The following is a simple public$-$key cryptosystem for character strings in ASCII code:

The decryption function is P $=$ C$^5$ mod $35.$ The corresponding encryption function C $=$ P$$ mod $35$ is kept secret.

Each hexadecimal code of an ASCII character has $2$ digits. Each digit of the pair is encrypted separately using the above function.

Ex: The hexadecimal code for the ASCII character B is $42.$ The two digits $4$ and $2$ are encrypted as $(4$ mod $35,2$ mod $35).$

$($a$)$

Decrypt the ciphertext:

$(9,4)(32,0)(6,15)(7,7)(6,10)(32,0)(7,4)(6,15)(7,10)(32,0)(32,9)(33,1)(32,17)(33,0)(33,0)(33,0)(32,17)(33,0)(33,0)(33,0)(32,1).$

$($The numbers are given in decimal. The parentheses and the commas are not part of the ciphertext but are used only to increase readability.$)$

$($b$)$

The RSA code is based on $2$ principles:

n is the product of $2$ prime numbers, p and q

e $*$ d mod $(($p $-1)*($q $-1))=1$

Break the above simple encryption scheme by finding the corresponding encryption function by using the two underlying principles of the scheme.