import os
import hashlib
import secrets

def hash_password(password: str) -> str:
    salt = secrets.token_hex(16)
    key = hashlib.pbkdf2_hmac("sha256", password.encode("utf-8"), salt.encode("utf-8"), 100000)
    return f"{salt}${key.hex()}"

def verify_password(stored_password_hash: str, provided_password: str) -> bool:
    try:
        salt, key_hex = stored_password_hash.split("$", 1)
        new_key = hashlib.pbkdf2_hmac("sha256", provided_password.encode("utf-8"), salt.encode("utf-8"), 100000)
        return secrets.compare_digest(new_key.hex(), key_hex)
    except Exception:
        return False