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 = ""

    try:
        while True:
            line = r.recvuntil(b"Basis : ", timeout=5).decode()
            if not line:
                break

            # Get qubit number
            match = re.search(r"Qubit (\d+)/(\d+)", line)
            if match:
                current = int(match.group(1))
                total = int(match.group(2))
                print(f"Processing qubit {current}/{total}")
            else:
                print("Could not find qubit number")
                break

            basis = r.recvline().decode().strip()
            print(f"Basis: {basis}")

            r.recvuntil(b"Measurement of qubit 0 : ")
            m0 = int(r.recvline().decode().strip())

            r.recvuntil(b"Measurement of qubit 1 : ")
            m1 = int(r.recvline().decode().strip())

            print(f"M0: {m0}, M1: {m1}")

            instructions = ""
            if m0 == 0 and m1 == 0:
                instructions = "Z:2;Z:2" # No-op (Z^2 = I)
            elif m0 == 0 and m1 == 1:
                instructions = "X:2"
            elif m0 == 1 and m1 == 0:
                instructions = "Z:2"
            elif m0 == 1 and m1 == 1:
                instructions = "X:2;Z:2"

            r.recvuntil(b"Specify the instructions : ")
            r.sendline(instructions.encode())

            r.recvuntil(b"Specify the measurement basis : ")
            r.sendline(basis.encode())

            r.recvuntil(b"Measurement of qubit 2 : ")
            res = int(r.recvline().decode().strip())
            print(f"Result: {res}")

            first_bit = "0" if basis == "Z" else "1"
            second_bit = str(res)
            flag_bits += first_bit + second_bit

            if current == total:
                break

    except EOFError:
        print("Connection closed")
    except Exception as e:
        print(f"Error: {e}")

    print(f"Collected bits: {flag_bits}")

    # Convert bits to bytes
    flag_bytes = bytearray()
    for i in range(0, len(flag_bits), 8):
        byte_str = flag_bits[i : i + 8]
        if len(byte_str) == 8:
            flag_bytes.append(int(byte_str, 2))

    print(f"Flag: {flag_bytes.decode(errors='ignore')}")

if __name__ == "__main__":
    solve()

Key Indicators

Use this technique when:

• The task mentions quantum teleportation.
• Measurement results of two qubits are given and gates need to be applied to a third.
• The qutip library or similar quantum computing libraries are used.