment if any doubts