1.3. Shamir's (n, t) Secret Sharing Scheme

Try these first

1. 1.

   What does n represent in the (n, t) secret sharing model?

   Hint

   What does the 'n' signify?

2. 2.

   List one practical example where secret sharing may be useful.

   Hint

   Think of scenarios where multiple people have access to sensitive information.

3. 3.

   What does 't' represent in the (n, t) secret sharing scheme?

   • Total shareholders
   • Threshold for reconstruction
   • Secret value

   Hint

   What threshold must be met for the secret to be recovered?

4. 4.

   True or False: Any group of fewer than t shareholders can reconstruct the secret.

   • True
   • False

   Hint

   Remember the rules of polynomial degree.

5. 5.

   If the dealer selects a polynomial of degree 3 and has 5 shareholders, what is the minimum number of shareholders required to securely reconstruct the secret?

   Hint

   Remember the relationship between polynomial degree and necessary shares.

6. 6.

   Demonstrate how two distinct quadratic polynomials can only intersect at a maximum of 2 points. Use a visual example to support your explanation.

   Hint

   Visualize the properties of parabolas and the laws of intersection.