Tags: crypto rsa

Rating:

the provided text file shows really big numbers

- lotta_numbers.txt


c: 34709089913401150635163820358938916881993556790698827096314474131695180194656373592831158701400832173951061153349955626770351918715134102729180082310540500929299260384727841272328651482716425284903562937949838801126975821205390573428889205747236795476232421245684253455346750459684786949905537837807616524618

p: 7049378199874518503065880299491083072359644394572493724131509322075604915964637314839516681795279921095822776593514545854149110798068329888153907702700969

q: 11332855855499101423426736341398808093169269495239972781080892932533129603046914334311158344125602053367004567763440106361963142912346338848213535638676857

e: 65537


and if you haven't noticed the challenge name and description give off that this is a RSA algorithm challenge

- $p, q$ large prime numbers
- $c$ is the ciphered message
- $e$ is a part of the public key

now we can easily compute $n = p * q$ and we'll have the public key (e, n)

we can compute phi from $\phi(n) = (p-1) * (q-1)$

and lastly $d$ the modular inverse of $e$ from [this calculator](https://www.dcode.fr/modular-inverse)

the decrypted message can be acquired from the following formula:

$$m = c^d \enspace mod \enspace n$$

we have all the required parameters to crack the cipher so plug them into [this calculator](https://www.dcode.fr/rsa-cipher)

and u get the flag

### flag

kqctf{y0uv3_6r4du473d_fr0m_r54_3l3m3n74ry_5ch00l_ac8770bdcebc}