重合指数 | Putao0v0のBlog

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Jun 22, 2022

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重合指数

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重合指数

针对已知密文求明文，密钥未知且重复多次，可以用重合指数来做

例题

[XNUCA2018]baby_crypto


The 26 letters a, b, c, ..., y, z correspond to the integers 0, 1, 2, ..., 25
len(key_a) = m
len(key_k) = n
c[i] = (p[i] * key_a[i % m] + key_k[i % n]) % 26

p is plain text, only lowercase letters are refered to.
c is encrypted text

I have appended the flag at the end of plain text, the format of which is like 'flagis......'
Now you have the encrypted text, Good luck!

伪代码，很好理解,给了两组key 都不知道且长度也不知道密文是明文的线性变化，有点像词频分析啊但是网站又解不出来

刚拿到这道题无从下手，看着大师傅的博客一步步做下来，有很多收获。 ### 密钥长度

首先我们可以知道密钥是循环使用的，那么加密过程中不免有相同的单词使用相同的密钥，那么我们就可以来爆破密钥长度了，找到密文中出现次数大于20次的字符串，参照博客取了长度为4的，然后取其中之一找出期出现的相应位置，算出间隔，取其最大公因子就是密钥长度了


from itertools import *

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"
x='abcdefghijklmnopqrstuvwxyz'
# for i in product(x,repeat=4):
#     h=''.join(i)
#     if(s.count(h)>=20):
#         print(h)
def find_sub_n_index(str,substr,time):
    begin=0
    while(str.find(substr,begin)!=-1 and time>0):
        begin=str.index(substr,begin)+4
        time-=1
    return begin-4
position=[]
key="erui"
for i in range(1,20):
    site = find_sub_n_index(s, key, i)
    position.append(site)
print(position)
gcd_=[]
for i in range(18):
    gcd_.append(position[i+1]-position[i])
print(gcd_)
for i in range(2,min(gcd_)):
    flag=1
    for j in gcd_:
        if(j%i!=0):
            flag=0
            break
    if(flag==1):
        g=i
print(g)

一轮的长度实际上是两个密钥长度的最大公倍数，我们还是无法得知具体两个密钥各有多长，不过没关系，直接当6处理，其中重复出现的求出来了自然就知道多长了。

爆破密钥

接下来就是和重合指数有关了

需要知道大量英文中每个字母出现的频率是有统计意义上的平均值的，一篇单词数足够的文章，其重合指数接近0.065，那么解密出来的明文应该是符合这个常数的。

因为密钥是6位，为了方便就将密文6位一组分好


dic_index={'a': 0.08167,'b': 0.01492,'c': 0.02782,'d':0.04253,'e': 0.12702,'f':0.02228,'g': 0.02015,'h':0.06094,'i':0.06966,'j':0.00153,'k':0.00772,'l':0.04025,'m':0.02406,'n':0.06749,'o':0.07507,'p':0.01929,'q':0.00095,'r':0.05987,'s':0.06327,'t':0.09056,'u':0.02758,'v':0.00978,'w':0.02360,'x':0.00150,'y':0.01974,'z':0.00074}

def mm(c,i,j):
    fre=[0]*26
    sum=0
    for k in c:
        m=chr((ord(k)-ord('a')-j)*inverse(i,26)%26+97)
        fre[ord(m)-ord('a')]+=1
    for k in range(26):
        sum+=(fre[k]/len(c))*dic_index[chr(ord('a')+k)]#计算重合指数
    return sum
def fine_key(c):
    index=1
    for i in range(26):
        if(i%13==0 or i%2==0):
            continue
        for j in range(26):
            if(math.fabs(mm(c,i,j)-0.065)<index):
                index=math.fabs(mm(c,i,j)-0.065)
                key1=i
                key2=j
    return key1,key2

key_a=[]
key_k=[]
for i in range(6):
    temp = "".join(s[cycle * 6 + i] for cycle in range(len(s) // 6))
    key_a.append(fine_key(temp)[0])
    key_k.append(fine_key(temp)[1])
print(key_a)
print(key_k)

求解


key_a=[19, 7, 23]
key_k=[10, 9, 3, 24, 14, 15]

for k in range(len(s)):
    m = chr((ord(s[k]) - ord('a') - key_k[k%6]) * inverse(key_a[k%3], 26) % 26 + 97)
    print(m,end='')

flag{helloxnucagoodluck}