RSA Noob

We are given these numbers:

e: 1
c: 108193852288406505568171818194994500452464483136775497973720445
n: 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139

We have the exponent , the modulus and the ciphertext .

It is clear that we have an RSA cryptosystem. Let’s review how RSA works:

Two prime numbers and are chosen so that we have the modulus . Then an exponent is chosen (usually 3 or 65537) so that it is coprime with .

In order to encrypt a message (in numeric format), this operation must be performed:

So that is the ciphertext. And to decrypt the ciphertext, we must first calculate and then compute this:

At this point, the public key is the set , whereas the private key is formed by .

This time, the exponent , so as well, because it is the multiplicative inverse (1 is the identity element over the multiplication). Hence, .

The only thing we need to do is decode the message from number to ASCII bytes:

$ python3 -q
>>> bytes.fromhex('108193852288406505568171818194994500452464483136775497973720445')
b'CTFlearn{b3tter_up_y0ur_e}'