Question $1$

Please decrypt the$$cyphertext$$below$.$We assume that XOR encryption method was used with

$111111$

as a private key. Thus, every letter is coded and encrypted as a six$-$digit string of $1\text{'}$s and $0\text{'}$s$.$

$$Please consult the handout for the coding scheme.

ENCRYPTED MESSAGE:

$110111111110101001111010111111111001101010110001$

Question $2$

Diffie$-$Hellman Algorithm and Encryption

Please describe $$Diffie $-$Hellman rounds for four participants:

assign a private key to each participant,$$

use the same one$-$way function as in the handout and$$

design the protocol $($who is sending a number to whom$).$

At the end of the fourth round, all participants are supposed to arrive at the same number$$convert this number to binary.

Use this binary number as a key for XOR Encryption. Encrypt your name $($maybe a shorter version$).$

$$Question $3$

Please provide your own example of the RSA algorithm. Consult the handout and select private and public keys for Alice, respecting their relations.

Suppose the message is just number $2($M$=2).$ Explain how it is going to be encrypted and decrypted.

$4\mathrm{.}0$ VERSION OF QUESTION $3$

Provide an example of RSA with a digital signature. In this case, Bob sends Alice a pair of numbers where X is an encrypted message and Y is an encrypted signature.

Alice has to extract M from X and from Y$.$ If the messages extracted from X and Y are the same, she will know that it was a message sent by Bob.

$1.$ Select private and public keys for Alice and Bob

$2.$ We know how to compute X$,$ which is an encrypted message. To get Y$,$ Bob takes the message and puts his private key $($under mod$).$ We can call it a signature, and Alice will cancel Bob's private key by applying his public key. However, this signature has to be encrypted for Alice. The encrypted signature is Y$.$

You don't have to use big numbers for your example.

Question $4$

Cryptoanalysis

In the class, I distributed the handout with cipher text and frequency analysis. We don't know anything about the encryption method.

We do know that English text was encrypted. Please decrypt the text using the frequency information and your knowledge of English.