SameMod

題目如下

{6266565720726907265997241358331585417095726146341989755538017122981360742813498401533594757088796536341941659691259323065631249,773}
{6266565720726907265997241358331585417095726146341989755538017122981360742813498401533594757088796536341941659691259323065631249,839}

message1=3453520592723443935451151545245025864232388871721682326408915024349804062041976702364728660682912396903968193981131553111537349
message2=5672818026816293344070119332536629619457163570036305296869053532293105379690793386019065754465292867769521736414170803238309535

可從中看出n固定，屬於共模攻擊。

當n不變的情況下，知道n, e1, e2, c1, c2可以在不知道d1,d2的情況下，解出m。

首先假設，e1, e2互質，此時則有e1∗s1+e2∗s2=1e1*s1+e2*s2=1。式子中，s1, s2皆為整數，但是一正一負。

通過擴展歐幾里德算法，我們可以得到該式子的一組解(s1,s2)，假設s1為正數,s2為負數.

因為c1=me1modnc1=m^{e1} mod n 和 c2=me2modnc2=m^{e2} mod n，所以(c1s1∗c2s2)modn=((me1modn)s1∗(me2modn)s2)modn(c1^{s1}*c2^{s2}) mod n = ((m^{e1} mod n)^{s1}*(m^{e2} mod n)^{s2}) mod n。

根據模運算性質，可以化簡為(c1s1∗c2s2)modn=((me1modn)s1∗(me2modn)s2)modn=(mc1s1∗c2s2)modn(c1^{s1}*c2^{s2}) mod n = ((m^{e1} mod n)^{s1}*(m^{e2} mod n)^{s2}) mod n = (m^{c1^{s1}*c2^{s2}}) mod n。

代入e1∗s1+e2∗s2=1e1*s1+e2*s2=1，得到(c1s1∗c2s2)modn=(m1)modn(c1^{s1}*c2^{s2}) mod n=(m^1) mod n，再推出$(c1{s1}*c2{s2}) mod n = m mod n。

最後可得出c1s1∗c2s2=mc1^{s1}*c2^{s2} = m。

from gmpy2 import invert

def commonModulusAttack(n, c1, c2, e1, e2): # 共模攻擊腳本
    def egcd(a, b):
        if b == 0:
            return a, 0
        else:
            x, y = egcd(b, a % b)
            return y, x - (a // b) * y

    s = egcd(e1, e2)
    s1 = s[0]
    s2 = s[1]
    if s1 < 0:
        s1 = - s1
        c1 = invert(c1, n)
    elif s2 < 0:
        s2 = - s2
        c2 = invert(c2, n)
    m = pow(c1, s1, n) * pow(c2, s2, n) % n
    return m


(n, e1) = (
    6266565720726907265997241358331585417095726146341989755538017122981360742813498401533594757088796536341941659691259323065631249,
    773)
(n, e2) = (
    6266565720726907265997241358331585417095726146341989755538017122981360742813498401533594757088796536341941659691259323065631249,
    839)
c1 = 3453520592723443935451151545245025864232388871721682326408915024349804062041976702364728660682912396903968193981131553111537349
c2 = 5672818026816293344070119332536629619457163570036305296869053532293105379690793386019065754465292867769521736414170803238309535

result = commonModulusAttack(n, c1, c2, e1, e2)
print(result)   # 1021089710312311910410111011910111610410511010710511610511511211111511510598108101125
# flag=long_to_bytes(result)
result = str(result)
flag = ""
i = 0
while i < len(result):
    if result[i] == '1':
        c = chr(int(result[i:i + 3]))
        i += 3
    else:
        c = chr(int(result[i:i + 2]))
        i += 2
    flag += c
print(flag)

另外這一題一開始將結果轉bytes，但發現不能轉，觀察可以發現是分組的ascii，把字串切割解出flag。

輸出

flag{whenwethinkitispossible}

[网鼎杯 2020 青龙组]you_raise_me_up

題目如下

#!/usr/bin/env python
# -*- coding: utf-8 -*-
from Crypto.Util.number import *
import random

n = 2 ** 512
m = random.randint(2, n-1) | 1
c = pow(m, bytes_to_long(flag), n)
print('m = ' + str(m))
print('c = ' + str(c))

求離散對數問題，直接硬解。

import sympy
from Crypto.Util.number import *

m = 391190709124527428959489662565274039318305952172936859403855079581402770986890308469084735451207885386318986881041563704825943945069343345307381099559075
c = 6665851394203214245856789450723658632520816791621796775909766895233000234023642878786025644953797995373211308485605397024123180085924117610802485972584499
n = 2 ** 512

fl = sympy.discrete_log(n, c, m)
print(long_to_bytes(fl))

取得flag。

[UTCTF2020]basic-crypto

題目給定如下

01010101 01101000 00101101 01101111 01101000 00101100 00100000 01101100 01101111 01101111 01101011 01110011 00100000 01101100 01101001 01101011 01100101 00100000 01110111 01100101 00100000 01101000 01100001 01110110 01100101 00100000 01100001 01101110 01101111 01110100 01101000 01100101 01110010 00100000 01100010 01101100 01101111 01100011 01101011 00100000 01101111 01100110 00100000 01110100 01100101 01111000 01110100 00101100 00100000 01110111 01101001 01110100 01101000 00100000 01110011 01101111 01101101 01100101 00100000 01110011 01101111 01110010 01110100 00100000 01101111 01100110 00100000 01110011 01110000 01100101 01100011 01101001 01100001 01101100 00100000 01100101 01101110 01100011 01101111 01100100 01101001 01101110 01100111 00101110 00100000 01000011 01100001 01101110 00100000 01111001 01101111 01110101 00100000 01100110 01101001 01100111 01110101 01110010 01100101 00100000 01101111 01110101 01110100 00100000 01110111 01101000 01100001 01110100 00100000 01110100 01101000 01101001 01110011 00100000 01100101 01101110 01100011 01101111 01100100 01101001 01101110 01100111 00100000 01101001 01110011 00111111 00100000 00101000 01101000 01101001 01101110 01110100 00111010 00100000 01101001 01100110 00100000 01111001 01101111 01110101 00100000 01101100 01101111 01101111 01101011 00100000 01100011 01100001 01110010 01100101 01100110 01110101 01101100 01101100 01111001 00101100 00100000 01111001 01101111 01110101 00100111 01101100 01101100 00100000 01101110 01101111 01110100 01101001 01100011 01100101 00100000 01110100 01101000 01100001 01110100 00100000 01110100 01101000 01100101 01110010 01100101 00100000 01101111 01101110 01101100 01111001 00100000 01100011 01101000 01100001 01110010 01100001 01100011 01110100 01100101 01110010 01110011 00100000 01110000 01110010 01100101 01110011 01100101 01101110 01110100 00100000 01100001 01110010 01100101 00100000 01000001 00101101 01011010 00101100 00100000 01100001 00101101 01111010 00101100 00100000 00110000 00101101 00111001 00101100 00100000 01100001 01101110 01100100 00100000 01110011 01101111 01101101 01100101 01110100 01101001 01101101 01100101 01110011 00100000 00101111 00100000 01100001 01101110 01100100 00100000 00101011 00101110 00100000 01010011 01100101 01100101 00100000 01101001 01100110 00100000 01111001 01101111 01110101 00100000 01100011 01100001 01101110 00100000 01100110 01101001 01101110 01100100 00100000 01100001 01101110 00100000 01100101 01101110 01100011 01101111 01100100 01101001 01101110 01100111 00100000 01110100 01101000 01100001 01110100 00100000 01101100 01101111 01101111 01101011 01110011 00100000 01101100 01101001 01101011 01100101 00100000 01110100 01101000 01101001 01110011 00100000 01101111 01101110 01100101 00101110 00101001 00001010 01010100 01101101 01010110 00110011 01001001 01000111 01001110 01101111 01011001 01010111 01111000 01110011 01011010 01010111 00110101 01101110 01011010 01010011 01000101 01100111 01010001 00110010 01000110 01110101 01001001 01001000 01101100 01110110 01100100 01010011 01000010 01101101 01100001 01010111 01100100 00110001 01100011 01101101 01010101 01100111 01100010 00110011 01010110 00110000 01001001 01001000 01100100 01101111 01011001 01011000 01010001 01101110 01100011 01111001 01000010 01101110 01100010 00110010 01101100 01110101 01011010 01111001 01000010 01110110 01100010 01101001 01000010 01101111 01011010 01011000 01001010 01101100 01010000 01111001 01000010 01001010 01100100 01000011 01000010 01110011 01100010 00110010 00111001 01110010 01100011 01111001 01000010 01110011 01100001 01010111 01110100 01101100 01001001 01001000 01010010 01101111 01011010 01010011 01000010 01110011 01011010 01011000 01010010 00110000 01011010 01011000 01001010 01111010 01001001 01000111 01000110 01111001 01011010 01010011 01000010 01111010 01100001 01000111 01101100 01101101 01100100 01000111 01010110 01101011 01001001 01000111 01001010 00110101 01001001 01001000 01001110 01110110 01100010 01010111 01010101 01100111 01011001 00110010 00111001 01110101 01100011 00110011 01010010 01101000 01100010 01101110 01010001 01110101 01001001 01000011 01101000 01101111 01100001 01010111 00110101 00110000 01001111 01101001 01000010 00110101 01100010 00110011 01010101 01100111 01100010 01010111 01101100 01101110 01100001 01001000 01010001 01100111 01100100 00110010 01000110 01110101 01100100 01000011 01000010 00110000 01100010 01111001 01000010 01111010 01100100 01000111 01000110 01111001 01100100 01000011 01000010 01110011 01100010 00110010 00111001 01110010 01100001 01010111 00110101 01101110 01001001 01001000 01010110 01110111 01001001 01000110 01001010 01110110 01100010 01010111 01000110 01110101 01001001 01001000 01000010 01101100 01100010 00110011 01000010 01110011 01011010 01010011 01101011 01110101 01000011 01101101 01110100 00110010 01011001 01101110 01001110 01111000 01100011 01101101 01010001 01110011 01001001 01000111 01101100 00110101 01011010 01010011 01100100 01101001 01100010 01111001 01000010 01110010 01100100 01101110 01100100 00110101 01011001 00110010 01010001 01100111 01011010 01001000 01001010 01110110 01011001 01101101 00111000 01101000 01001001 01000110 01101000 00110101 01011010 01111001 01000010 01110111 01100101 01010111 01001001 01100111 01011010 01001000 01001010 01110110 01001001 01001000 01000010 01111010 01100101 01000111 01110100 00110010 01001001 01000011 01101000 01110010 01100101 01000111 00110100 01100111 01100100 00110010 01110100 01110000 01100010 01000111 00111000 01100111 01011010 01001000 01001010 01110110 01001001 01001000 01001010 01110010 01011001 01101101 00110101 01110110 01011001 00110010 01010001 01110101 01001100 01101001 00110100 01110000 01001001 01001000 01110000 01110010 01011001 01101101 01010001 00110110 01001001 01000111 01110011 01100111 01011001 00110010 01010110 01110011 01011001 00110010 01010010 01111010 01011010 01000111 01010110 01101011 01100011 00110011 01101100 00110100 01001001 01000111 00110001 01111010 01100101 01101110 01001010 01110110 01011001 01101001 00110100 01100111 01010101 00110011 01100111 01100111 01011010 01001000 01001010 01110110 01001001 01001000 01000010 00110101 01100100 01101110 01011010 00110101 01011010 00110011 01001110 00110100 01100011 01010011 01000010 01101011 01100010 00110010 01101000 01101011 01001100 01000011 01000010 01010100 01001010 00110010 01011010 01110110 01001001 01000111 01010010 01110010 01100100 01010111 00111001 00110100 01001001 01001000 01100100 01110000 01001001 01001000 01100100 01110110 01011001 00110010 01001110 01110010 01100011 01010111 00111000 01100111 01100001 00110011 01101000 01110101 01001001 01000111 01001010 01110110 01100101 01101110 01011010 01110010 01100010 01010111 00111001 01110101 01001001 01000111 00111001 01101101 01100010 00110010 01001010 01110000 01001001 01000111 01110100 00110010 01100101 01101110 01001010 01110010 01100010 01000111 00111001 01101011 01100011 00110010 00110000 01100111 01100010 01011000 01001010 01110010 01011001 01101101 01110100 01110100 01011010 01000111 00111001 01101001 01001001 01000111 01100100 01111010 01011010 01001000 01001001 01100111 01100001 01111001 01000010 01110100 01100101 01010111 01001010 01101001 01100010 00110010 01001110 00110110 01100101 01011000 01101000 01110101 01100010 00110011 01101000 01110100 01100010 01111001 01000010 01101011 01100101 01010011 01000010 01110010 01001001 01000111 00110101 01111010 01100011 01001000 01000010 01110110 01011001 01101101 00111001 00110100 01011010 01000011 01000010 01110100 01100011 01101101 01110100 01101001 01100001 00110010 00110001 01101011 01100010 00110010 01001001 01100111 01001100 01010011 01000010 00110001 01100101 01001000 01101100 01101110 01100101 01000011 01000010 01110010 01011001 01111001 01000010 01110010 01001001 01000111 01001110 01101100 01100010 01000111 01001110 01101011 01100011 00110010 01010010 01101100 01011010 01001000 01001110 00110101 01100101 01000011 01000010 01110100 01100011 00110011 01110000 01111001 01100010 00110010 01001001 01110101 01001001 01000101 00110001 01110010 01100101 01000011 01000010 01110000 01100101 01010111 01010101 01100111 01100011 01001000 01001110 00110100 01100010 01101001 01000010 01101011 01100011 01101101 00111000 01100111 01100011 01001000 01001110 00110100 01100001 00110011 01011001 01100111 01100011 01001000 01011010 01110010 01100011 01010100 00111000 01100111 01100011 01101110 01001110 00110100 01011010 01000100 01101111 01100111 01010010 00110010 00111000 01100111 01100100 01011000 01101000 00110101 01011010 01111001 01000010 01101011 01100011 01101101 01110100 01101011 01001001 01000111 01010010 01111001 01100010 01111001 01000010 01110111 01100100 01101101 01110100 01111000 01001001 01001000 01001110 01101010 01001001 01001000 01000110 00110101 01100011 00110011 01101000 01111000 01001001 01000111 01010010 00110101 01001001 01000111 01111000 01110110 01001001 01001000 01101100 01110111 01001001 01000111 01010010 01111001 01100010 01111001 01000010 01110111 01100101 01010111 01001010 00110011 01100001 00110010 01010001 01100111 01011010 01010111 01010010 01110111 01100100 01101101 01110100 01111000 01100101 01111001 00110100 01110101 01001100 01101110 00110000 01100111 01001100 01010011 01000010 01101110 01100011 01101110 01001110 01110100 01100011 01101001 01000010 00110011 01100010 00110010 01110100 00110100 01011001 01111001 01000010 01101011 01100011 01101101 01110100 01101011 01001001 01001000 01001110 01110111 01001001 01000111 01101100 00110101 01011010 01010011 01000010 01101010 01100010 00110010 00111000 01100111 01011010 01001000 01001010 01110010 01011010 01000011 01000010 00110110 01100001 00110010 01010010 01101011 01100010 00110010 01001010 00110100 01001100 01000011 01000010 01110000 01100101 01010111 01010101 01100111 01100100 01011000 01101000 00110101 01011010 01111001 01000010 01101110 01100011 01101101 01110100 01101011 01001001 01000111 01010010 01111001 01100010 01111001 01000010 01110100 01100101 01010111 01001010 01101001 01100010 00110010 01001110 00110110 01100101 01011000 01101000 01110101 01100010 00110011 01101000 01110100 01100010 00110010 01001101 01100111 01100011 01001000 01101100 01101001 01001001 01000111 01010101 01110011 01001001 01000111 01010001 01110011 01001001 01001000 01000001 01110011 01001001 01001000 01011001 01100111 01100001 01111001 01110111 01100111 01100001 00110011 01101000 01110101 01001001 01001000 01000101 01100111 01100001 00110010 01001010 01110110 01001100 01101001 01000010 01001010 01100101 01010111 01010101 01100111 01100010 01010111 01110100 00110100 01001001 01001000 01110000 01101001 01100101 01010111 01111000 01110010 01100010 01001000 01011010 01110000 01001001 01000111 01100100 00110101 01011001 01101110 01010101 01100111 01100101 01010111 01010110 01101011 01001001 01000111 01010010 01111001 01100010 01111001 01000010 01101001 01100010 00110011 01100100 01110010 01100011 00110011 01101000 01111010 01100101 01001000 01000101 01100111 01100010 01011000 01001010 01110010 01011001 01101101 01110100 01110100 01011010 01000111 00111001 01101001 01011001 01111001 01000010 01110011 01100001 01010011 01000010 01101001 01100010 00110011 01110000 00110010 01100001 00110010 00110001 01111010 01100101 01001000 01000101 01100111 01011010 01001000 01001010 01110110 01100100 01111001 01000010 01110010 01100101 01000111 00110100 01100111 01100011 00110011 01101000 01110111 01100010 00110010 01001010 01101001 01100011 00110011 01101000 01111000 01001001 01000111 00110001 00110101 01100100 00110011 01100100 00110101 01100101 01000011 01000010 01101110 01100101 01010111 01001010 01110101 01011001 01111001 01000010 01111010 01100101 01000011 01000010 01101011 01100011 01101101 00111000 01100111 01010100 00110011 01101000 01111000 01100100 01101110 01001110 01101010 01100011 01101001 01000010 00110010 01100001 00110011 01101000 01111000 01011010 01010111 01110100 01111000 01100010 01111001 00110100 01100111 01010011 00110011 01101000 00110101 01011010 01001000 01001010 01110110 01011001 01101001 01000010 01111000 01011001 01101101 00111001 01110010 01011010 01000011 01000010 00110011 01100010 00110010 01010010 01111001 01100101 01010111 00110100 01100111 01100011 00110010 01001101 01100111 01011010 01001000 01101011 01100111 01011010 01010111 01001110 01110110 01001001 01001000 01000010 01101001 01100010 00110010 01000110 01101100 01100010 00110011 01101000 01110100 01100001 01010011 01000010 01110010 01100101 01000111 01110100 00110010 01100001 01010111 01001110 01111010 01011001 01111010 01101111 01100111 01011010 00110010 00111000 01100111 01100100 01011000 01101000 00110101 01011010 01111001 01000010 01101011 01100011 01101101 01110100 01101011 01001001 01000011 01100100 01110110 01001010 01111001 01000010 01101010 01100011 01101110 01101100 01101110 01011001 01111001 01000010 01101100 01100101 01101001 01000010 00110011 01100101 01010111 01001110 01101011 01001001 01001000 01101100 01110111 01011010 01000111 00111001 00110100 01001001 01001000 01001110 00110100 01001001 01000111 01010010 01111001 01100010 01111001 01000010 01110010 01100100 01101110 01110000 01111001 01100001 00110010 01111000 01110110 01011010 01000011 01110111 01100111 01011001 00110011 01101011 01100111 01011010 01001000 01001010 01110010 01011010 01000011 01100100 01101010 01001001 01001000 01110000 01101001 01100101 01010111 01111000 01110010 01100010 01001000 01011010 01110000 01001001 01000111 01010010 01111001 01100010 01111001 01000010 00110011 01100101 01010111 01001110 01101011 01001001 01000111 00110001 00110101 01100100 00110011 01100100 00110101 01100101 01000011 01000010 01110100 01100011 01101101 01110100 01101001 01100001 00110010 00110001 01101011 01100010 00110010 01001001 01100111 01100011 00110011 01100111 01100111 01011010 01001000 01001010 01110110 01001001 01000111 01010010 01110110 01100001 01000111 01010001 01110011 01001001 01001000 01000010 00110101 01100100 01101110 01011010 00110101 01011010 00110010 00111001 01110101 01001001 01000111 01111000 01110000 01001001 01000011 01100100 01101011 01001010 01111001 01110111 01100111 01100001 00110011 01101000 01110101 01001001 01000111 01001110 00110101 01001001 01001000 01101100 00110100 01001100 01101001 01000010 01011010 01100101 01000111 00110001 01110110 01001001 01000111 01101100 00110101 01011010 01010011 01000010 00110001 01100101 01001000 01101100 01101110 01001001 01000111 01110011 01100111 01100011 01000111 00111001 01101110 01001001 01000111 00110001 01111001 01100001 00110010 01001010 01110010 01100010 01010111 01010010 01110110 01011001 01101101 01001101 01110011 01001001 01000111 01101100 00110101 01011010 01010011 01000010 01110100 01100001 00110011 01100111 01100111 01100011 00110011 01101000 01110111 01100010 00110010 01001001 01100111 01011010 01001000 01001010 01110110 01001001 01000111 01001010 01110110 01011001 00110010 01010001 01100111 01100101 01011000 01000001 01100111 01011010 01001000 01001010 01110110 01001001 01000111 01100100 00110101 01011001 01101101 00110101 01101010 01001001 01000111 01111000 01110010 01011001 00110010 00111001 01110101 01001001 01001000 01101100 00110100 01001001 01000111 00110001 00110101 01100100 00110011 01100100 00110101 01100101 01000011 01000010 01101110 01100101 01010111 01001010 01110101 01011001 01111001 01000010 01101011 01100011 01101101 01110100 01101011 01001001 01000111 01001110 01111001 01100101 01010111 01100011 01100111 01011010 01011000 01101111 01100111 01100011 00110011 01100111 01100111 01011010 01001000 01001010 01110110 01001001 01000101 00111001 00110100 01100011 01011000 01011010 01111010 01011001 00110011 01001001 01100111 01100100 01101101 01110100 00110100 01100011 01010111 01010110 01110010 01100011 01010111 00111000 01110101 01000011 01101110 01001010 01101110 01100001 01000111 00110101 00110100 01100011 00110010 01010010 01101101 01100101 01011000 01001110 01101011 01100100 01000111 01100100 01101111 01100100 01010011 01000101 01100111 01100011 01010111 01100100 01101101 01001001 01000111 01101100 01111010 01011001 01010111 01110011 01100111 01011001 00110011 01010010 01101111 01100100 01001000 01010110 01110000 01100001 00110010 01010101 01100111 01011010 01000111 01101100 01110010 01001001 01001000 01110000 01110010 01100010 01101110 01010010 01101111 01100001 01000111 01110100 00110100 01001001 01001000 01001010 00110100 01100011 01010111 01111000 01101011 01011010 00110010 00110101 00110100 01100011 00110010 01111000 01110000 01100011 01010011 01000010 01111001 01100001 01011000 01001110 00110101 01100101 01010111 01110100 01101111 01100010 01101101 01110011 01110101 01001001 01000111 01101100 01110010 01100101 01000111 01110011 01100111 01100100 01001000 01010101 01100111 01100011 01111001 01000010 01101010 01100101 01011000 01001110 01110101 01001001 01000111 01001110 01101110 01100101 01000011 01000010 01111010 01100101 01011000 01101011 01100111 01100011 01010111 01100100 01101101 01100101 01000011 01000010 01110000 01100011 00110011 01101000 01101100 01001001 01000111 01110100 01101010 01011001 00110010 01100100 00110100 01011010 01001000 01010101 00110110 01001001 01000111 01011010 01101011 01011001 00110011 01101100 01111010 01100010 01101110 01110100 01101111 01001101 01001000 01011010 01100110 01011010 01000111 01101011 00110000 01011010 01001000 01010110 01100110 01100100 01101101 01101011 00110000 01011010 01000110 00111001 00110000 01011000 00110011 01001001 00110000 01100101 01011000 01101100 01100110 01100011 01101110 01101000 01111000 01100010 01000111 01010001 01110111 01100110 01010011 00110100 01100111 01100011 01010111 01100100 01101101 01001001 01001000 01011010 00110000 01100101 01011000 01101011 01100111 01011001 00110011 01010010 01101111 01011010 01010011 01000010 01101011 01100001 01011000 01001110 01101011 01001001 01001000 01001101 01100111 01100101 01010111 01100100 01101011 01001001 01000111 01100100 01101010 01001001 01001000 01001010 00110100 01100011 01010111 01111000 01101011 01011010 00110010 00110101 00110100 01100011 00110010 01111000 01110000 01100011 01010011 01000010 00110000 01100100 01010011 01000010 01110111 01011010 01101110 01010110 01101011 01001001 01001000 01110000 01101101 01100100 01001000 01101100 01101100 01100100 01000111 01101000 01110101 01001001 01000111 01100100 01101010 01011001 01111001 01000010 01101011 01100001 01011000 01010010 00110001 01001001 01001000 01010110 01101110 01100101 01000111 01010001 01100111 01011010 00110010 01001101 01100111 01100101 01101110 01001110 00110001 01100100 01001000 01001001 01100111 01011001 01101101 01101000 01101110 01100100 01101110 01101100 01110010 01011010 01010111 00110101 01110010 01001100 01000011 01000010 01111010 01100001 01000111 01010101 01100111 01100100 01000111 01010001 01100111 01100101 01000111 01110100 01111010 01100101 01011000 01101100 01111000 01001001 01001000 01010010 00110001 01001001 01000111 01101000 01101110 01011010 01000011 01000010 00110001 01011010 01111001 01000010 00110110 01100011 00110010 01010101 01100111 01100011 00110010 01001110 01101011 01100001 00110011 01100111 01100111 01100011 00110011 01101100 00110101 01001100 01101001 01000010 01110000 01011010 00110010 01111000 01110010 01001001 01001000 01000110 01101110 01011010 01101001 01000010 01110010 01100001 01001000 01000010 01101110 01100011 01010111 01110100 01101100 01001001 01000111 01010010 01110000 01100001 01111001 01000010 01111001 01100001 01011000 01001110 00110101 01100101 01010111 01110100 01101111 01100010 01101101 01110011 01101000

八個二進為一組，感覺起來就是byte，寫一下轉碼腳本。

from Crypto.Util.number import *

f = open('G:\\project\\buuctf\\attachment.txt', 'r')
line = f.readline()
byte = str.split(line)

str = b''
for i in byte:
    str+=long_to_bytes(int(i,base=2))

print(str)

輸出以下內容

b"Uh-oh, looks like we have another block of text, with some sort of special encoding. Can you figure out what this encoding is? (hint: if you look carefully, you'll notice that there only characters present are A-Z, a-z, 0-9, and sometimes / and +. See if you can find an encoding that looks like this one.)\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"

接下來依據提示猜出是base64，破解後得到下一串亂碼。

New challenge! Can you figure out what's going on here? It looks like the letters are shifted by some constant. (hint: you might want to start looking up Roman people).

kvbsqrd, iye'bo kvwycd drobo! Xyg pyb dro psxkv (kxn wkilo dro rkbnocd...) zkbd: k celcdsdedsyx mszrob. Sx dro pyvvygsxq dohd, S'fo dkuox wi wocckqo kxn bozvkmon ofobi kvzrklodsm mrkbkmdob gsdr k mybboczyxnoxmo dy k nsppoboxd mrkbkmdob - uxygx kc k celcdsdedsyx mszrob. Mkx iye psxn dro psxkv pvkq? rsxd: Go uxyg drkd dro pvkq sc qysxq dy lo yp dro pybwkd edpvkq{...} - grsmr wokxc drkd sp iye coo drkd zkddobx, iye uxyg grkd dro mybboczyxnoxmoc pyb e, d, p, v k, kxn q kbo. Iye mkx zbylklvi gybu yed dro bowksxsxq mrkbkmdobc li bozvkmsxq drow kxn sxpobbsxq mywwyx gybnc sx dro Oxqvscr vkxqekqo. Kxydrob qbokd wodryn sc dy eco pboaeoxmi kxkvicsc: go uxyg drkd 'o' crygc ez wycd ypdox sx dro kvzrklod, cy drkd'c zbylklvi dro wycd mywwyx mrkbkmdob sx dro dohd, pyvvygon li 'd', kxn cy yx. Yxmo iye uxyg k pog mrkbkmdobc, iye mkx sxpob dro bocd yp dro gybnc lkcon yx mywwyx gybnc drkd cryg ez sx dro Oxqvscr vkxqekqo.rghnxsdfysdtghu! qgf isak cthtuike dik zknthhkx rxqldgnxsliq risyykhnk. ikxk tu s cysn cgx syy qgfx isxe kccgxdu: fdcysn{h0v_di4du_vi4d_t_r4yy_rxqld0}. qgf vtyy cthe disd s ygd gc rxqldgnxsliq tu pfud zftyethn gcc ditu ugxd gc zsutr bhgvykenk, she td xksyyq tu hgd ug zse scdkx syy. iglk qgf khpgqke dik risyykhnk!"

原本以為是簡單的凱撒密碼(rot13)，做完發現不是，丟 https://quipqiup.com/ 做詞頻分析，找到下一步做法。

alright, you're almost there! Now for the final (and maybe the hardest...) part: a substitution cipher. 

In the following tezt, I've taken my message and replaced every alphabetic character with a correspondence to a different character - known as a substitution cipher. 

Can you find the final flag? hint: We know that the flag is going to be of the format utflag{...} - which means that if you see that pattern, you know what the correspondences for u, t, f, l a, and g are. 

You can probably work out the remaining characters by replacing them and inferring common words in the English language. 

Another great method is to use frequency analysis: we know that 'e' shows up most often in the alphabet, so that's probably the most common character in the tezt, followed by 't', and so on. 

Once you know a few characters, you can infer the rest of the words based on common words that show up in the English language.

hwzdnitvoitjwzk! gwv yiqa sjzjkyau tya padjzzan hngbtwdnibyg hyiooazda. yana jk i soid swn ioo gwvn yinu asswntk: vtsoid{z0l_ty4tk_ly4t_j_h4oo_hngbt0}. gwv ljoo sjzu tyit i owt ws hngbtwdnibyg jk fvkt pvjoujzd wss tyjk kwnt ws pikjh rzwloauda, izu jt naioog jk zwt kw piu istan ioo. ywba gwv azfwgau tya hyiooazda!

取最後一行，輸入 vtsoid=utflag 條件後再讓他繼續跑詞頻分析。

utflag{n0w_th4ts_wh4t_i_c4ll_crypt0}. you will find that a lot of cryptography is just building off this sort of basic knowledge, and it really is not so bad after all. hope you enjoyed the challenge!

flag{n0w_th4ts_wh4t_i_c4ll_crypt0}

[NPUCTF2020]EzRSA

題目給定如下

from gmpy2 import lcm , powmod , invert , gcd , mpz
from Crypto.Util.number import getPrime
from sympy import nextprime
from random import randint
p = getPrime(1024)
q = getPrime(1024)
n = p * q
gift = lcm(p - 1 , q - 1)
e = 54722
flag = b'NPUCTF{******************}'
m = int.from_bytes(flag , 'big')
c = powmod(m , e , n)
print('n: ' , n)
print('gift: ' , gift)
print('c: ' , c)

#n:  17083941230213489700426636484487738282426471494607098847295335339638177583685457921198569105417734668692072727759139358207667248703952436680183153327606147421932365889983347282046439156176685765143620637107347870401946946501620531665573668068349080410807996582297505889946205052879002028936125315312256470583622913646319779125559691270916064588684997382451412747432722966919513413709987353038375477178385125453567111965259721484997156799355617642131569095810304077131053588483057244340742751804935494087687363416921314041547093118565767609667033859583125275322077617576783247853718516166743858265291135353895239981121
#gift:  2135492653776686212553329560560967285303308936825887355911916917454772197960682240149821138177216833586509090969892419775958406087994054585022894165950768427741545736247918410255804894522085720642952579638418483800243368312702566458196708508543635051350999572787188236243275631609875253617015664414032058822919469443284453403064076232765024248435543326597418851751586308514540124571309152787559712950209357825576896132278045112177910266019741013995106579484868768251084453338417115483515132869594712162052362083414163954681306259137057581036657441897428432575924018950961141822554251369262248368899977337886190114104
#c:  3738960639194737957667684143565005503596276451617922474669745529299929395507971435311181578387223323429323286927370576955078618335757508161263585164126047545413028829873269342924092339298957635079736446851837414357757312525158356579607212496060244403765822636515347192211817658170822313646743520831977673861869637519843133863288550058359429455052676323196728280408508614527953057214779165450356577820378810467527006377296194102671360302059901897977339728292345132827184227155061326328585640019916328847372295754472832318258636054663091475801235050657401857262960415898483713074139212596685365780269667500271108538319

題目給定的資訊有n, c, e 和 p-1 與 q-1 的最小公倍數。

先用factordb分解n，就可以找到p, q了。

由於e和phi不互質，gcd(e,phi)=2gcd(e, phi) = 2。

所以將c=memodnc = m^e mod n變形成c=((m2)e/2)modnc = ((m^2)^e/2) mod n，把m2m^2當成密文，解密出m2m^2之後再開根號得到flag就好了。

from Crypto.Util.number import *
import gmpy2

n = 17083941230213489700426636484487738282426471494607098847295335339638177583685457921198569105417734668692072727759139358207667248703952436680183153327606147421932365889983347282046439156176685765143620637107347870401946946501620531665573668068349080410807996582297505889946205052879002028936125315312256470583622913646319779125559691270916064588684997382451412747432722966919513413709987353038375477178385125453567111965259721484997156799355617642131569095810304077131053588483057244340742751804935494087687363416921314041547093118565767609667033859583125275322077617576783247853718516166743858265291135353895239981121
e = 54722
c = 3738960639194737957667684143565005503596276451617922474669745529299929395507971435311181578387223323429323286927370576955078618335757508161263585164126047545413028829873269342924092339298957635079736446851837414357757312525158356579607212496060244403765822636515347192211817658170822313646743520831977673861869637519843133863288550058359429455052676323196728280408508614527953057214779165450356577820378810467527006377296194102671360302059901897977339728292345132827184227155061326328585640019916328847372295754472832318258636054663091475801235050657401857262960415898483713074139212596685365780269667500271108538319
p = 161136651053130509602530659420755324119806487925813087617466818245407407797561810253722204813002837916779909309520498985459703212021249251124954613236122142746302911323565396331355397916764254680629384957057354297855676493062493901977415968666512459829211010720514167083018352796496733697235524845188512914793
q = 106021448991021391444550749375115277080844281746248845802565680557785009341952320484175568763707424932172033597514861602114171459176440279045761846695231788376075050452154924141266290931413542110639081792550648106240966552406813059396358355737185354885474455248579946190266152416149137616855791805617206153497

phi = (p - 1) * (q - 1)
e = e // 2
d = gmpy2.invert(e, phi)
m = gmpy2.iroot(pow(c, d, n), 2)[0]
flag = long_to_bytes(int(m))
print(flag)

輸出

b'NPUCTF{diff1cult_rsa_1s_e@sy}'

[WUSTCTF2020]dp_leaking_1s_very_d@angerous

題目如下

e = 65537
n = 156808343598578774957375696815188980682166740609302831099696492068246337198792510898818496239166339015207305102101431634283168544492984586566799996471150252382144148257236707247267506165670877506370253127695314163987084076462560095456635833650720606337852199362362120808707925913897956527780930423574343287847
c = 108542078809057774666748066235473292495343753790443966020636060807418393737258696352569345621488958094856305865603100885838672591764072157183336139243588435583104423268921439473113244493821692560960443688048994557463526099985303667243623711454841573922233051289561865599722004107134302070301237345400354257869
dp = 734763139918837027274765680404546851353356952885439663987181004382601658386317353877499122276686150509151221546249750373865024485652349719427182780275825

dp的意思是d mod (p-1)，用來快速解密用的，但一個dp好像不能解，沒琢磨出東西來，就直接用n拆p, q，暴力硬做了。

from gmpy2 import *
from Crypto.Util.number import *

e = 65537
n = 156808343598578774957375696815188980682166740609302831099696492068246337198792510898818496239166339015207305102101431634283168544492984586566799996471150252382144148257236707247267506165670877506370253127695314163987084076462560095456635833650720606337852199362362120808707925913897956527780930423574343287847
c = 108542078809057774666748066235473292495343753790443966020636060807418393737258696352569345621488958094856305865603100885838672591764072157183336139243588435583104423268921439473113244493821692560960443688048994557463526099985303667243623711454841573922233051289561865599722004107134302070301237345400354257869
dp = 734763139918837027274765680404546851353356952885439663987181004382601658386317353877499122276686150509151221546249750373865024485652349719427182780275825

p = 12204917011499204793467396627331950459243603269732530719870032567474409945243640569351016419835483810515390876443640549604664275934407520354979414742015923
q = 12847964754765427496399764780328918622503990027015223921752369659611143245908239173177604049265523011184163182090867099853786582101440246414647619495980989

phi = (p - 1) * (q - 1)
d = invert(e, phi)
m = pow(c, d, n)
flag = long_to_bytes(m)
print(flag)

輸出

b'wctf2020{dp_leaking_1s_very_d@angerous}'

dp_leaking_1s_very_d@angerous，糟…糟糕，dp洩漏到底是哪個部份危險，我去看別人的題解好了。

懂了，知道n, e, dp之後，可以快速求出p, q，我把推導抄下來。

φ(N)=(p−1)∗(q−1)ed≡1(modφ(N))ed=1+kφ(N)ed=1+k∗(p−1)∗(q−1)ed≡1(modp−1)dp=ddp≡d(modp−1)dp∗e≡ed≡1(modp−1)dp∗e=k(p−1)+1dp∗e−1=k(p−1)φ(N)=(p−1)∗(q−1)\\ ed≡1(modφ(N))\\ ed=1+kφ(N)\\ ed=1+k∗(p−1)∗(q−1)\\ ed≡1(modp−1)\\ dp=d%(p−1)\\ dp≡d(modp−1)\\ dp∗e≡ed≡1(modp−1)\\ dp∗e=k(p−1)+1\\ dp∗e−1=k(p−1)

而未知數k可以被爆破。

def solve_dp(dp, e, n):
    for i in range(1, dp * e):
        if (dp * e - 1) % i == 0:
            p = (dp * e - 1) // i + 1
            if n % p == 0:
                print(p)
                q = n // p
                return p, q

在n未知可以被哪些數字分解的情況下，感覺滿好用的，我跳過步驟了。

[BJDCTF2020]Polybius

題目給定如下

密文：ouauuuoooeeaaiaeauieuooeeiea
hint：VGhlIGxlbmd0aCBvZiB0aGlzIHBsYWludGV4dDogMTQ=
flag:解出明文后，请加上BJD{}

先以Polybius crypto進行搜尋，找到相關線索。

The Polybius square, also known as the Polybius checkerboard, is a device invented by the ancient Greeks Cleoxenus and Democleitus, and made famous by the historian and scholar Polybius. The device is used for fractionating plaintext characters so that they can be represented by a smaller set of symbols, which is useful for telegraphy, steganography, and cryptography. The device was originally used for fire signalling, allowing for the coded transmission of any message, not just a finite amount of predetermined options as was the convention before. --維基百科

然後hint中有個=先盲猜是base64，解密成ascii後得到The length of this plaintext: 14的資訊。

密文中的aeiou剛好是五個母音，盲猜為行列，但依據一般的解碼方式沒辦法解出來，最後去找了wp才發現是硬爆。

wp

import itertools
key = []
cipher = "ouauuuoooeeaaiaeauieuooeeiea"
for i in itertools.permutations('aeiou', 5):
    key.append(''.join(i))
for each in key:
    temp_cipher = ""
    result = ""
    for temp in cipher:
        temp_cipher += str(each.index(temp))    
        #這裡是將字母的表換成數字的表以便後續計算
    for i in range(0,len(temp_cipher),2):
        current_ascii = int(temp_cipher[i])*5+int(temp_cipher[i+1])+97
        #因为棋盘密码是采用两位一起表示一个字母
        if current_ascii>ord('i'):
            current_ascii+=1
        result += chr(current_ascii)
    if "flag" in result:
        print(each,result)