**Challenge:** Magical Oracle
**Category:** Cryptography
**Points:** 436

### Introduction

Ah, the "Magical Oracle." The name itself promised some arcane cryptographic wizardry, and it did not disappoint. When we first connected, we were greeted by a classic setup: a prime `p`, a bunch of parameters, and an oracle that leaked *just enough* information to be interesting.

The core of the problem was a textbook (well, almost) Hidden Number Problem, or HNP. The oracle would take a random number `t`, calculate `(alpha * t) % p` where `alpha` was the secret key, and give us back a value `z` that was *really* close to the real result. Our mission, should we choose to accept it, was to use these slightly-off results to uncover the exact value of `alpha` and use it to decrypt the flag. Easy, right?

### FULL SOLUTION : [Magical Oracle - L3AK-CTF 2025 Write-up](https://writeups.thebusfactoris1.online/posts/2025-07-14-Magical-Oracle-writeup)

Original writeup (https://writeups.thebusfactoris1.online/posts/2025-07-14-Magical-Oracle-writeup).