ctf-writeup/WaniCTF 2023/EZDORSA_Lv3

EZDORSA_Lv3

The power of mathematics is staggering!

About the Challenge

We were given a zip file (You can download the file here). There are 2 files inside the zip file, chall.py and out.txt. Here is the content of chall.py

from Crypto.Util.number import *

e = 65537

n = 1
prime_list = []
while len(prime_list) < 100:
    p = getPrime(25)
    if not (p in prime_list):
        prime_list.append(p)

for i in prime_list:
    n *= i

m = b"FAKE{DUMMY_FLAG}"
c = pow(bytes_to_long(m), e, n)

print(f"n = {n}")
print(f"e = {e}")
print(f"c = {c}")

The given Python code generates a 100-digit RSA public key with exponent e=65537 and modulus n, which is the product of 100 randomly generated 25-bit prime numbers. A message m="FAKE{DUMMY_FLAG}" is encrypted using the RSA encryption algorithm and the resulting ciphertext c is printed along with the public key parameters. The code demonstrates how RSA encryption can be used to securely transmit messages over an insecure communication channel, where only the intended recipient who possesses the private key can decrypt and recover the original message.

And here is the content of out.txt

n = 22853745492099501680331664851090320356693194409008912025285744113835548896248217185831291330674631560895489397035632880512495471869393924928607517703027867997952256338572057344701745432226462452353867866296639971341288543996228186264749237402695216818617849365772782382922244491233481888238637900175603398017437566222189935795252157020184127789181937056800379848056404436489263973129205961926308919968863129747209990332443435222720181603813970833927388815341855668346125633604430285047377051152115484994149044131179539756676817864797135547696579371951953180363238381472700874666975466580602256195404619923451450273257882787750175913048168063212919624027302498230648845775927955852432398205465850252125246910345918941770675939776107116419037
e = 65537
c = 1357660325421905236173040941411359338802736250800006453031581109522066541737601274287649030380468751950238635436299480021037135774086215029644430055129816920963535754048879496768378328297643616038615858752932646595502076461279037451286883763676521826626519164192498162380913887982222099942381717597401448235443261041226997589294010823575492744373719750855298498634721551685392041038543683791451582869246173665336693939707987213605159100603271763053357945861234455083292258819529224561475560233877987367901524658639475366193596173475396592940122909195266605662802525380504108772561699333131036953048249731269239187358174358868432968163122096583278089556057323541680931742580937874598712243278738519121974022211539212142588629508573342020495

How to Solve?

To solve this chall, im using this tool and then choose Multi Prime Number

FLAG{fact0r1z4t10n_c4n_b3_d0n3_3as1ly}