import hashlib
import os


def hash_password(password: str) -> str:
    """Hash password using PBKDF2-HMAC-SHA256 with 100,000 iterations and a random salt."""
    salt = os.urandom(16)
    key = hashlib.pbkdf2_hmac('sha256', password.encode('utf-8'), salt, 100000)
    return salt.hex() + ":" + key.hex()


def verify_password(password: str, hashed: str) -> bool:
    """Verify password against a pbkdf2 hash string."""
    try:
        salt_hex, key_hex = hashed.split(":")
        salt = bytes.fromhex(salt_hex)
        key = bytes.fromhex(key_hex)
        new_key = hashlib.pbkdf2_hmac('sha256', password.encode('utf-8'), salt, 100000)
        return key == new_key
    except Exception:
        return False