Problem $1.($Reverse$)$ Implement the function $\_$reverse$()$ in

reverse.py that reverses the one$-$dimensional list $a$ in place, ie$,$ without creating a new list.

Problem $2.($Euclidean Distance$)$ Implement the function $\_$distance$()$ in

distance.py that returns the Euclidean distance between the vectors $x$ and $y$ represented as one$-$dimensional lists of floats. The Euclidean distance is calculated as the square root of the sums of the squares of the differences between the corresponding entries. You may assume that $x$ and $y$ have the same length.Problem $3.($Transpose$)$ Implement the function $\_$transpose$()$ in transpose.py that creates and returns a new matrix that is the transpose of the matrix represented by the argument a$.$ Note that a need not have the same number rows and columns. Recall that the transpose of an m$-$by$-$ n matrix A is an n$-$by$-$ m matrix B such that B$\_($ij$)=$A$\_($ji$),$ where i $$ n and j $$ m$.$

Problem $4.($Palindrome$)$ Implement the function $\_$isPalindrome$()$ in

palindrome.py that returns True if the argument $s$ is a palindrome $($ie$,$ reads the same forwards and backwards$),$ and False otherwise. You may assume that $s$ is all lower case and doesn't contain any whitespace characters$\mathrm{.}1//4$

Assignment $4($RSA Crpytosystem$)$

Problem $5.($Sine Function$)$ Implement the function $\_$sin$()$ in

sin$.$py that calculates the sine of the argument $x($in radians$),$ using the formula

$sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+$cdots.Part II: RSA CryptosystemBackground: RSA $($Rivest$-$Shamir$-$Adleman$)$ cryptosystem is widely used for secure communication in browsers, bank ATM machines, credit card machines, mobile phones, smart cards, and operating systems. It works by manipulating integers. To thwart eavesdroppers, the RSA cryptosystem must manipulate huge integers $($hundreds of digits$),$ which is naturally supported by the int data type in Python. Your task is to implement a library that supports core functions needed for developing the RSA cryptosystem, and implement programs for encrypting and decrypting messages using RSA.

The Math Behind: The RSA cryptosystem involves three integers $n,e,$ and $d$ that satisfy certain mathematical properties. The public key $(n,e)$ is made public on the Internet, while the private key $(n,d)$ is only known to Bob. If Alice wants to send Bob a message xin$[0,n),$ she encrypts it using the function

$E(x)=x^e$modn,

where $n=pq$ for two distinct large prime numbers $p$ and $q$ chosen at random, and $e$ is a random prime number less than $m=(p-1)(q-1)$ such that $e$ does not divide $m.$

For example, suppose $p=47$ and $q=79.$ Then $n=3713$ and $m=3588.$ Further suppose $e=7.$ If Alice wants to send the message $x=2020$ to Bob, she encrypts it as

$E(2020)={2020}^7$mod$3713=516.$

When Bob receives the encrypted message $y,$ he decrypts it using the function

$D(y)=y^d$modn,

where din$[1,m)$ is the multiplicative inverse of emodm, ie$,d$ is an integer that satisfies the equation edmodm$=1.$

Continuing the example above, if $d=2563,$ then when Bob receives the encrypted message $y=516$ from Alice, he decrypts it to recover the original message as

$D(516)={516}^{2563}$mod$3713=2020$