{ "cells": [ { "cell_type": "markdown", "id": "2f9451c3", "metadata": { "id": "2f9451c3" }, "source": [ "# 🔐 **Teoría de la Información y la Comunicación**\n", "\n", "**Tema:** Tipos de Comunicación y Fundamentos Probabilísticos\n", "\n", "---\n", "\n", "Este notebook cubre los tres bloques conceptualmente más complejos de la semana 2:\n", "\n", "| Bloque | Tema |\n", "|--------|------|\n", "| 1 | Entropía de Shannon — cálculo paso a paso |\n", "| 2 | Canal Binario Simétrico (BSC) y ruido |\n", "| 3 | Fuentes con y sin memoria — Cadenas de Markov |\n", "\n", "> **Contexto:** todos los ejemplos usan escenarios de ciberseguridad (logs, autenticación, ataques) siguiendo una organización ficticia **SecureData Corp**.\n" ] }, { "cell_type": "markdown", "id": "14bdbf11", "metadata": { "id": "14bdbf11" }, "source": [ "## ⚙️ Importaciones" ] }, { "cell_type": "code", "execution_count": null, "id": "62d1f580", "metadata": { "execution": { "iopub.execute_input": "2026-05-26T19:37:42.199223Z", "iopub.status.busy": "2026-05-26T19:37:42.199014Z", "iopub.status.idle": "2026-05-26T19:37:42.655839Z", "shell.execute_reply": "2026-05-26T19:37:42.653608Z" }, "colab": { "base_uri": "https://localhost:8080/" }, "id": "62d1f580", "outputId": "669e92ab-d9d4-4272-a6fa-ff295335b82b" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "✅ Librerías cargadas correctamente.\n" ] } ], "source": [ "# Importamos las librerías necesarias\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib.patches as mpatches\n", "from collections import Counter\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "# Establecimos una paleta de colores\n", "plt.rcParams.update({\n", " 'figure.facecolor': 'white',\n", " 'axes.facecolor': '#f8f9fa',\n", " 'axes.edgecolor': '#1F3864',\n", " 'axes.labelcolor': '#1F3864',\n", " 'axes.titlecolor': '#1F3864',\n", " 'font.family': 'sans-serif',\n", " 'font.size': 11,\n", " 'axes.titlesize': 13,\n", " 'axes.labelsize': 11,\n", " 'xtick.color': '#1F3864',\n", " 'ytick.color': '#1F3864',\n", "})\n", "\n", "print(\"✅ Librerías cargadas correctamente.\")\n" ] }, { "cell_type": "markdown", "id": "dbc26f42", "metadata": { "id": "dbc26f42" }, "source": [ "---\n", "## Bloque 1 — Entropía de Shannon\n", "\n", "### ¿Qué es la entropía?\n", "\n", "Shannon (1948) definió la entropía como la **incertidumbre promedio** de una fuente discreta:\n", "\n", "$$H(X) = -\\sum_{i=1}^{n} p(x_i) \\log_2 p(x_i)$$\n", "\n", "**Propiedades clave:**\n", "- $H(X) = 0$ cuando un evento ocurre con probabilidad 1 → certeza total, sin sorpresa.\n", "- $H(X)$ es máxima cuando todos los eventos son **equiprobables**.\n", "- La unidad es **bits** (con logaritmo en base 2).\n", "\n", "### Ejemplo de la clase — Caso 1 vs Caso 2 (SecureData Corp)\n", "\n", "| | Acceso exitoso | Acceso fallido |\n", "|--|--|--|\n", "| Caso 1 (normal) | 0.9 | 0.1 |\n", "| Caso 2 (incidente) | 0.5 | 0.5 |\n" ] }, { "cell_type": "code", "execution_count": null, "id": "80c0d970", "metadata": { "execution": { "iopub.execute_input": "2026-05-26T19:37:42.658372Z", "iopub.status.busy": "2026-05-26T19:37:42.658051Z", "iopub.status.idle": "2026-05-26T19:37:42.668139Z", "shell.execute_reply": "2026-05-26T19:37:42.667167Z" }, "id": "80c0d970", "outputId": "d36383fc-2401-438d-c9e0-fbb0a58aa947" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "=======================================================\n", " SecureData Corp — Análisis de Entropía de Autenticación\n", "=======================================================\n", "\n", "📌 Caso 1 (operación normal)\n", " Evento P(x) I(x) [bits]\n", " --------------------------------------------\n", " Acceso exitoso 0.90 0.1520 bits\n", " Acceso fallido 0.10 3.3219 bits\n", " ────────────────────────────────────────────\n", " Entropía H(X) = 0.4690 bits\n", "\n", "📌 Caso 2 (posible incidente)\n", " Evento P(x) I(x) [bits]\n", " --------------------------------------------\n", " Acceso exitoso 0.50 1.0000 bits\n", " Acceso fallido 0.50 1.0000 bits\n", " ────────────────────────────────────────────\n", " Entropía H(X) = 1.0000 bits\n" ] } ], "source": [ "# ─── Función de entropía ───\n", "def entropia(probs):\n", " \"\"\"\n", " Calcula H(X) en bits.\n", " probs: lista o array de probabilidades (deben sumar 1)\n", " \"\"\"\n", " probs = np.array(probs, dtype=float)\n", " assert abs(probs.sum() - 1.0) < 1e-9, \"Las probabilidades deben sumar 1\"\n", " # Evitamos log(0): si p=0, el término contribuye 0\n", " return -np.sum([p * np.log2(p) for p in probs if p > 0])\n", "\n", "# ─── Información de un evento individual ───\n", "def informacion(p):\n", " \"\"\"I(x) = -log2(p) en bits\"\"\"\n", " if p <= 0:\n", " return float('inf')\n", " return -np.log2(p)\n", "\n", "# ─── Caso 1: distribución asimétrica (operación normal) ───\n", "caso1 = {'Acceso exitoso': 0.9, 'Acceso fallido': 0.1}\n", "\n", "# ─── Caso 2: distribución uniforme (posible incidente) ───\n", "caso2 = {'Acceso exitoso': 0.5, 'Acceso fallido': 0.5}\n", "\n", "print(\"=\" * 55)\n", "print(\" SecureData Corp — Análisis de Entropía de Autenticación\")\n", "print(\"=\" * 55)\n", "\n", "for nombre, dist in [(\"Caso 1 (operación normal)\", caso1),\n", " (\"Caso 2 (posible incidente)\", caso2)]:\n", " eventos = list(dist.keys())\n", " probs = list(dist.values())\n", " H = entropia(probs)\n", "\n", " print(f\"\\n📌 {nombre}\")\n", " print(f\" {'Evento':<20} {'P(x)':<8} {'I(x) [bits]'}\")\n", " print(f\" {'-'*44}\")\n", " for ev, p in zip(eventos, probs):\n", " I = informacion(p)\n", " print(f\" {ev:<20} {p:<8.2f} {I:.4f} bits\")\n", " print(f\" {'─'*44}\")\n", " print(f\" Entropía H(X) = {H:.4f} bits\")\n" ] }, { "cell_type": "markdown", "id": "f0e7380e", "metadata": { "id": "f0e7380e" }, "source": [ "### 🔎 ¿Qué significa ese número?\n", "\n", "- **Caso 1 → H ≈ 0.469 bits:** el sistema es muy predecible. Con pocas preguntas de sí/no (bits) se puede predecir el siguiente evento. Operación **normal**.\n", "- **Caso 2 → H = 1.000 bit:** máxima incertidumbre para 2 eventos. No se puede predecir el siguiente evento mejor que lanzar una moneda. Señal de **alerta** (¿ataque de fuerza bruta?).\n", "\n", "> En ciberseguridad: un **aumento brusco de entropía** en los logs de autenticación es un indicador de anomalía.\n" ] }, { "cell_type": "markdown", "id": "ca4a499b", "metadata": { "id": "ca4a499b" }, "source": [ "### Curva de entropía binaria — visualización completa" ] }, { "cell_type": "code", "execution_count": null, "id": "346737a8", "metadata": { "execution": { "iopub.execute_input": "2026-05-26T19:37:42.670128Z", "iopub.status.busy": "2026-05-26T19:37:42.669895Z", "iopub.status.idle": "2026-05-26T19:37:43.129704Z", "shell.execute_reply": "2026-05-26T19:37:43.127887Z" }, "id": "346737a8", "outputId": "0bbed803-3250-4d39-da29-a092625cb42f" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "✅ Figura guardada.\n" ] } ], "source": [ "p_vals = np.linspace(0.001, 0.999, 500)\n", "H_vals = [-p*np.log2(p) - (1-p)*np.log2(1-p) for p in p_vals]\n", "\n", "fig, ax = plt.subplots(figsize=(9, 4))\n", "\n", "ax.plot(p_vals, H_vals, color='#2E75B6', linewidth=2.5)\n", "ax.fill_between(p_vals, H_vals, alpha=0.15, color='#2E75B6')\n", "\n", "# Marcar los dos casos\n", "for label, p_caso, color in [(\"Caso 1\\n(p=0.1)\", 0.1, '#1D6F3B'),\n", " (\"Caso 2\\n(p=0.5)\", 0.5, '#C00000')]:\n", " H_caso = -p_caso*np.log2(p_caso) - (1-p_caso)*np.log2(1-p_caso)\n", " ax.plot(p_caso, H_caso, 'o', color=color, markersize=10, zorder=5)\n", " ax.annotate(f\"{label}\\nH={H_caso:.3f} bits\",\n", " xy=(p_caso, H_caso), xytext=(p_caso + 0.06, H_caso - 0.12),\n", " fontsize=9, color=color,\n", " arrowprops=dict(arrowstyle='->', color=color, lw=1.5))\n", "\n", "ax.axhline(1.0, color='gray', linestyle='--', linewidth=1, alpha=0.6)\n", "ax.set_xlabel(\"Probabilidad de acceso fallido p(x)\")\n", "ax.set_ylabel(\"Entropía H(X) [bits]\")\n", "ax.set_title(\"Entropía binaria — SecureData Corp: autenticación\")\n", "ax.set_xlim(0, 1)\n", "ax.set_ylim(0, 1.15)\n", "ax.grid(True, alpha=0.3)\n", "\n", "plt.tight_layout()\n", "plt.savefig('/home/claude/fig_entropia.png', dpi=150, bbox_inches='tight')\n", "plt.show()\n", "print(\"✅ Figura guardada.\")\n" ] }, { "cell_type": "markdown", "id": "7b24298d", "metadata": { "id": "7b24298d" }, "source": [ "### Fuente con más de 2 eventos — registro de eventos en SIEM\n", "\n", "SecureData Corp registra 5 tipos de eventos en su SIEM. Calculamos la entropía del día normal vs día de ataque.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "c0ee51c2", "metadata": { "execution": { "iopub.execute_input": "2026-05-26T19:37:43.132044Z", "iopub.status.busy": "2026-05-26T19:37:43.131839Z", "iopub.status.idle": "2026-05-26T19:37:43.743937Z", "shell.execute_reply": "2026-05-26T19:37:43.742776Z" }, "id": "c0ee51c2", "outputId": "53881d38-0b63-48d9-cc82-9b9f7cd108b3" }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Entropía máxima posible (5 eventos equiprobables): 2.3219 bits\n", "Diferencia entre ataque y normal: Δ = +0.5585 bits\n" ] } ], "source": [ "eventos_siem = ['Login OK', 'Login FAIL', 'Acceso archivo', 'Alerta FW', 'Tráfico anómalo']\n", "\n", "# Distribución típica (día normal)\n", "dist_normal = [0.60, 0.10, 0.20, 0.08, 0.02]\n", "\n", "# Distribución bajo ataque DDoS + fuerza bruta\n", "dist_ataque = [0.20, 0.35, 0.15, 0.20, 0.10]\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4.5))\n", "\n", "for ax, dist, titulo, color_bar in zip(\n", " axes,\n", " [dist_normal, dist_ataque],\n", " [\"Día normal\", \"Día bajo ataque\"],\n", " ['#2E75B6', '#C00000']):\n", "\n", " H = entropia(dist)\n", " bars = ax.bar(eventos_siem, dist, color=color_bar, alpha=0.85, edgecolor='white', linewidth=1.2)\n", "\n", " # Anotación de probabilidad sobre cada barra\n", " for bar, p in zip(bars, dist):\n", " ax.text(bar.get_x() + bar.get_width()/2, bar.get_height() + 0.005,\n", " f'{p:.2f}', ha='center', va='bottom', fontsize=9, color='#1F3864')\n", "\n", " ax.set_ylim(0, 0.65)\n", " ax.set_title(f\"{titulo}\\nH(X) = {H:.4f} bits\", fontsize=12, fontweight='bold')\n", " ax.set_ylabel(\"Probabilidad\")\n", " ax.tick_params(axis='x', rotation=20)\n", " ax.grid(axis='y', alpha=0.3)\n", "\n", "plt.suptitle(\"SIEM — SecureData Corp: entropía por distribución de eventos\",\n", " fontsize=13, fontweight='bold', y=1.02)\n", "plt.tight_layout()\n", "plt.savefig('/home/claude/fig_siem.png', dpi=150, bbox_inches='tight')\n", "plt.show()\n", "\n", "print(f\"Entropía máxima posible (5 eventos equiprobables): {entropia([0.2]*5):.4f} bits\")\n", "print(f\"Diferencia entre ataque y normal: Δ = {entropia(dist_ataque) - entropia(dist_normal):+.4f} bits\")\n" ] }, { "cell_type": "markdown", "id": "be967812", "metadata": { "id": "be967812" }, "source": [ "---\n", "## Bloque 2 — Canal Binario Simétrico (BSC) y Ruido\n", "\n", "### Definición\n", "\n", "El BSC es el modelo más simple de canal con ruido. Cada bit transmitido tiene probabilidad **p** de invertirse (error) y **(1-p)** de llegar correcto:\n", "\n", "| Enviado | Recibido | Probabilidad |\n", "|---------|----------|-------------|\n", "| 0 | 0 | 1 − p |\n", "| 0 | 1 | p |\n", "| 1 | 1 | 1 − p |\n", "| 1 | 0 | p |\n", "\n", "En ciberseguridad, **p > 0** puede representar:\n", "- Errores de transmisión (físicos)\n", "- Interferencias electromagnéticas\n", "- **Manipulación intencional de paquetes** (ruido adversarial)\n" ] }, { "cell_type": "code", "execution_count": null, "id": "4782ff7b", "metadata": { "execution": { "iopub.execute_input": "2026-05-26T19:37:43.746090Z", "iopub.status.busy": "2026-05-26T19:37:43.745891Z", "iopub.status.idle": "2026-05-26T19:37:43.760509Z", "shell.execute_reply": "2026-05-26T19:37:43.759444Z" }, "id": "4782ff7b", "outputId": "1531b425-c0bf-4bb8-e59a-e4e1994b7514" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mensaje de 200 bits transmitido por SecureData Corp\n", "───────────────────────────────────────────────────────\n", "Escenario Errores BER Impacto\n", "───────────────────────────────────────────────────────\n", "Canal limpio (p=0.01) 1 0.005 ✅ Aceptable\n", "Canal degradado (p=0.10) 26 0.130 ⚠️ Degradado\n", "Ataque activo (p=0.30) 51 0.255 🚨 Crítico\n" ] } ], "source": [ "def simular_bsc(bits_enviados, p_error):\n", " \"\"\"\n", " Simula transmisión por canal BSC.\n", " Cada bit se invierte con probabilidad p_error.\n", " \"\"\"\n", " ruido = np.random.binomial(1, p_error, len(bits_enviados))\n", " bits_recibidos = np.bitwise_xor(bits_enviados.astype(int), ruido)\n", " errores = np.sum(ruido)\n", " return bits_recibidos, errores, ruido\n", "\n", "# ─── Simulación: mensaje de 200 bits enviado por SecureData Corp ───\n", "np.random.seed(42)\n", "N_BITS = 200\n", "mensaje = np.random.randint(0, 2, N_BITS) # mensaje binario aleatorio\n", "\n", "escenarios = {\n", " \"Canal limpio (p=0.01)\": 0.01,\n", " \"Canal degradado (p=0.10)\": 0.10,\n", " \"Ataque activo (p=0.30)\": 0.30,\n", "}\n", "\n", "print(f\"Mensaje de {N_BITS} bits transmitido por SecureData Corp\")\n", "print(f\"{'─'*55}\")\n", "print(f\"{'Escenario':<30} {'Errores':>8} {'BER':>10} {'Impacto'}\")\n", "print(f\"{'─'*55}\")\n", "\n", "resultados = {}\n", "for nombre, p in escenarios.items():\n", " recibido, errores, ruido_vec = simular_bsc(mensaje, p)\n", " ber = errores / N_BITS\n", " if ber < 0.05:\n", " impacto = \"✅ Aceptable\"\n", " elif ber < 0.15:\n", " impacto = \"⚠️ Degradado\"\n", " else:\n", " impacto = \"🚨 Crítico\"\n", " resultados[nombre] = (recibido, errores, ber, ruido_vec)\n", " print(f\"{nombre:<30} {errores:>8} {ber:>10.3f} {impacto}\")\n" ] }, { "cell_type": "code", "execution_count": null, "id": "892ea08e", "metadata": { "execution": { "iopub.execute_input": "2026-05-26T19:37:43.763157Z", "iopub.status.busy": "2026-05-26T19:37:43.762377Z", "iopub.status.idle": "2026-05-26T19:37:43.770181Z", "shell.execute_reply": "2026-05-26T19:37:43.769245Z" }, "id": "892ea08e", "outputId": "b11b19a4-838d-4144-cee9-557d8249a2dc" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mensaje de 200 bits - SecureData Corp\n", "-------------------------------------------------------\n", "Canal limpio (p=0.01) 1 0.005 Aceptable\n", "Canal degradado (p=0.10) 26 0.130 Degradado\n", "Ataque activo (p=0.30) 51 0.255 Critico\n" ] } ], "source": [ "def simular_bsc(bits_enviados, p_error):\n", " ruido = np.random.binomial(1, p_error, len(bits_enviados))\n", " bits_recibidos = np.bitwise_xor(bits_enviados.astype(int), ruido)\n", " errores = np.sum(ruido)\n", " return bits_recibidos, errores, ruido\n", "\n", "np.random.seed(42)\n", "N_BITS = 200\n", "mensaje = np.random.randint(0, 2, N_BITS)\n", "\n", "escenarios = {'Canal limpio (p=0.01)': 0.01,\n", " 'Canal degradado (p=0.10)': 0.10,\n", " 'Ataque activo (p=0.30)': 0.30}\n", "\n", "print('Mensaje de {} bits - SecureData Corp'.format(N_BITS))\n", "print('-' * 55)\n", "\n", "resultados = {}\n", "for nombre, p in escenarios.items():\n", " recibido, errores, ruido_vec = simular_bsc(mensaje, p)\n", " ber = errores / N_BITS\n", " impacto = 'Aceptable' if ber < 0.05 else ('Degradado' if ber < 0.15 else 'Critico')\n", " resultados[nombre] = (recibido, errores, ber, ruido_vec)\n", " print('{:<30} {:>8} {:>10.3f} {}'.format(nombre, errores, ber, impacto))\n" ] }, { "cell_type": "markdown", "id": "cbf0d1ef", "metadata": { "id": "cbf0d1ef" }, "source": [ "fig, axes = plt.subplots(len(escenarios) + 1, 1, figsize=(14, 7), sharex=True)\n", "N_VIZ = 60\n", "x = np.arange(N_VIZ)\n", "\n", "axes[0].step(x, mensaje[:N_VIZ], color='#1F3864', linewidth=1.4, where='post')\n", "axes[0].set_ylabel('Original', fontsize=9)\n", "axes[0].set_ylim(-0.2, 1.4)\n", "axes[0].set_yticks([0, 1])\n", "axes[0].fill_between(x, mensaje[:N_VIZ], step='post', alpha=0.15, color='#1F3864')\n", "\n", "colores = ['#1D6F3B', '#E69A00', '#C00000']\n", "for i, (nombre, p) in enumerate(escenarios.items()):\n", " recibido, errores, ber, ruido_vec = resultados[nombre]\n", " ax = axes[i + 1]\n", " for j in range(N_VIZ):\n", " c = '#C00000' if ruido_vec[j] == 1 else colores[i]\n", " ax.bar(j, recibido[j], color=c, width=0.8, alpha=0.85)\n", " ax.set_ylabel('p={}'.format(p), fontsize=9)\n", " ax.set_ylim(-0.2, 1.4)\n", " ax.set_yticks([0, 1])\n", " color_ber = '#C00000' if ber > 0.05 else '#1D6F3B'\n", " ax.text(0.98, 0.75, 'BER={:.3f}'.format(ber), transform=ax.transAxes,\n", " ha='right', fontsize=9, color=color_ber)\n", "\n", "axes[-1].set_xlabel('Indice de bit (primeros 60 bits)')\n", "fig.suptitle('BSC - Efecto del ruido sobre transmision en SecureData Corp (rojo = bit erroneo)',\n", " fontsize=12, fontweight='bold')\n", "plt.tight_layout()\n", "plt.savefig('/home/claude/fig_bsc.png', dpi=150, bbox_inches='tight')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": null, "id": "286f8143", "metadata": { "execution": { "iopub.execute_input": "2026-05-26T19:37:43.772067Z", "iopub.status.busy": "2026-05-26T19:37:43.771887Z", "iopub.status.idle": "2026-05-26T19:37:44.472400Z", "shell.execute_reply": "2026-05-26T19:37:44.471179Z" }, "id": "286f8143", "outputId": "0b89de04-aa13-42cd-d52b-715346ec2c7d" }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Canal limpio p=0.01: C=0.919\n", "Degradado p=0.10: C=0.531\n", "Bajo ataque p=0.30: C=0.119\n" ] } ], "source": [ "p_range = np.linspace(0.001, 0.499, 300)\n", "H_b = lambda p: -p*np.log2(p) - (1-p)*np.log2(1-p)\n", "C_bsc = 1 - H_b(p_range)\n", "\n", "fig, ax = plt.subplots(figsize=(9, 4))\n", "ax.plot(p_range, C_bsc, color='#2E75B6', linewidth=2.5, label='Capacidad C(p)')\n", "ax.fill_between(p_range, C_bsc, alpha=0.12, color='#2E75B6')\n", "\n", "for p_mark, label, color in [(0.01, 'Canal limpio', '#1D6F3B'),\n", " (0.10, 'Degradado', '#E69A00'),\n", " (0.30, 'Ataque', '#C00000')]:\n", " c_mark = 1 - H_b(p_mark)\n", " ax.plot(p_mark, c_mark, 'o', color=color, markersize=9, zorder=5)\n", " texto = label + ' C=' + '{:.3f}'.format(c_mark)\n", " ax.annotate(texto,\n", " xy=(p_mark, c_mark), xytext=(p_mark + 0.025, c_mark + 0.05),\n", " fontsize=8.5, color=color,\n", " arrowprops=dict(arrowstyle='->', color=color, lw=1.2))\n", "\n", "ax.set_xlabel('Probabilidad de error p')\n", "ax.set_ylabel('Capacidad C [bits/uso]')\n", "ax.set_title('Capacidad del Canal BSC -- SecureData Corp')\n", "ax.set_xlim(0, 0.5)\n", "ax.set_ylim(0, 1.05)\n", "ax.grid(True, alpha=0.3)\n", "ax.legend()\n", "plt.tight_layout()\n", "plt.savefig('/home/claude/fig_capacidad.png', dpi=150, bbox_inches='tight')\n", "plt.show()\n", "\n", "print('Canal limpio p=0.01: C={:.3f}'.format(1 - H_b(0.01)))\n", "print('Degradado p=0.10: C={:.3f}'.format(1 - H_b(0.10)))\n", "print('Bajo ataque p=0.30: C={:.3f}'.format(1 - H_b(0.30)))\n" ] }, { "cell_type": "markdown", "id": "7136e7a5", "metadata": { "id": "7136e7a5" }, "source": [ "---\n", "## Bloque 3 — Fuentes con y sin memoria (Cadenas de Markov)\n", "\n", "### ¿Qué diferencia una fuente con memoria de una sin memoria?\n", "\n", "| | Fuente sin memoria | Fuente con memoria |\n", "|--|--|--|\n", "| Definición | Cada símbolo es independiente del anterior | La probabilidad del siguiente símbolo **depende del estado actual** |\n", "| Entropía conjunta | $H(X_1, ..., X_n) = \\sum H(X_i)$ | $H(X_1, ..., X_n) < \\sum H(X_i)$ |\n", "| Modelo | Variable aleatoria i.i.d. | Cadena de Markov |\n", "| Ejemplo ciber | Tráfico completamente aleatorio (raro) | Ataques de fuerza bruta (eventos correlacionados) |\n", "\n", "### Cadena de Markov para eventos de seguridad\n", "\n", "SecureData Corp identifica 3 estados en su sistema:\n", "- **S** = Sesión normal\n", "- **F** = Login fallido\n", "- **A** = Alerta activa\n" ] }, { "cell_type": "code", "execution_count": null, "id": "494ee00b", "metadata": { "execution": { "iopub.execute_input": "2026-05-26T19:37:44.474391Z", "iopub.status.busy": "2026-05-26T19:37:44.474188Z", "iopub.status.idle": "2026-05-26T19:37:45.175609Z", "shell.execute_reply": "2026-05-26T19:37:45.174140Z" }, "id": "494ee00b", "outputId": "d1e6e478-8ce4-4a5b-a9f3-831d84c0126c" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "✅ Matriz 'operación normal' válida.\n", "✅ Matriz 'bajo ataque' válida.\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# ─── Matriz de transición de Markov ───\n", "# Filas = estado actual, Columnas = estado siguiente\n", "# Estados: 0=Normal (S), 1=Fallo (F), 2=Alerta (A)\n", "\n", "ESTADOS = ['Normal (S)', 'Fallo (F)', 'Alerta (A)']\n", "\n", "# Operación normal: es probable volver a Normal\n", "P_normal = np.array([\n", " [0.85, 0.10, 0.05], # desde Normal\n", " [0.60, 0.30, 0.10], # desde Fallo → tiende a recuperarse\n", " [0.40, 0.20, 0.40], # desde Alerta\n", "])\n", "\n", "# Bajo ataque de fuerza bruta: los fallos se auto-refuerzan\n", "P_ataque = np.array([\n", " [0.50, 0.35, 0.15], # desde Normal → más fallos\n", " [0.10, 0.70, 0.20], # desde Fallo → el fallo persiste\n", " [0.05, 0.30, 0.65], # desde Alerta → alerta sostenida\n", "])\n", "\n", "def verificar_matriz(P, nombre):\n", " assert np.allclose(P.sum(axis=1), 1.0), f\"Filas no suman 1 en {nombre}\"\n", " print(f\"✅ Matriz '{nombre}' válida.\")\n", "\n", "verificar_matriz(P_normal, \"operación normal\")\n", "verificar_matriz(P_ataque, \"bajo ataque\")\n", "\n", "# ─── Visualización de matrices ───\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n", "\n", "for ax, P, titulo in zip(axes, [P_normal, P_ataque],\n", " [\"Operación Normal\", \"Bajo Ataque\"]):\n", " im = ax.imshow(P, cmap='Blues', vmin=0, vmax=1)\n", " ax.set_xticks(range(3)); ax.set_yticks(range(3))\n", " ax.set_xticklabels(ESTADOS, rotation=15, fontsize=9)\n", " ax.set_yticklabels(ESTADOS, fontsize=9)\n", " ax.set_xlabel(\"Estado siguiente\"); ax.set_ylabel(\"Estado actual\")\n", " ax.set_title(f\"Matriz de transición\\n{titulo}\", fontweight='bold')\n", " for i in range(3):\n", " for j in range(3):\n", " ax.text(j, i, f\"{P[i,j]:.2f}\", ha='center', va='center',\n", " color='white' if P[i,j] > 0.5 else '#1F3864', fontsize=10)\n", " fig.colorbar(im, ax=ax, fraction=0.046)\n", "\n", "plt.suptitle(\"SecureData Corp — Cadenas de Markov para estados de seguridad\",\n", " fontsize=12, fontweight='bold')\n", "plt.tight_layout()\n", "plt.savefig('/home/claude/fig_markov_matrices.png', dpi=150, bbox_inches='tight')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": null, "id": "e8747757", "metadata": { "execution": { "iopub.execute_input": "2026-05-26T19:37:45.178416Z", "iopub.status.busy": "2026-05-26T19:37:45.178205Z", "iopub.status.idle": "2026-05-26T19:37:46.078295Z", "shell.execute_reply": "2026-05-26T19:37:46.077065Z" }, "id": "e8747757", "outputId": "724357c2-8ef4-4bcd-c4d0-7b63ff3e4372" }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# ─── Simulación de secuencias de estados ───\n", "def simular_markov(P, estado_inicial, n_pasos, semilla=None):\n", " if semilla: np.random.seed(semilla)\n", " estados = [estado_inicial]\n", " estado_actual = estado_inicial\n", " for _ in range(n_pasos - 1):\n", " siguiente = np.random.choice(3, p=P[estado_actual])\n", " estados.append(siguiente)\n", " estado_actual = siguiente\n", " return np.array(estados)\n", "\n", "N = 100\n", "seq_normal = simular_markov(P_normal, estado_inicial=0, n_pasos=N, semilla=7)\n", "seq_ataque = simular_markov(P_ataque, estado_inicial=0, n_pasos=N, semilla=7)\n", "\n", "# ─── Visualización de secuencias ───\n", "fig, axes = plt.subplots(2, 1, figsize=(14, 5), sharex=True)\n", "colores_estado = {0: '#1D6F3B', 1: '#E69A00', 2: '#C00000'}\n", "labels_estado = {0: 'Normal', 1: 'Fallo', 2: 'Alerta'}\n", "\n", "for ax, seq, titulo in zip(axes, [seq_normal, seq_ataque],\n", " [\"Operación Normal\", \"Bajo Ataque\"]):\n", " for i in range(len(seq)):\n", " ax.bar(i, 1, color=colores_estado[seq[i]], width=1.0, alpha=0.85)\n", " ax.set_yticks([])\n", " ax.set_ylabel(titulo, fontsize=10, fontweight='bold')\n", " # Leyenda\n", " parches = [mpatches.Patch(color=colores_estado[k], label=labels_estado[k])\n", " for k in range(3)]\n", " ax.legend(handles=parches, loc='upper right', fontsize=8)\n", " # Estadísticas\n", " counts = Counter(seq)\n", " stats = \" | \".join([f\"{labels_estado[k]}: {counts[k]}\" for k in range(3)])\n", " ax.text(0.01, 0.85, stats, transform=ax.transAxes, fontsize=8.5, color='#1F3864')\n", "\n", "axes[-1].set_xlabel(\"Paso de tiempo (evento en el SIEM)\")\n", "plt.suptitle(\"SecureData Corp — Secuencias de estados (100 eventos)\",\n", " fontsize=12, fontweight='bold')\n", "plt.tight_layout()\n", "plt.savefig('/home/claude/fig_secuencias.png', dpi=150, bbox_inches='tight')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "a4db67ea", "metadata": { "id": "a4db67ea" }, "source": [ "### Entropía de fuente con memoria vs sin memoria" ] }, { "cell_type": "code", "execution_count": null, "id": "af07d296", "metadata": { "execution": { "iopub.execute_input": "2026-05-26T19:37:46.080308Z", "iopub.status.busy": "2026-05-26T19:37:46.080107Z", "iopub.status.idle": "2026-05-26T19:37:46.110175Z", "shell.execute_reply": "2026-05-26T19:37:46.109217Z" }, "id": "af07d296", "outputId": "6f138c49-d691-4eeb-c591-01640697208a" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "📌 Operación Normal\n", " Distribución estacionaria: {'Normal (S)': np.float64(0.777), 'Fallo (F)': np.float64(0.136), 'Alerta (A)': np.float64(0.087)}\n", " H marginal (sin memoria): 0.9818 bits/símbolo\n", " H condicional (con memoria): 0.8897 bits/símbolo\n", " Reducción por correlación: 0.0921 bits ← información que 'ahorra' la memoria\n", " H_cond < H_marginal: True ✅ (verifica H(X₁,...,Xₙ) < ΣH(Xᵢ))\n", "\n", "📌 Bajo Ataque\n", " Distribución estacionaria: {'Normal (S)': np.float64(0.137), 'Fallo (F)': np.float64(0.511), 'Alerta (A)': np.float64(0.351)}\n", " H marginal (sin memoria): 1.4184 bits/símbolo\n", " H condicional (con memoria): 1.1903 bits/símbolo\n", " Reducción por correlación: 0.2281 bits ← información que 'ahorra' la memoria\n", " H_cond < H_marginal: True ✅ (verifica H(X₁,...,Xₙ) < ΣH(Xᵢ))\n" ] } ], "source": [ "def entropia_condicional_markov(P, pi):\n", " \"\"\"\n", " Entropía condicional H(X_{t+1} | X_t) para una cadena de Markov\n", " con distribución estacionaria pi.\n", " Equivale a la entropía de la fuente con memoria.\n", " \"\"\"\n", " H_cond = 0.0\n", " for i in range(len(pi)):\n", " for j in range(P.shape[1]):\n", " if P[i, j] > 0:\n", " H_cond -= pi[i] * P[i, j] * np.log2(P[i, j])\n", " return H_cond\n", "\n", "def distribucion_estacionaria(P, n_iter=10000):\n", " \"\"\"Distribución estacionaria por potencias de la matriz.\"\"\"\n", " pi = np.ones(P.shape[0]) / P.shape[0]\n", " for _ in range(n_iter):\n", " pi = pi @ P\n", " return pi\n", "\n", "# Entropía marginal (sin memoria): H basada en distribución estacionaria\n", "for nombre_P, P in [(\"Operación Normal\", P_normal), (\"Bajo Ataque\", P_ataque)]:\n", " pi = distribucion_estacionaria(P)\n", " H_marginal = entropia(pi) # fuente sin memoria\n", " H_condicional = entropia_condicional_markov(P, pi) # fuente con memoria\n", "\n", " print(f\"\\n📌 {nombre_P}\")\n", " print(f\" Distribución estacionaria: {dict(zip(ESTADOS, pi.round(3)))}\")\n", " print(f\" H marginal (sin memoria): {H_marginal:.4f} bits/símbolo\")\n", " print(f\" H condicional (con memoria): {H_condicional:.4f} bits/símbolo\")\n", " print(f\" Reducción por correlación: {H_marginal - H_condicional:.4f} bits ← información que 'ahorra' la memoria\")\n", " print(f\" H_cond < H_marginal: {H_condicional < H_marginal} ✅ (verifica H(X₁,...,Xₙ) < ΣH(Xᵢ))\")\n" ] }, { "cell_type": "markdown", "id": "d3e5d66d", "metadata": { "id": "d3e5d66d" }, "source": [ "### 🔎 Interpretación\n", "\n", "- **Sin memoria** → cada evento del SIEM es completamente independiente. La entropía marginal es el peor caso: necesitamos el máximo de bits para describirlo.\n", "- **Con memoria (Markov)** → los eventos están correlacionados. Si estamos en estado \"Fallo\", el siguiente evento es probablemente también un fallo (bajo ataque). Esto **reduce la entropía real** de la fuente.\n", "- La diferencia `H_marginal − H_condicional` cuantifica exactamente cuánta información \"regala\" la correlación: si modelamos bien la cadena, podemos comprimir más los logs y detectar patrones anómalos con mayor precisión.\n", "\n", "> Este es el principio detrás de los motores de correlación de los sistemas SIEM: explotan la **dependencia temporal** de los eventos para identificar secuencias características de ataques.\n" ] }, { "cell_type": "markdown", "id": "4250b7f6", "metadata": { "id": "4250b7f6" }, "source": [ "---\n", "## 📋 Resumen — Conceptos clave de la Clase 2\n", "\n", "| Concepto | Fórmula | Qué mide en ciberseguridad |\n", "|----------|---------|---------------------------|\n", "| Información de un evento | $I(x) = -\\log_2 p(x)$ | Rareza / sorpresa de un evento del SIEM |\n", "| Entropía de Shannon | $H(X) = -\\sum p(x_i)\\log_2 p(x_i)$ | Incertidumbre promedio del flujo de logs |\n", "| Capacidad BSC | $C = 1 - H_b(p)$ | Tasa máxima confiable ante ruido/ataque |\n", "| Fuente sin memoria | $H(X_1,...,X_n) = \\sum H(X_i)$ | Eventos de seguridad independientes |\n", "| Fuente con memoria | $H(X_1,...,X_n) < \\sum H(X_i)$ | Ataques con correlación temporal (fuerza bruta, APT) |\n", "\n", "### Señales de alerta basadas en entropía (SecureData Corp)\n", "\n", "```\n", "H(login_events) sube abruptamente → posible ataque de fuerza bruta\n", "H(tráfico_red) cae a casi 0 → canal comprometido / tunelización encubierta \n", "BER sube en canal interno → posible inyección de paquetes\n", "H_condicional baja mucho → patrón repetitivo = comportamiento automatizado (bot/malware)\n", "```\n" ] } ], "metadata": { "language_info": { "name": "python" }, "colab": { "provenance": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" } }, "nbformat": 4, "nbformat_minor": 5 }