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134 lines
4.1 KiB
Python
134 lines
4.1 KiB
Python
#!/usr/bin/env python3
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"""
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Simulation of the Quantum Key Distribution (QKD) protocol called BB84,
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created by Charles Bennett and Gilles Brassard in 1984.
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BB84 is a key-distribution protocol that ensures secure key distribution
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using qubits instead of classical bits. The generated key is the result
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of simulating a quantum circuit. Our algorithm to construct the circuit
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is as follows:
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Alice generates two binary strings. One encodes the basis for each qubit:
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- 0 -> {0,1} basis.
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- 1 -> {+,-} basis.
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The other encodes the state:
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- 0 -> |0> or |+>.
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- 1 -> |1> or |->.
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Bob also generates a binary string and uses the same convention to choose
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a basis for measurement. Based on the following results, we follow the
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algorithm below:
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X|0> = |1>
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H|0> = |+>
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HX|0> = |->
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1. Whenever Alice wants to encode 1 in a qubit, she applies an
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X (NOT) gate to the qubit. To encode 0, no action is needed.
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2. Wherever she wants to encode it in the {+,-} basis, she applies
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an H (Hadamard) gate. No action is necessary to encode a qubit in
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the {0,1} basis.
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3. She then sends the qubits to Bob (symbolically represented in
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this circuit using wires).
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4. Bob measures the qubits according to his binary string for
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measurement. To measure a qubit in the {+,-} basis, he applies
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an H gate to the corresponding qubit and then performs a measurement.
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References:
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https://en.wikipedia.org/wiki/BB84
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https://qiskit.org/textbook/ch-algorithms/quantum-key-distribution.html
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"""
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import numpy as np
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import qiskit
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def bb84(key_len: int = 8, seed: int | None = None) -> str:
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"""
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Performs the BB84 protocol using a key made of `key_len` bits.
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The two parties in the key distribution are called Alice and Bob.
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Args:
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key_len: The length of the generated key in bits. The default is 8.
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seed: Seed for the random number generator.
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Mostly used for testing. Default is None.
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Returns:
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key: The key generated using BB84 protocol.
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>>> bb84(16, seed=0)
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'0111110111010010'
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>>> bb84(8, seed=0)
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'10110001'
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"""
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# Set up the random number generator.
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rng = np.random.default_rng(seed=seed)
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# Roughly 25% of the qubits will contribute to the key.
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# So we take more than we need.
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num_qubits = 6 * key_len
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# Measurement basis for Alice's qubits.
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alice_basis = rng.integers(2, size=num_qubits)
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# The set of states Alice will prepare.
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alice_state = rng.integers(2, size=num_qubits)
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# Measurement basis for Bob's qubits.
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bob_basis = rng.integers(2, size=num_qubits)
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# Quantum Circuit to simulate BB84
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bb84_circ = qiskit.QuantumCircuit(num_qubits, name="BB84")
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# Alice prepares her qubits according to rules above.
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for index, _ in enumerate(alice_basis):
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if alice_state[index] == 1:
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bb84_circ.x(index)
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if alice_basis[index] == 1:
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bb84_circ.h(index)
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bb84_circ.barrier()
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# Bob measures the received qubits according to rules above.
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for index, _ in enumerate(bob_basis):
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if bob_basis[index] == 1:
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bb84_circ.h(index)
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bb84_circ.barrier()
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bb84_circ.measure_all()
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# Simulate the quantum circuit.
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sim = qiskit.Aer.get_backend("aer_simulator")
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# We only need to run one shot because the key is unique.
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# Multiple shots will produce the same key.
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job = qiskit.execute(bb84_circ, sim, shots=1, seed_simulator=seed)
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# Returns the result of measurement.
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result = job.result().get_counts(bb84_circ).most_frequent()
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# Extracting the generated key from the simulation results.
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# Only keep measurement results where Alice and Bob chose the same basis.
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gen_key = "".join(
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[
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result_bit
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for alice_basis_bit, bob_basis_bit, result_bit in zip(
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alice_basis, bob_basis, result
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)
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if alice_basis_bit == bob_basis_bit
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]
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)
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# Get final key. Pad with 0 if too short, otherwise truncate.
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key = gen_key[:key_len] if len(gen_key) >= key_len else gen_key.ljust(key_len, "0")
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return key
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if __name__ == "__main__":
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print(f"The generated key is : {bb84(8, seed=0)}")
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from doctest import testmod
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testmod()
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