Rating:
# Table of contents
- ## [factorize](#challenge-name-factorize)
---
# Notes
### I'm using Ubuntu 20.04 as my environment.
---
# Challenge Name: factorize
## Information
1. ```c``` the encrypted message, was given
2. ```n``` the modulus, was given
3. ```n``` is constructed by two primes ```p,q``` which in this question, it's easily crackable and can be found on [factordb.com](http://factordb.com/index.php?query=23135514747783882716888676812295359006102435689848260501709475114767217528965364658403027664227615593085036290166289063788272776788638764660757735264077730982726873368488789034079040049824603517615442321955626164064763328102556475952363475005967968681746619179641519183612638784244197749344305359692751832455587854243160406582696594311842565272623730709252650625846680194953309748453515876633303858147298846454105907265186127420148343526253775550105897136275826705375222242565865228645214598819541187583028360400160631947584202826991980657718853446368090891391744347723951620641492388205471242788631833531394634945663)
## My solution
```
# Fermat at first, using yafu or factordb
c = 17830167351685057470426148820703481112309475954806278304600862043185650439097181747043204885329525211579732614665322698426329449125482709124139851522121862053345527979419420678255168453521857375994190985370640433256068675028575470040533677286141917358212661540266638008376296359267047685745805295747215450691069703625474047825597597912415099008745060616375313170031232301933185011013735135370715444443319033139774851324477224585336813629117088332254309481591751292335835747491446904471032096338134760865724230819823010046719914443703839473237372520085899409816981311851296947867647723573368447922606495085341947385255
n = 23135514747783882716888676812295359006102435689848260501709475114767217528965364658403027664227615593085036290166289063788272776788638764660757735264077730982726873368488789034079040049824603517615442321955626164064763328102556475952363475005967968681746619179641519183612638784244197749344305359692751832455587854243160406582696594311842565272623730709252650625846680194953309748453515876633303858147298846454105907265186127420148343526253775550105897136275826705375222242565865228645214598819541187583028360400160631947584202826991980657718853446368090891391744347723951620641492388205471242788631833531394634945663
p = 152103631606164757991388657189704366976433537820099034648874538500153362765519668135545276650144504533686483692163171569868971464706026329525740394016509191077550351496973264159350455849525747355370985161471258126994336297660442739951587911017897809328177973473427538782352524239389465259173507406981248869793
q = 152103631606164757991388657189704366976433537820099034648874538500153362765519668135545276650144504533686483692163171569868971464706026329525740394016509185464641520736454955410019736330026303289754303711165526821866422766844554206047678337249535003432035470125187072461808523973483360158652600992259609986591
e = 0x10001
# calculate lotietn
import gmpy
lcm = gmpy.lcm(p-1,q-1)
#private key d
d = gmpy.invert(e,lcm)
d = int(d)
m = pow(c,d,n)
# print(m.bit_length())
print(m.to_bytes(48,"big"))
```
Output
```
$ python3 solve.py
b'\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00flag{just_g0tta_f@ct0rize_1t4536}'
```
## Flag: flag{just_g0tta_f@ct0rize_1t4536}
---
