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 cryptographycrc press isbn 0849385237 october 1996 and it seems to run nicely 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 select large prime number one primitive root on modulo p private_key have to be greater than 2 for safety
import os
import random
import sys

from . import cryptomath_module as cryptomath
from . import rabin_miller

min_primitive_root = 3


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)  
    e_1 = primitive_root(p)  
    d = random.randrange(3, p)  
    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()