From af2dd8ca06fd22e63f0d18cb69636cb26867de16 Mon Sep 17 00:00:00 2001
From: Hatter Jiang <jht5945@gmail.com>
Date: Sat, 19 Jul 2025 11:08:54 +0800
Subject: [PATCH] feat: update rsa.ipynb

---
 rsa.ipynb | 40 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 40 insertions(+)

diff --git a/rsa.ipynb b/rsa.ipynb
index 1455439..6a34329 100644
--- a/rsa.ipynb
+++ b/rsa.ipynb
@@ -10,6 +10,26 @@
     "$\\phi(n)=n\\prod_{p|n}\\left(1-\\frac{1}{p}\\right)$"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "84b0bbc4-48f4-4dc9-a1a9-0cab8f68829a",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "4\n",
+      "12\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(euler_phi(12))\n",
+    "print(euler_phi(13))"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "0be1d436-5075-4f2f-96ec-e225179209a7",
@@ -21,6 +41,26 @@
     "\n",
     "$a^{\\phi(n)}\\equiv1 \\bmod n$"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "34b39cb0-1bc0-4f35-8c9f-ff47d575bc9e",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1\n",
+      "1\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(gcd(7,13))\n",
+    "print(pow(7,euler_phi(13),13))"
+   ]
   }
  ],
  "metadata": {