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2.11 Alice and Bob agree to communicate privately via e-mail using a scheme based on

RC4, but they want to avoid using a new secret key for each transmission. Alice and

Bob privately agree on a 128-bit key k. To encrypt a message m consisting of a string

of bits, the following procedure is used.

1. Choose a random 80-bit value v

2. Generate the ciphertext c= RC4(v || k) + m

3. Send the bit string (v || c)

a. Suppose Alice uses this procedure to send a message m to Bob. Describe how

Bob can recover the message m from (v|c) using k.

b.

If an adversary observes several values (v₁|c₁), (v₂|| c₂),... transmitted be-

tween Alice and Bob, how can he or she determine when the same key stream

has been used to encrypt two messages?