攻防世界-精选免费训练题-rsa | Crypto

利用下面的命令可以解出公钥

openssl rsa -pubin -in .\pubkey.pem -text -noout

from math import isqrt
from pathlib import Path

from Crypto.PublicKey import RSA


def fermat_factor(n: int) -> tuple[int, int]:
    x = isqrt(n)
    if x * x < n:
        x += 1

    while True:
        y2 = x * x - n
        y = isqrt(y2)
        if y * y == y2:
            return x - y, x + y
        x += 1


def strip_pkcs1_v15(block: bytes) -> bytes:
    if len(block) >= 2 and block[0] == 0 and block[1] == 2:
        sep = block.find(b"\x00", 2)
        if sep != -1:
            return block[sep + 1 :]
    return block.lstrip(b"\x00")


def extract_flag(data: bytes) -> str:
    start = data.find(b"flag{")
    if start != -1:
        end = data.find(b"}", start)
        if end != -1:
            return data[start : end + 1].decode()
    return data.decode(errors="ignore").strip()


def main() -> None:
    base = Path(__file__).resolve().parent
    public_key = RSA.import_key((base / "pubkey.pem").read_bytes())
    n = public_key.n
    e = public_key.e

    p, q = fermat_factor(n)
    phi = (p - 1) * (q - 1)
    d = pow(e, -1, phi)

    ciphertext = int.from_bytes((base / "flag.enc").read_bytes(), "big")
    plaintext_int = pow(ciphertext, d, n)
    block = plaintext_int.to_bytes((n.bit_length() + 7) // 8, "big")
    message = strip_pkcs1_v15(block)

    print(extract_flag(message))


if __name__ == "__main__":
    main()