4 Bail-Out Money As soon as Barack took office, he decided to embrace modern technology by communicating with cabinet members over the Internet using a device that supports cryptographic protocols. In a first attempt, Barack ex- changes with Tim brief text messages, encrypted with public-key cryptography, to decide the exact amounts of bailout money to give to the largest 10 banks in the country. Let pB and pT be the public keys of Barack and Tim, respectively. A message m sent by Barack to Tim is transmitted as EpT (m) and the reply r from Tim to Barack is transmitted as EpB(r). The attacker can eavesdrop the communication and knows the following information: Public keys pB and pT and the encryption algorithm This encryption algorithm has the following property. Given a public key, the same plaintext is always encrypted to the same ciphertext, i.e., the encryption algorithm is deterministic. The total amount of bailout money authorized by congress is $900B. The names of the largest 10 banks The amount each bank will get is a multiple of $1B Messages and replies are terse exchanges of the following form: Barack: How much to Citibank? Tim: $144B. Barack: How much to Bank of America? Tim: $201B. ... 2. As a result of the above attack, Barack decides to modify the protocol for exchanging messages. Describe two simple modifications of the protocol that will make the above attack much more difficult. The first one should use random numbers and the second one should use symmetric encryption.