文章 - [NSSRound#11 Basic]ez_signin

Problem: [NSSRound#11 Basic]ez_signin

from pwn import *
from gmpy2 import *
from Crypto.Util.number import *
#------------ 交互部分 ------------
host = 'node4.anna.nssctf.cn'
port = 28223
conn = remote(host, port)

def interact_with_server(conn):
    data1 = conn.recvline().decode()
    data2 = conn.recvline().decode()
    data3 = conn.recvline().decode()
    data4 = conn.recvline().decode()

    num1 = int(re.findall(r'num1= (\d+)', data1)[0])
    num2 = int(re.findall(r'num2= (\d+)', data2)[0])
    n = int(re.findall(r'n= (\d+)', data3)[0])
    c = int(re.findall(r'c= (\d+)', data4)[0])
    return num1, num2, n, c


# ------------ 解密部分 ------------
num1, num2, n, c = interact_with_server(conn)
e = 65536

p = gcd(n,(num1 + num2 ) % n)
q = n//p

cs = [c]

def rabin_decrypt(c,p,q):
    mp = pow(c, (p + 1) // 4, p)
    mq = pow(c, (q + 1) // 4, q)

    yp = inverse(p,q)
    yq = inverse(q,p)

    r = (yp * p * mq + yq * q * mp) % n
    r_ = n - r
    s = (yp * p * mq - yq * q * mp) % n
    s_ = n - s
    return r,r_,s,s_

for i in range(16):
    ps = []

    for c2 in cs:
        r,r_,s,s_ = rabin_decrypt(c2,p,q)
        if r not in ps:
            ps.append(r)
        if r_ not in ps:
            ps.append(r_)
        if s not in ps:
            ps.append(s)
        if s_ not in ps:
            ps.append(s_)
   # print(ps)
    cs = ps

for i in range(len(cs)):
    print(long_to_bytes(cs[i]))