#### Elgamal Key Generator

p
```import os
import random
import sys

from . import cryptomath_module as cryptomath
from . import rabin_miller

min_primitive_root = 3

# I have written my code naively same as definition of primitive root
# however every time I run this program, memory exceeded...
# so I used 4.80 Algorithm in
# Handbook of Applied Cryptography(CRC Press, ISBN : 0-8493-8523-7, October 1996)
# and it seems to run nicely!
def primitive_root(p_val: int) -> int:
print("Generating primitive root of p")
while True:
g = random.randrange(3, p_val)
if pow(g, 2, p_val) == 1:
continue
if pow(g, p_val, p_val) == 1:
continue
return g

def generate_key(key_size: int) -> tuple[tuple[int, int, int, int], tuple[int, int]]:
print("Generating prime p...")
p = rabin_miller.generate_large_prime(key_size)  # select large prime number.
e_1 = primitive_root(p)  # one primitive root on modulo p.
d = random.randrange(3, p)  # private_key -> have to be greater than 2 for safety.
e_2 = cryptomath.find_mod_inverse(pow(e_1, d, p), p)

public_key = (key_size, e_1, e_2, p)
private_key = (key_size, d)

return public_key, private_key

def make_key_files(name: str, key_size: int) -> None:
if os.path.exists(f"{name}_pubkey.txt") or os.path.exists(f"{name}_privkey.txt"):
print("\nWARNING:")
print(
f'"{name}_pubkey.txt" or "{name}_privkey.txt" already exists. \n'
"Use a different name or delete these files and re-run this program."
)
sys.exit()

public_key, private_key = generate_key(key_size)
print(f"\nWriting public key to file {name}_pubkey.txt...")
with open(f"{name}_pubkey.txt", "w") as fo:
fo.write(f"{public_key[0]},{public_key[1]},{public_key[2]},{public_key[3]}")

print(f"Writing private key to file {name}_privkey.txt...")
with open(f"{name}_privkey.txt", "w") as fo:
fo.write(f"{private_key[0]},{private_key[1]}")

def main() -> None:
print("Making key files...")
make_key_files("elgamal", 2048)
print("Key files generation successful")

if __name__ == "__main__":
main()
```