2.1. Setup of Shamir’s Secret Sharing Scheme

Try these first

1. 1.

   What does 'n' represent in Shamir's Secret Sharing?

   Hint

   Think of it as the number of people holding a key.

2. 2.

   What is the main purpose of secret sharing?

   Hint

   Consider why it's important not to trust just one person.

3. 3.

   What does the term (n, t) signify in secret sharing?

   • n: number of parties
   • t: minimum needed to reconstruct
   • t: number of parties
   • n: maximum allowed
   • n: party identifiers
   • t: total shares

   Hint

   Think about what these letters usually represent in mathematics.

4. 4.

   True or False: If one party knows a share, they can reconstruct the secret.

   • True
   • False

   Hint

   Consider how many pieces of the puzzle are needed to complete it.

5. 5.

   You are required to design a secret sharing scheme for five parties where at least three are needed to reveal the secret. Describe your polynomial setup and how shares are distributed.

   Hint

   Think about polynomial properties and how evaluating at different points works.

6. 6.

   Explain how the security of Shamir's scheme is upheld when parties with fewer than 't' shares attempt to reconstruct the secret.

   Hint

   Reflect on polynomial characteristics in relation to degrees and roots.