Crypto CTF 2021 | Do RSA

#cryptoctf2021

#!/usr/bin/env python3

from Crypto.Util.number import *
from math import gcd
from flag import FLAG

def keygen(nbit, dbit):
    assert 2*dbit < nbit
    while True:
        u, v = getRandomNBitInteger(dbit), getRandomNBitInteger(nbit // 2 - dbit)
        p = u * v + 1
        if isPrime(p):
            while True:
                x, y = getRandomNBitInteger(dbit), getRandomNBitInteger(nbit // 2 - dbit)
                q = u * y + 1
                r = x * y + 1
                if isPrime(q) and isPrime(r):
                    while True:
                        e = getRandomNBitInteger(dbit)
                        if gcd(e, u * v * x * y) == 1:
                            phi = (p - 1) * (r - 1)
                            d = inverse(e, phi)
                            k = (e * d - 1) // phi
                            s = k * v + 1
                            if isPrime(s):
                                n_1, n_2 = p * r, q * s
                                return (e, n_1, n_2)

def encrypt(msg, pubkey):
    e, n = pubkey
    return pow(msg, e, n)

nbit, dbit = 1024, 256

e, n_1, n_2 = keygen(nbit, dbit)

FLAG = int(FLAG.encode("utf-8").hex(), 16)

c_1 = encrypt(FLAG, (e, n_1))
c_2 = encrypt(FLAG, (e, n_2))

print('e =', e)
print('n_1 =', n_1)
print('n_2 =', n_2)

print('enc_1 =', c_1)
print('enc_2 =', c_2)

多少特殊な作り方でRSAのインスタンスを2つ作っている