Question: 5. Use the baby step, giant step method to solve 2k = 7 mod 13 (3 marks). 6. For the ElGamal cryptosystem, let the public

5. Use the baby step, giant step method to solve 2k = 7 mod 13 (3 marks). 6. For the ElGamal cryptosystem, let the public key of Alice be (p, g, h), where p is a big prime, and g is a generator for mod p, and h=ga. The secret key for Alice is a. Bob wants to communicate with Alice, he will encrypt the messages m1m2m3 m4 in order as specified by ElGamal and send the ciphertexts c1c2c3c4 to Alice in ordere. Eve wants to attack this encrypted communication between Alice and Bob. Assume that Eve can have one plaintext m1, show an attack that how Eve can recover all the encrypted c2c3c4 if Bob uses a broken random number generator that only outputs a constant value, say b = 2 (2 marks). One step further, if the random number generator is not broken, but it is bad in the sense that it outputs b = 2 with probability 90%, then what is the probability that Eve can recover c2, can recover c3, and can recover c3c4 (2 marks)?

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