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Homework 5 ICS 247 Security Algorithms
Please answer the following questions, each of which is worth 10 points.
1. Describe a protocol for electronic poker that is resistant to collusions between pairs of players.
2. Is there a way to modify the (Shamir) secret sharing scheme described in class so that we distribute shares to four individuals, x1, x2, x3, and x4, such that the secret is revealed only if the subgroup contains x1 and x2? Why or why not?
3. Is there a way to modify the (Shamir) secret sharing scheme described in class so that we distribute shares to four individuals, x1, x2, x3, and x4, such that the secret is revealed only if the subgroup contains the subset {x1, x2} or {x3, x4}? Why or why not?
4. Peggy claims to have a fast algorithm for graph isomorphism, and for two given graphs G1 and G2, Peggy says these two are definitely not isomorphic. Describe a zero-knowledge proof for Peggy to show Victor that she is right, with very high probability.
5. Formulate an encryption scheme and operator ∗ so that
E(M1) ∗ E(M2) = E(M1 + M2),
where + denotes modular addition.