1.4. Description of Finite Field and Polynomial Properties

Try these first

1. 1.

   What is a finite field?

   Hint

   Think about the definition involving primes.

2. 2.

   Explain what a polynomial is.

   Hint

   Recall the structure of mathematical relationships.

3. 3.

   What is a finite field?

   • An infinite set of numbers
   • A set of finite elements in which operations are defined
   • Both A and B

   Hint

   Think about modular operations.

4. 4.

   True or False: In Shamir's secret sharing scheme, any singular share can reconstruct the secret.

   • True
   • False

   Hint

   Consider the minimum share requirement.

5. 5.

   Propose a variation of Shamir's secret sharing scheme for a group needing to combine their knowledge to gain access to a resource securely. What modifications would you suggest?

   Hint

   Think about how many distinct combinations you need.

6. 6.

   Analyze a failure scenario where one party in a three-party confidential sharing arrangement loses their share. What implications does this have for reconstructing the secret?

   Hint

   Consider how redundancy impacts security.