#### Diffie

I
```from __future__ import annotations

def find_primitive(modulus: int) -> int | None:
"""
Find a primitive root modulo modulus, if one exists.

Args:
modulus : The modulus for which to find a primitive root.

Returns:
The primitive root if one exists, or None if there is none.

Examples:
>>> find_primitive(7)  # Modulo 7 has primitive root 3
3
>>> find_primitive(11)  # Modulo 11 has primitive root 2
2
>>> find_primitive(8) == None # Modulo 8 has no primitive root
True
"""
for r in range(1, modulus):
li = []
for x in range(modulus - 1):
val = pow(r, x, modulus)
if val in li:
break
li.append(val)
else:
return r
return None

if __name__ == "__main__":
import doctest

doctest.testmod()

prime = int(input("Enter a prime number q: "))
primitive_root = find_primitive(prime)
if primitive_root is None:
print(f"Cannot find the primitive for the value: {primitive_root!r}")
else:
a_private = int(input("Enter private key of A: "))
a_public = pow(primitive_root, a_private, prime)
b_private = int(input("Enter private key of B: "))
b_public = pow(primitive_root, b_private, prime)

a_secret = pow(b_public, a_private, prime)
b_secret = pow(a_public, b_private, prime)

print("The key value generated by A is: ", a_secret)
print("The key value generated by B is: ", b_secret)
```