> For the complete documentation index, see [llms.txt](https://r3yc0n1c.gitbook.io/writeups/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://r3yc0n1c.gitbook.io/writeups/2021/csaw-qualification-round/crypto/gotta-decrypt-them-all.md).

# Gotta Decrypt Them All

253 solves / 175 points

Source files and Solve Script:  [CSAW-Quals/crypto/Gotta Decrypt Them All](https://github.com/r3yc0n1c/CTF-Writeups/tree/main/2021/CSAW-Quals/crypto/Gotta%20Decrypt%20Them%20All)

### Attack Idea

**STEP 1:** Identify the [Morse ](https://en.wikipedia.org/wiki/Morse_code)encoded string

**STEP 2:** Decrypt to get Integers

**STEP 3:** Convert them to ASCII characters

**STEP 4:** Identify [Base64](https://en.wikipedia.org/wiki/Base64) and decode it to get [RSA ](https://en.wikipedia.org/wiki/RSA_\(cryptosystem\))parameters and encrypted message

**STEP 5:** Check the **small public exponent (e)** and take the **eth root** to get the message

{% hint style="info" %}
Why STEP 5 works?

In practice, we pick the RSA parameters and the message such that$$m^{e} \geq n$$. If we use a small message and a small exponent then it just becomes$$c = m^{e}$$ and we can directly calculate$$m = \sqrt\[e]{}c$$ to get back our message.
{% endhint %}