1.2. General Problem Definition of (n, t) Secret Sharing

Try these first

1. 1.

   What does the (n, t) in secret sharing refer to?

   Hint

   Consider what happens when trying to reconstruct the secret with fewer parties.

2. 2.

   Who is the dealer in the (n, t) secret sharing method?

   Hint

   Think about who manages the distribution of keys in a vault example.

3. 3.

   In an (n, t) secret sharing scheme, if n=3 and t=1, how many shares are required to reconstruct the secret?

   • 1
   • 2
   • 3

   Hint

   Think about the definition of t in this context.

4. 4.

   True or False: A single shareholder can reconstruct the shared secret in an (n, t) scheme.

   • True
   • False

   Hint

   Recall the minimum requirements of the scheme.

5. 5.

   If you have 7 shareholders and want to create an (n, t) secret sharing scheme where any 4 can reconstruct the secret, describe how you would set up the polynomial for share distribution.

   Hint

   Remember the polynomial degree must relate to the threshold policy.

6. 6.

   Imagine two dealers independently share the same secret using different polynomials in an (n, t) framework. What can you infer if one group can reconstruct the secret while the other cannot?

   Hint

   Reflect on how the polynomial degree influences the threshold for reconstructing the secret.