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 exchanges 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.

1. describe how the attacker can learn the bailout amount for each bank even if he cannot derive the
private keys.