Quantum Cryptography¶

Introduction to Quantum Cryptography¶

Quantum cryptography leverages the principles of quantum mechanics to provide secure communication. It offers security based on the fundamental laws of physics, making it theoretically immune to computational attacks.

Quantum Key Distribution (QKD)¶

Quantum Key Distribution (QKD) is a method used to securely distribute cryptographic keys between two parties. It ensures that any attempt to eavesdrop on the key exchange will be detected.

BB84 Protocol¶

The BB84 protocol, proposed by Charles Bennett and Gilles Brassard in 1984, is one of the first and most well-known QKD protocols. It uses the principles of quantum mechanics to securely distribute a key between two parties, typically referred to as Alice and Bob.

Example Implementation of BB84 using Qiskit¶

In [ ]:
from qiskit import QuantumCircuit, execute, Aer
from qiskit.visualization import plot_histogram
import numpy as np

# Define the BB84 protocol
def bb84_protocol():
    # Step 1: Alice prepares qubits
    alice_bases = np.random.randint(2, size=100)
    alice_bits = np.random.randint(2, size=100)
    alice_qubits = []
    for i in range(100):
        qc = QuantumCircuit(1, 1)
        if alice_bases[i] == 0:
            if alice_bits[i] == 1:
                qc.x(0)
        else:
            qc.h(0)
            if alice_bits[i] == 1:
                qc.x(0)
        alice_qubits.append(qc)
    
    # Step 2: Alice sends qubits to Bob
    bob_bases = np.random.randint(2, size=100)
    bob_results = []
    for i in range(100):
        qc = alice_qubits[i]
        if bob_bases[i] == 1:
            qc.h(0)
        qc.measure(0, 0)
        backend = Aer.get_backend('qasm_simulator')
        result = execute(qc, backend, shots=1).result()
        counts = result.get_counts()
        bob_results.append(int(list(counts.keys())[0]))
    
    # Step 3: Alice and Bob compare bases
    matching_bases = alice_bases == bob_bases
    alice_key = alice_bits[matching_bases]
    bob_key = np.array(bob_results)[matching_bases]
    
    return alice_key, bob_key

# Run the BB84 protocol
alice_key, bob_key = bb84_protocol()

# Display the keys
print("Alice's key:", alice_key)
print("Bob's key:  ", bob_key)

Quantum Fingerprinting¶

Quantum fingerprinting is a technique used to compare two strings with high accuracy using significantly fewer resources than classical methods. It leverages the principles of quantum mechanics to create a unique "fingerprint" for each string.

Quantum Secure Communication Protocols¶

Quantum secure communication protocols use quantum mechanics to ensure the security of communication channels. These protocols can detect any attempt to eavesdrop on the communication, providing a high level of security.

Example Implementation of Quantum Secure Communication Protocol¶

In [ ]:
from qiskit import QuantumCircuit, execute, Aer
from qiskit.visualization import plot_histogram

# Define a simple quantum secure communication protocol
def quantum_secure_communication():
    # Step 1: Alice prepares a qubit in a random state
    alice_bit = np.random.randint(2)
    alice_basis = np.random.randint(2)
    qc = QuantumCircuit(1, 1)
    if alice_basis == 0:
        if alice_bit == 1:
            qc.x(0)
    else:
        qc.h(0)
        if alice_bit == 1:
            qc.x(0)
    
    # Step 2: Alice sends the qubit to Bob
    # (In a real implementation, this would involve sending the qubit over a quantum channel)
    
    # Step 3: Bob measures the qubit in a random basis
    bob_basis = np.random.randint(2)
    if bob_basis == 1:
        qc.h(0)
    qc.measure(0, 0)
    
    # Step 4: Bob measures the qubit
    backend = Aer.get_backend('qasm_simulator')
    result = execute(qc, backend, shots=1).result()
    counts = result.get_counts()
    bob_bit = int(list(counts.keys())[0])
    
    # Step 5: Alice and Bob compare bases
    if alice_basis == bob_basis:
        return alice_bit == bob_bit
    else:
        return None

# Run the quantum secure communication protocol
result = quantum_secure_communication()

# Display the result
if result is None:
    print("Alice and Bob used different bases.")
else:
    print("Alice and Bob used the same basis. The bits match:", result)

Conclusion¶

In this notebook, we have explored the fundamental concepts of quantum cryptography, including Quantum Key Distribution (QKD), quantum fingerprinting, and quantum secure communication protocols. Understanding these concepts is crucial for leveraging quantum mechanics to provide secure communication. As quantum computing technology continues to advance, these techniques will play a key role in ensuring the security of communication channels.