Write a program which implements the Caesar cipher. It is required that the encryption and decryption algorithms in your implementation will use the functions implemented in Question $2.$ Your submission must include the code of your program as well as screenshots showing three test runs for the plaintext $$back$$ and the values of key $3,5,19.$c$)$

$24+14=(mod26)$

$24+14=38$

$38-261=38-26=12$

Therefore, $24+14-=12(mod26)$

$[15$ points $=5$ points per item$]$

$[$Modular arithmetic: implementation$]$ Write a program

which implements a modular addition and a modular

subtraction. For simplicity, you may fix the modulus to be $26.$

A modular addition will be implemented as a function

m$\_$add$($a$,$b$)$ which take integers $"$a$"$ and $"$b$"$ as inputs and

outputs

$a+b(mod26).$ For simplicity, you may assume that $,$

$1,$dots,$25.$ Similarly, a function $m_{?}$sub$($a$,$b$)$ will implement a

b $($mod $26).$ Your submission must include the code of your

program $($enclosed as a separate file$)$ as well as screenshots

$($included into the homework report$)$ showing test runs for the

values from Question $1$ items $($b$)$ and $($c$).$

$[40$ points: $20$ points per function$]$

$[$Caesar cipher: implementation$]$ Write a program which

implements the Caesar cipher. It is required that the

encryption and decryption algorithms in your implementation

will use the functions implemented in Question $2.$ Your

submission must include the code of your program as well as

screenshots showing three test runs for the plaintext "back"

and the values of key $3,5,19.$

$[15$ points$]$

$[$Exclusive$-$OR using modular arithmetic$]$ Let us consider a

representation of the Exclusive$-$OR $($XOR$)$ function using

modular arithmetic. Compute the following:

a$)1+1=(mod2)$

Explanation:

$1+1=2$

$2-12=2-2=0$

Therefore: $1+1=0(mod2).$ This result aligns with the

behavior of the XOR function, where the sum of two

equal bits is $0.$