[LitCTF 2023]e的学问

题目分数：439

题目标签： RSAe与 φ(n)不互素

题目描述：

- 题目描述:当e不是65537了，该怎么办呢？
- 出题人：dbuj7flag以NSSCTF{}形式提交

附件：

from Crypto.Util.number import *
m=bytes_to_long(b'xxxxxx')
p=getPrime(256)
q=getPrime(256)
e=74
n=p*q
c=pow(m,e,n)
print("p=",p)
print("q=",q)
print("c=",c)
#p= 86053582917386343422567174764040471033234388106968488834872953625339458483149
#q= 72031998384560188060716696553519973198388628004850270102102972862328770104493
#c= 3939634105073614197573473825268995321781553470182462454724181094897309933627076266632153551522332244941496491385911139566998817961371516587764621395810123

解题：

import gmpy2
from Crypto.Util.number import *

# 当e约去公约数后与phi互素
def decrypt(p, q, e, c):
    n = p * q
    phi = (p - 1) * (q - 1)
    t = gmpy2.gcd(e, phi)
    d = gmpy2.invert(e // t, phi)
    m = pow(c, d, n)
    print(m)
    msg = gmpy2.iroot(m, t)
    print(msg)
    if msg[1]:
        print(long_to_bytes(msg[0]))
e=74
p= 86053582917386343422567174764040471033234388106968488834872953625339458483149
q= 72031998384560188060716696553519973198388628004850270102102972862328770104493
c= 3939634105073614197573473825268995321781553470182462454724181094897309933627076266632153551522332244941496491385911139566998817961371516587764621395810123

decrypt(p, q, e, c)
# LitCTF{e_1s_n0t_@_Prime}