Flagportation — HackTheBox

Description

Every 24 hours, Qubitrix will release a secret message to our partners. Please follow the instructions we sent you by email from [email protected].

Analysis

The server implements a quantum teleportation protocol. The flag is split into pairs of bits. Each pair is encoded into the state of qubit 0:

• 00 -> $|0\rangle$ (Z basis)
• 01 -> $|1\rangle$ (Z basis)
• 10 -> $|+\rangle$ (X basis)
• 11 -> $|-\rangle$ (X basis)

Then an entangled pair (Bell state) is created on qubits 1 and 2. CNOT(0,1) and H(0) operations are performed, after which qubits 0 and 1 are measured in the Z basis. The measurement results $M_0$ and $M_1$ are communicated to the user.

The user must:

1. Enter correction gates for qubit 2.
2. Choose the measurement basis for qubit 2.

According to the quantum teleportation protocol, the state of qubit 2 after measurements $M_0$ and $M_1$ differs from the original state of qubit 0 by Pauli operators:

• If $M_0=0, M_1=0$: state $| \psi \rangle$ (no correction needed)
• If $M_0=0, M_1=1$: state $X | \psi \rangle$ (need $X$ correction)
• If $M_0=1, M_1=0$: state $Z | \psi \rangle$ (need $Z$ correction)
• If $M_0=1, M_1=1$: state $ZX | \psi \rangle$ (need $XZ$ or $ZX$ correction)

The first bit of the pair is determined by the basis (Z -> 0, X -> 1), the second bit — by the measurement result of qubit 2 in that basis.

Solution

from pwn import *
import re

def solve():
    # host = "94.237.122.188"
    # port = 52871
    # r = remote(host, port)
    
    # For local testing or if server is running via docker
    r = remote("localhost", 1337) 

    flag_bits = ""

...