I have to solve this problem, any insights would be helpful.

Alice represents a company AAA that is considering buying Bob’s company, BBB. Eve knows about the proposed transaction and she will be able to gain financial advantage if she can find out as quickly as possible the details of the deal. Eve can intercept the messages from Alice to Bob. She knows that they will communicate using the RSA public-key encryption algorithm. She has Bob’s public key (e,n) where e=3 and n is 128-bit long. She does not have Bob’s private key. Eve also knows that the messages will be constructed as follows:

1. An initial e-mail is sent by Alice to Bob to let him know of AAA’s decision about trying or not to buy BBB. For a “no” decision, the message is 0. For “yes”, the message is 1. The value 0 or 1, respectively, is then encrypted using the RSA algorithm.

2. The next day, Alice sends Bob an e-mail to inform him of the proposed price offered. The message consists of a number representing the price in pounds. This number is encrypted using RSA. Eve estimates the price to be between 20 million and 30 million.

3. A third message is sent on the third day from Alice, consisting of a longer text discussing some initial details of the deal. For this e-mail, she uses the following method of encryption: each individual character of the text is viewed as the ASCII code of that character. The number thus obtained for each character is then encrypted using the RSA algorithm, and the resulting list of numbers is sent.

4. The following day Alice again writes a long e-mail discussing further details of the deal. For this e-mail, she uses the following method of encryption: each single word of the text is viewed as a number by concatenating the 8-bit ASCII codes of each letter. The number thus obtained for each word is then encrypted using the RSA algorithm and the resulting list of numbers is sent.

Discuss whether Eve can find efficient methods of retrieving each of the original messages. If you can think of several methods, describe them all. However, do not describe generic attacks, only attacks that are particularly suited to this specific scenario.

For each attack you identified, give a rough estimation of the time Eve would need to succeed, using only one computer. The estimates of the time should be of the type: a few seconds, a few minutes, 1 hour, a few hours, one day, one week or longer. You may make assumptions about the speed of her computer, for example you could assume it can perform RSA to encrypt or to decrypt (if encryption, respectively decryption key is given) one number in 1 millisecond.

For each of the attacks you identified, propose changes to the encryption scheme to prevent such an attack.

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