# Challenge Name: baby


## Description

I want to do an RSA!

Author : EvilMuffinHa

[output.txt](output.txt)

## Detailed solution

We have an RSA encryption
```
n: 228430203128652625114739053365339856393
e: 65537
c: 126721104148692049427127809839057445790
```

An RSA modulus is the product of two secret prime numbers p and q : N = pq. for factoring we gonna use factordb


We need to calcul :
`phi = ( q — 1 ) * ( p — 1 )` Euler’s Totient for the number N.
`d = inverse( e, phi )` the private key with the MODULAR INVERSE of e and phi.

To decrypt the message :

`m ≡ c^d (mod n)`

I'm gonna use the python library **Pycryptodome** [baby.py](baby.py)

```python
from Crypto.Util.number import long_to_bytes, inverse

n = 228430203128652625114739053365339856393
e = 65537
c = 126721104148692049427127809839057445790

p = 12546190522253739887
q = 18207136478875858439

phi = (p-1)*(q-1)

d = inverse(e, phi)

flag = pow(c,d,n)

print(long_to_bytes(flag).decode())
```

## Flag

```
flag{68ab82df34}
```

Original writeup (https://github.com/BaadMaro/CTF/tree/main/redpwnCTF%202021/Crypto%20-%20baby).