1. Homework #3
Consider a verifyable secret sharing scheme (VSS) based on Shamir's polynomial secret sharing as follows.
A dealer has a secret S, a public prime p and a public generator g of Zp*.
The dealer gives player pj a share s(j) in a degree-t polynomial whose value at zero is a random a0.
The dealer publicizes S * a0, as well as commitments to all shares in the form gs(j) (mod p).
Suppose that an auditing agency wishes to check that the dealer is not corrupt. The agency can view all public information, but no secret data (in particular, no private share of any player). Furthermore, it cannot interact with the players, who might not be on-line during the check.
Describe how the auditing agency can verify that all the commitments to shares are consistent, i.e., that any subset of t+1 commitments defines the same, unique committed secret.

2. Homework #3
Suppose Bob has split a secret amongst n people such that k out of them can reconstruct the secret.
Suppose Bob wants to increase k?
Increase n?
Decrease k?
Decrease n?
What should he do?

3. Homework #3 Voting schemes: You want to arrange a Yes/No vote so that
Everyones vote is secret
Anyone can verify that the final result is correct
What can you do?
Look up the literature on voting schemes.