Problem: [强网杯 2022]ASR
思路
- 转到和e互素的pq下求解
EXP
- 具体攻击代码
-
from math import *
from Crypto.Util.number import bytes_to_long
from sympy import *
from Crypto.Util.number import *
from gmpy2 import *
n = 8250871280281573979365095715711359115372504458973444367083195431861307534563246537364248104106494598081988216584432003199198805753721448450911308558041115465900179230798939615583517756265557814710419157462721793864532239042758808298575522666358352726060578194045804198551989679722201244547561044646931280001
e = 3
c = 945272793717722090962030960824180726576357481511799904903841312265308706852971155205003971821843069272938250385935597609059700446530436381124650731751982419593070224310399320617914955227288662661442416421725698368791013785074809691867988444306279231013360024747585261790352627234450209996422862329513284149
p=218566259296037866647273372633238739089
q=223213222467584072959434495118689164399
r3=225933944608558304529179430753170813347
r4=260594583349478633632570848336184053653
print(p2*q2r3**2r42==n)
phi=(p2-p)(q**2-q)(r32-r3)*(r42-r4)
print(gcd(e,phi))
print(gcd(e,(p2-p)))
print(gcd(e,(q2-q)))
print(gcd(e,(r32-r3)))
print(gcd(e,(r42-r4)))
d=inverse(e, (q2-q)*(r42-r4))
m=powmod(c,d,q2*r42)
print(long_to_bytes(m))
总结
- 对该题的考点总结