Consider the following pseudo-WEP protocol. The key is 4 bits and the IV is 2 bits . The IV is appended to the end of the key when generating the keystream. Suppose that the shared secret key is 10 IO. The keystreams for the four possible inputs are as follows :
101000: 001010 1101010101001011 010100100...
10100l: 1010011011001010110100100101101 . . .
101010: 0001101000111100010100101001111...
I01011: 1111101010000000101010100010111 . . .
Suppose all messages are 8-bits long. Suppose the ICV (integrity check) is 4bits long, and is calculated by XOR-ing the first 4 bits of data with the last 4 bits of data. Suppose the pseudo-WEP packet consists of three fields: first the IV field, then the message field, and last the ICV field, with some of these fields encrypted.
a. We want to send the message m =10100000 using the IV = II and using WEP. What will be the values in the three WEP fields?
b. Show that when the receiver decrypts the WEP packet, it recovers the message and the ICV.
c. Suppose Trudy intercepts a WEP packet (not necessarily with the IV = 11) and wants to modify it before forwarding it to the receiver. Suppose Trudy flips the first ICV bit. Assuming that Trudy does not know the key streams for any of the IVs, what other bit(s) must Trudy also flip so that the received packet passes the ICV check?
d. Justify your answer by modifying the bits in the WEP packet in part (a), decrypting the resulting packet, and verifying that the integrity check.