## Related questions with answers

Now use the RSA cryptosystem to send and receive secret messages. Working with your teacher, form teams with your classmates. Choose a name for your team. Your team should choose one of the public encryption keys listed in the public-key directory shown below. Write your team name next to your public key on a copy of the Public-Key Directory. Your teacher will hand each group their corresponding private key. Thus, each team has its own pair of keys-a public key and the associated private key.

Public-Key Directory

$\begin{array}{|c|c|c|} \hline \text { Team Name } & \boldsymbol{n} & e \\ \hline & 85 & 13 \\ \hline & 55 & 23 \\ \hline & 161 & 19 \\ \hline & 95 & 31 \\ \hline & 91 & 29 \\ \hline & 65 & 29 \\ \hline & 35 & 13 \\ \hline \end{array}$

a. Your team should use the RSA cryptosystem to encrypt and send at least one single-word secret message to another team. As per the cryptosystem rules, use the receiving team's public key to encrypt the message.

b. Decrypt any messages you receive. As per the cryptosystem rules, use your own private key to decrypt the message you receive.

c. Based on this public-key cryptosystem, discuss and answer the following questions.

i. Can any team send any other team a secret encrypted message? What information do you need to encrypt a secret message so that only the target team can read it?

ii. Once you encrypt a secret message to a target team, can any other team decrypt it and read the message? Explain.

iii. Suppose you receive an encrypted message from another team. What information did that team need to encrypt the message? What information do you need to decrypt it? Can any other team decrypt the message?

Solution

Verifieda.)

To encrypt a message that can be read by a certain group, do the following:

- Convert each letter in the plaintext into numbers based on the arrangement of the letters in the alphabet.
- Raise each number by a power of $e$. You can get $e$ in the public directory or from the other group.
- Reduce each number mod $n$. You can get $n$ in the public directory or from the other group.

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