from qiskit import QuantumCircuit, Aer, execute
from qiskit.utils import QuantumInstance
import math
import numpy as np
from qiskit.circuit.library import QFT
def near_practical_ecdsa_attack(public_point, generator_point, order, a, p):
"""
Highly conceptual demonstration of a quantum ECDLP solver.
EXTREME WARNING: This code is still theoretical and DOES NOT break real ECDSA.
It represents a "near-practical" approach only in terms of increased
complexity, but it's far from a real attack.
"""
def qft_dagger(qc, n):
"""n-qubit QFTdagger the first n qubits in circ."""
for qubit in range(n // 2):
qc.swap(qubit, n - qubit - 1)
for j in range(n):
for m in range(j):
qc.cp(-np.pi / float(2**(j - m)), m, j)
qc.h(j)
def controlled_point_addition(qc, control_qubits, point_qubits, generator_point, a, p):
"""
Simulates controlled point addition with more realistic modular addition.
Still highly simplified compared to a real quantum circuit.
"""
n_qubits_point = len(point_qubits) // 2
generator_x = bin(generator_point[0])[2:].zfill(n_qubits_point)
generator_y = bin(generator_point[1])[2:].zfill(n_qubits_point)
for i in range(n_qubits_point):
if generator_x[n_qubits_point - 1 - i] == '1':
for control_qubit in control_qubits:
#Simulated modular addition using ccx gates.
qc.mcx([control_qubit, point_qubits[i]], point_qubits[i]+n_qubits_point*2)
qc.cx(point_qubits[i]+n_qubits_point*2,point_qubits[i])
qc.mcx([control_qubit, point_qubits[i]], point_qubits[i]+n_qubits_point*2)
if generator_y[n_qubits_point - 1 - i] == '1':
for control_qubit in control_qubits:
qc.mcx([control_qubit, point_qubits[i + n_qubits_point]], point_qubits[i]+n_qubits_point*2)
qc.cx(point_qubits[i]+n_qubits_point*2,point_qubits[i + n_qubits_point])
qc.mcx([control_qubit, point_qubits[i + n_qubits_point]], point_qubits[i]+n_qubits_point*2)
n_qubits_order = int(math.ceil(math.log2(order)))
n_qubits_point = int(math.ceil(math.log2(p)))
qc = QuantumCircuit(n_qubits_order + 2 * n_qubits_point + n_qubits_point *2, n_qubits_order)
generator_x_bin = bin(generator_point[0])[2:].zfill(n_qubits_point)
generator_y_bin = bin(generator_point[1])[2:].zfill(n_qubits_point)
for i in range(n_qubits_point):
if generator_x_bin[n_qubits_point - 1 - i] == '1':
qc.x(n_qubits_order + i)
if generator_y_bin[n_qubits_point - 1 - i] == '1':
qc.x(n_qubits_order + n_qubits_point + i)
qc.h(range(n_qubits_order))
for i in range(n_qubits_order):
controlled_point_addition(qc, [i], range(n_qubits_order, n_qubits_order + 2 * n_qubits_point), generator_point, a, p)
qft_dagger(qc, n_qubits_order)
qc.measure(range(n_qubits_order), range(n_qubits_order))
backend = Aer.get_backend('qasm_simulator')
quantum_instance = QuantumInstance(backend, shots=1024)
result = quantum_instance.execute(qc)
counts = result.get_counts()
max_count = 0
max_value = 0
for value, count in counts.items():
if count > max_count:
max_count = count
max_value = int(value, 2)
estimated_private_key = max_value
print(f"Estimated Private Key (highly conceptual): {estimated_private_key}")
print("WARNING: The output is a highly unreliable estimate. Due to the lack of proper elliptic curve operations, the simulated private key does NOT reliably match the actual private key. This is a purely theoretical demonstration and does NOT break real ECDSA.")