RSA-2018-08-02.ipynb

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   "source": [
    "p = next_prime(3291)\n",
    "q = next_prime(10000)\n",
    "n = p*q\n",
    "e = 11\n",
    "gcd(e, euler_phi(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
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     "execution_count": 2,
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   "source": [
    "_, d, _ = xgcd(e, euler_phi(n))\n",
    "d"
   ]
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     "execution_count": 3,
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   ],
   "source": [
    "# 確かめ\n",
    "e * d % euler_phi(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[11, 33013093]"
      ]
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     "execution_count": 4,
     "metadata": {},
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   ],
   "source": [
    "# 公開鍵\n",
    "[e,n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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     "data": {
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       "[11999923, 33013093]"
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     },
     "execution_count": 5,
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   "source": [
    "# 秘密鍵\n",
    "[d, n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "8355399"
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     "execution_count": 6,
     "metadata": {},
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   ],
   "source": [
    "# 暗号化\n",
    "x = 129487\n",
    "y = x^e % n\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "129487"
      ]
     },
     "execution_count": 7,
     "metadata": {},
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   ],
   "source": [
    "# 復号\n",
    "y^d % n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$e$ が大きいとき、$x^e$ (mod $n$) は、 `power_mod` という関数を使わないときつい。\n",
    "\n",
    "`power_mod(x, e, n)` で $x^e$ % $n$ を「賢く」やってくれる。"
   ]
  },
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   "execution_count": 8,
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     "execution_count": 8,
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   ],
   "source": [
    "power_mod(x,e,n)"
   ]
  }
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