efrei/algebre-non-lineaire/is_generator.py

#!/usr/bin/env python3

"""In ElGamal cyclic systems, there is at least one generator.

Find out if a given number is a generator.
"""

def main() -> None:
    """Ask for p and g and calculate"""

    p = int(input("p: "))
    g = int(input("g: "))

    print(is_generator(p, g))


def is_generator(p: int, g: int) -> bool:
    """Algorithm"""

    family_size = 0

    for i in range(1, p):
        total = pow(g, i, p)
        print(total)
        if total == 1:
            family_size = i
            break

    if family_size == p - 1:
        return True
    return False


if __name__ == "__main__":
    main()