Exercise $1$: Design and implement a simple package based on the RSA algorithm to provide encrypting$/$decrypting and digital signature signing and verifying. Using python and make GUI and don't forget to do point f

a$.$ Generate two prime numbers: $p$ and $q.$

b$.$ Miller Rabin: to test the prime number.

c$.$ Euclid's algorithm: to find the encryption key $($e$)$

d$.$ Extended Euclid's algorithm $($EEA$)$: to find the decryption key $($d$).$

e$.$ choose any hash function which is available as free source.

f$.$ A main method to show different usage of RSA including dialogues between two parties $($Alice and Bob$)$ that reflect encrypting$/$decrypting and digital signature signing

and verifying.

g$.$ Combine all of the above in a GUI model to test the functions.

Using python Exercise $2$: Finding a collision on hash function.

a$.$ Define a hash function $($SHA$60$v$)$ outputs the first $60$ bits $(15$ nibbles$)$ of SHA$-1.$ For

example, SHA$-1$ of $"$CYS$406"$ is:

$7148927503d75c8fa85bcd602828d93b061c90bf$

So$,($SHA$60$v$)$ should outputs $"7148927503d75c8.$

b$.$ Find any collision in SHA$60$v$.$ You should find two different messages such that the Linux

command:

echo $-$n msg $|$ sha$1$sum $-|$ cut $-$c$1-15$

produces the same answer when msg is replaced by each message. To enable us to verify

your answer, please make sure the two messages are typable on a regular keyboard!

Hint: You should not write the code for SHA$-1$; you should use an existing library. Also,

it's a good idea to find shorter collisions first. For example, start off finding a collision for

the first $24$ bits $(6$ nibbles$)$; that's a lot easier. The challenge that $60$ bits gives you is that

you probably can't store all the intermediate hashes you generate in memory $($Read

about Floyd's algorithm$).$ Nevertheless, you should be able to write a program which

finds a $60-$bit collision in a few hours on a regular desktop or laptop computer.