#wanictf2021spring
from Crypto.Util.number import getPrime, bytes_to_long
with open("flag.txt", "rb") as f:
flag = f.read()
p, q = getPrime(1024), getPrime(1024)
N = p * q
M = 2 * p + q
e = 0x10001
def encrypt(plaintext: bytes) -> int:
plaintext = bytes_to_long(plaintext)
c = pow(plaintext, e, N)
return c
if __name__ == "__main__":
c = encrypt(flag)
print(f"{N = }")
print(f"{M = }")
print(f"{e = }")
print(f"{c = }")
with open("output.txt") as f:
N = int(f.readline().strip().split(" = ")[1])
M = int(f.readline().strip().split(" = ")[1])
e = int(f.readline().strip().split(" = ")[1])
c = int(f.readline().strip().split(" = ")[1])
from gmpy2 import isqrt
N = 2*N
p = int((M + isqrt(M**2 - 4*N)) // 2)
q = int((M - isqrt(M**2 - 4*N)) // 2)
N = N // 2
p = p // 2
d = pow(e, -1, (p-1)*(q-1))
m = pow(c, d, N)
print(m.to_bytes(100, "big"))
がもらえる
と考えて phiがわかっているときの素因数分解 をやる
