HGAME-CRYPTO Writes up

Crypto

Word count: 472Reading time: 2 min

 2020/02/13   Share

Week 1

签到题 InfantRSA

发现我之前网上抄的脚本不太好用了

from libnum import n2s
def inverse(u, v):
    """The inverse of :data:`u` *mod* :data:`v`."""

    u3, v3 = u, v
    u1, v1 = 1, 0
    while v3 > 0:
        q = u3 // v3
        u1, v1 = v1, u1 - v1*q
        u3, v3 = v3, u3 - v3*q
    while u1<0:
        u1 = u1 + v
    return u1
p = 681782737450022065655472455411
q = 675274897132088253519831953441
e = 13
c = 275698465082361070145173688411496311542172902608559859019841
n=p*q
phi= (p-1)*(q-1)
d= inverse(e,phi)
m=pow(c,d,n)
s=n2s(m)
print (s) #hgame{t3Xt6O0k_R5A!!!}

Affine

题目：

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import gmpy2
from secret import A, B, flag
assert flag.startswith('hgame{') and flag.endswith('}')

TABLE = 'zxcvbnmasdfghjklqwertyuiop1234567890QWERTYUIOPASDFGHJKLZXCVBNM'
MOD = len(TABLE)

cipher = ''
for b in flag:
    i = TABLE.find(b)
    if i == -1:
        cipher += b
    else:
        ii = (A*i + B) % MOD
        cipher += TABLE[ii]

print(cipher)
# A8I5z{xr1A_J7ha_vG_TpH410}

根据之前招新赛那道mod
对于r0 = (y * m) % n
由于我们知道r0，y，n的值，先通过求y模n的乘法逆元，然后可以求得m

$y*y^{-1} mod\ n \equiv 1$ $r0 = (y * m) mod \ n$

两边同乘$y^{-1}$
修改：乍的一看应该是下面的形式

$r0*y^{-1}=m$

其实正确的换算应该是

$m= (r0*y^{-1}) mod\ n$

类似地，题目的关键是ii = (Ai + B) % MOD
提取A，得ii = (A（i + B//A)） % MOD
把A看做y，把MOD看做n，把ii看做r0，i + B//A看做待求的m
接下来先求出A和B的值
A=13,B=14

def inverse(u, v):
    """The inverse of :data:`u` *mod* :data:`v`."""

    u3, v3 = u, v
    u1, v1 = 1, 0
    while v3 > 0:
        q = u3 // v3
        u1, v1 = v1, u1 - v1*q
        u3, v3 = v3, u3 - v3*q
    while u1<0:
        u1 = u1 + v
    return u1
#求A的逆元，得到43
#A_1=inverse(13,62)
#print (A_1)  

TABLE = 'zxcvbnmasdfghjklqwertyuiop1234567890QWERTYUIOPASDFGHJKLZXCVBNM'
cipher = 'A8I5z{xr1A_J7ha_vG_TpH410}'
flag = ''
for b in cipher:
    i = TABLE.find(b)
    if i == -1:
        flag += b
    else:
        ii = ((i*43)%62)-44
        #print (ii)
        flag += TABLE[ii]
print(flag)

有个坑，不知道之后有没有机会填掉，我不知道玩什么是-44才能得到正确答案，我一开始是-1，因为14//13=1

Author：DGZ

原文链接：https://dgz-cyber.github.io/2020/02/13/HGAME-CRYPTO%20Writes%20up/

发表日期：February 13th 2020, 11:52:28 pm

更新日期：February 13th 2020, 11:52:30 pm

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CATALOG

1. Week 1
1. 1.1. 签到题 InfantRSA
2. 1.2. Affine

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