MATH 195: CRYPTOGRAPHY HOMEWORK #13

Problem 6.20(a). Suppose the ElGamal system is used with G = 𝔽_{71}^{∗}, g = 7, public key g^{b} = 3 and random integer a = 2. What is the cipher text of message x = 30?

Problem 6.27. Suppose the Diffie-Hellman method is used with group G = 𝔽_{32}^{∗} (where 𝔽_{32} = 𝔽_{2}[X]/(X^{5} + X^{2} + 1)), primitive root g = X + 1 = 00011, and with secret exponents a = 8 (X_{A}), b = 12 (X_{B}). What is the common secret key h (K) that is exchanged?

Problem 7.18. Let G, g be as in Problem 6.27. Use the baby step-giant step method to compute log_{g}(10101).

Problem 7.19. Let G = 𝔽_{131}^{∗}, with primitive root g = 2. Use the Pohlig-Hellman method with m = 10 · 13 (or 13 · 10) to find log_{2} 3.

Date: April 30, 2002.

6.20(a), 6.27, 7.18, 7.19.