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

V 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

abato noisgnarof bits, the following procedure is used.

16

1.

one2.

3.

Choose a random 80-bit value v

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

Send the bit string (v || c)

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

ford sleBob 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?