 # Implement your own implementations of specific functions rather tha...

## Question

Implement your own implementations of specific functions rather than a provided implementation from a library.
• Implement generation of random prime numbers of a specific bit length. Your testing of the primality of a potential candidate number should use a probabilistic prime test, you should implement the test based on research of the appropriate algorithms. A recommendation is the Miller-Rabin primaility test.
• Implement an efficient modular exponentiation algorithm.
Using python3.

## Solution Preview

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import random
import sys
import numpy as np

def factory(n):
s = 0
m = 0
odd = n & 1
# n should be an even number
while odd == 0:
s = s + 1
n = n >> 1 # n = n / 2
# odd or even checking
# for example n = 5 then its binary form is 101
# 5 & 1 = 101 & 001 = 001
# if n = 6 then its binary form is 110
# 110 & 001 = 6 & 1 = 000
odd = n & 1
m = n

# m should be an odd number now
return s, m...

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