Being Eve

File: cryptography/being-eve.txt (or being-eve.pdf)

You may work with a partner or on your own. Put name(s) at the top of the file you submit.

Goals

Practice with the computational mechanisms of the Diffie-Hellman key exchange
Practice with the computational mechanisms of RSA encryption and decryption
Think about where the security lives within these algorithms

Rubric

4/4 - [Diffie-Hellman] Value of the shared key K plus method of computing it 1/1 - [Diffie-Hellman] Explanation of why this wouldn't work with big integers 4/4 - [RSA] Message plus method of computing it, including encoding 1/1 - [RSA] Explanation of why this wouldn't work with big integers 1/1 - [RSA] Explanation of why the encoding is insecure independent of RSA

Background

Starting with the original RSA paper, cryptographic literature has used the names Alice and Bob as two parties who wish to communicate, and Eve as an eavesdropper (or occasionally an evil-doer) who surreptitiously obtains copies of Alice and Bob's communications. There's also a more complete cast of characters, including Trudy the intruder, Mal (Mallory/Malcolm/etc.) the malefactor/malicious person, etc.

For this assignment, you will play the role of Eve, who obtains copies of the messages sent between Alice and Bob during Diffie Hellman and RSA interactions. The assignment will provide you with the contents of the messages, and you will extract the information the parties are trying to hide.

What you (Eve) intercepted for Diffie Hellman

Alice and Bob agree on g = 7 and p = 61.

Alice sent Bob the number 30.

Bob sent Alice the number 17.

Your job for Diffie Hellman

Figure out the shared secret agreed upon by Alice and Bob. This will be an integer.
Show your work. Exactly how did you figure out the shared secret?
Show precisely where in your process you would have failed if the integers involved were much larger.

What you, Eve, intercepted for RSA

Here's Bob's public key:

(e_Bob, n_Bob) = (17, 170171)

Here's the encrypted data sent from Alice to Bob:

[65426, 79042, 53889, 42039, 49636, 66493, 41225, 58964, 126715, 67136, 146654, 30668, 159166, 75253, 123703, 138090, 118085, 120912, 117757, 145306, 10450, 135932, 152073, 141695, 42039, 137851, 44057, 16497, 100682, 12397, 92727, 127363, 146760, 5303, 98195, 26070, 110936, 115638, 105827, 152109, 79912, 74036, 26139, 64501, 71977, 128923, 106333, 126715, 111017, 165562, 157545, 149327, 60143, 117253, 21997, 135322, 19408, 36348, 103851, 139973, 35671, 93761, 11423, 41336, 36348, 41336, 156366, 140818, 156366, 93166, 128570, 19681, 26139, 39292, 114290, 19681, 149668, 70117, 163780, 73933, 154421, 156366, 126548, 87726, 41418, 87726, 3486, 151413, 26421, 99611, 157545, 101582, 100345, 60758, 92790, 13012, 100704, 107995]

Your job for RSA

Figure out the encrypted message sent from Alice to Bob.
Show your work. Exactly how did you figure out the message? (You should include an explanation of how the message from Alice to Bob is encoded. That is, how does Alice's intended message (whatever manner of message it may be) correspond to the integers in the plaintext that you end up with after decrypting the encrypted message?)
Show precisely where in your process you would have failed if the integers involved were much larger.
Explain, briefly, why the message encoding Alice used would be insecure even if Bob's keys involved larger integers.

Handing it in

In a folder called "cryptography" in your GitHub repository, put your results in a file called being-eve.txt or being-eve.pdf.

Have fun!

http://xkcd.com/177/