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# CIS 4360 Final

Alice and Bob use the Diffie-Hellman key exchange with common prime q = 11 and generator a = 2.

If the private key of Alice is X A = 6 what is her public key Y A?
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The ElGamal encryption scheme is based on the Diffie-Hellman key exchange. If q is the common modulus and a is a generator, then the public key of Alice is (Y A, q), where Y A = a^XA modq, XA backwards E Zq, and the private key is: (X A, q).

To encrypt a message m, 0 < m < q, Bob computers C1= a^k (modq), k backwards E Zq, and C2 = YA^k times m (modq),

Show how this is down for the special case: q = 11, a = 2, X A = 3, k = 2, m = 6. What is the public key Y A of Alice?
The ElGamal encryption scheme is based on the Diffie-Hellman key exchange. If q is the common modulus and a is a generator, then the public key of Alice is (Y A, q), where Y A = a^XA modq, XA backwards E Zq, and the private key is: (X A, q).

To encrypt a message m, 0 < m < q, Bob computers C1= a^k (modq), k backwards E Zq, and C2 = YA^k times m (modq),

Show how this is down for the special case: q = 11, a = 2, X A = 3, k = 2, m = 6. What is the encryption (C1,C2) of message m = 6?