birth.py

import random
import math
import matplotlib.pyplot as plt

def birthday_attack_sim(n, max_samples):
    seen = set()
    collisions = []
    probs = []

    for d in range(1, max_samples + 1):
        value = random.randint(0, n-1)

        if value in seen:
            collisions.append(1)
        else:
            collisions.append(0)
            seen.add(value)

        # probabilidad teórica
        prob = 1 - math.exp(-(d*(d-1))/(2*n))
        probs.append(prob)

    return collisions, probs


# Parámetro (simula tamaño del espacio)
n = 10000
max_samples = 300

collisions, probs = birthday_attack_sim(n, max_samples)

# Graficar
plt.figure()
plt.plot(range(1, max_samples+1), probs)
plt.xlabel("Número de mensajes interceptados")
plt.ylabel("Probabilidad de colisión")
plt.title("Birthday Attack aplicado a RSA")
plt.show()