{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "from cryptography.hazmat import backends\n",
    "from cryptography.hazmat.primitives import hashes\n",
    "from cryptography.hazmat.primitives.asymmetric import utils\n",
    "from cryptography.hazmat.primitives.asymmetric import rsa\n",
    "from cryptography.hazmat.primitives import serialization\n",
    "from cryptography.hazmat.primitives.asymmetric import padding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def int_to_bytes(x: int) -> bytes:\n",
    "    return x.to_bytes((x.bit_length() + 7) // 8, 'big')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Два открытых текста\n",
    "plain_text1 = b\"58\"\n",
    "plain_text2 = b\"4\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Генерация публичного ключа, public_exponent=3 (e), \n",
    "# TODO: попробуйте сгенерировать ключ длиной 256 битов. Объясните результат\n",
    "private_key = rsa.generate_private_key(public_exponent=3, key_size=512, backend=backends.default_backend())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[b'-----BEGIN RSA PRIVATE KEY-----',\n",
       " b'MIIBOwIBAAJBAMu1Plu+bLzcuZSEfAIqsvdKQjNRY+QSIHsQsk71LH1R1rWpugcb',\n",
       " b'TB+qxFnWSSQxyv5JaYs3W+9nr3jvcHeKNlUCAQMCQQCHzimSfvMokyZjAv1WxyH6',\n",
       " b'MYF3i5ftYWr8tcw0o3L+NV6Z08rFnW1DHDT/b12Wt/vExpq+JMuBVJczNv9ToFtz',\n",
       " b'AiEA6Ml6uPqOBOZnbUzbqJUBH5geoh1/C7u9SvV/UUWWU4sCIQDgBXFQ5CEjVJkH',\n",
       " b'jdOULRyxvwDfUIEe8auBtp2gNINZnwIhAJsw/HtRtANERPOIknBjVhUQFGwTqgfS',\n",
       " b'fjH4/4uDuY0HAiEAlVj2Ne1rbOMQr7PiYsi9y9SrP4sAv0vHq88TwCMCO78CIQDD',\n",
       " b'8fZsG321RePUlc2ljRBieV+oAP2VSNu4QeQPhA4tNg==',\n",
       " b'-----END RSA PRIVATE KEY-----']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Просмотр содержимого секретного ключа\n",
    "pem = private_key.private_bytes(\n",
    "        encoding=serialization.Encoding.PEM,\n",
    "        format=serialization.PrivateFormat.TraditionalOpenSSL,\n",
    "        encryption_algorithm=serialization.NoEncryption())\n",
    "\n",
    "# Формат для записи в файл/для передачи по сети\n",
    "pem.splitlines()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Секретное число, для которого e x d=1 mod ((p-1)(q-1))\n",
    "d = private_key.private_numbers().d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[b'-----BEGIN PUBLIC KEY-----',\n",
       " b'MFowDQYJKoZIhvcNAQEBBQADSQAwRgJBAMu1Plu+bLzcuZSEfAIqsvdKQjNRY+QS',\n",
       " b'IHsQsk71LH1R1rWpugcbTB+qxFnWSSQxyv5JaYs3W+9nr3jvcHeKNlUCAQM=',\n",
       " b'-----END PUBLIC KEY-----']"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# просмотр содержимого открытого ключа\n",
    "public_key = private_key.public_key()\n",
    "pem = public_key.public_bytes(\n",
    "    encoding=serialization.Encoding.PEM,\n",
    "    format=serialization.PublicFormat.SubjectPublicKeyInfo)\n",
    "\n",
    "# Формат для записи в файл/для передачи по сети\n",
    "pem.splitlines()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "e = public_key.public_numbers().e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = int(public_key.public_numbers().n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10669052760492704969889175507802197153705895081930185893657373545838235340277562771266395178505206456909397291234845763674171653256429076791779811616503381\n"
     ]
    }
   ],
   "source": [
    "print(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Шифрование \n",
    "cipher_text1 = public_key.encrypt(plain_text1, padding.PKCS1v15())\n",
    "cipher_text2 = public_key.encrypt(plain_text2, padding.PKCS1v15())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cipher text1 =  b'\\xb9\\ts\\xe8J\\xaa\\xcc/\\x0e|\\x9b\\x00`\\xab\\xe2kR\\x92\\xb7\\xa2\\x8f]C p\\x1a\\xfaqV)\\xa1m+\\x9a\\xae\\x99\\x1b0\\xd1\\xcd\\xa3;\\r|CU\\x06c\\xdc\\x11u\\x91\\xedC\\xc8\\x81t\\x83\\xf3?\\x1bI\\xde\\x96' 64\n",
      "Cipher text2 =  b'\\x8a\\x90\\xa7[\\xea\\xde\\t\\xa4\\x99\\x9f\\xda\\x14\\xd5@x\\xec\\x03\\xe9\\x89\\x80\\xff\\xba\\x81\\x99\\xa2\\x11c7\\x1a\\x80\\x90\\x08\\xb3\\x81fi8\\t@ %\\xda\\xb4Z6\\x16\\x00\\xa3\\xea$\\xb9`X\\x92r~\\xe2\\x15\\xff\\xe3Nl\\xb6D' 64\n"
     ]
    }
   ],
   "source": [
    "print(\"Cipher text1 = \", cipher_text1, len(cipher_text1))\n",
    "print(\"Cipher text2 = \", cipher_text2, len(cipher_text2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Расшифрование\n",
    "plain_text1 = private_key.decrypt(cipher_text1, padding.PKCS1v15())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "b'58'"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plain_text1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9691170111023022721564242860485637769769359078705157301955035945214579461290810277996451464058492530723777893831180468675682572818866644029400818930802326\n",
      "7257240725642937563206833412652178138599554586539650911269768134247934322094801380450846368625992444622025900827483661152188110918137198461902608650778180\n"
     ]
    }
   ],
   "source": [
    "# Преобразовать шифрограммы в большие числа\n",
    "int_cipher_text1 = int.from_bytes(cipher_text1,  byteorder='big')\n",
    "int_cipher_text2 = int.from_bytes(cipher_text2,  byteorder='big')\n",
    "int_n = int(public_key.public_numbers().n)\n",
    "print(int_cipher_text1)\n",
    "print(int_cipher_text2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# перемножить шифрограммы\n",
    "mult_cipher_texts = (int_cipher_text1 * int_cipher_text2) % int_n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Decryption failed.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-17-d5dbb7415aa1>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# TODO: объясните, почему данные не расшифровываются\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mmult_plain_texts\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mprivate_key\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdecrypt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint_to_bytes\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmult_cipher_texts\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpadding\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mPKCS1v15\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m~\\Anaconda31\\lib\\site-packages\\cryptography\\hazmat\\backends\\openssl\\rsa.py\u001b[0m in \u001b[0;36mdecrypt\u001b[1;34m(self, ciphertext, padding)\u001b[0m\n\u001b[0;32m    357\u001b[0m             \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Ciphertext length must be equal to key size.\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    358\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 359\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0m_enc_dec_rsa\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_backend\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mciphertext\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpadding\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    360\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    361\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mpublic_key\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda31\\lib\\site-packages\\cryptography\\hazmat\\backends\\openssl\\rsa.py\u001b[0m in \u001b[0;36m_enc_dec_rsa\u001b[1;34m(backend, key, data, padding)\u001b[0m\n\u001b[0;32m     66\u001b[0m         )\n\u001b[0;32m     67\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 68\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0m_enc_dec_rsa_pkey_ctx\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbackend\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpadding_enum\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpadding\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     69\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     70\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda31\\lib\\site-packages\\cryptography\\hazmat\\backends\\openssl\\rsa.py\u001b[0m in \u001b[0;36m_enc_dec_rsa_pkey_ctx\u001b[1;34m(backend, key, data, padding_enum, padding)\u001b[0m\n\u001b[0;32m    120\u001b[0m     \u001b[0mres\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcrypt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpkey_ctx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbuf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0moutlen\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    121\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mres\u001b[0m \u001b[1;33m<=\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 122\u001b[1;33m         \u001b[0m_handle_rsa_enc_dec_error\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbackend\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    123\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    124\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mbackend\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_ffi\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mbuffer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbuf\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[0moutlen\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda31\\lib\\site-packages\\cryptography\\hazmat\\backends\\openssl\\rsa.py\u001b[0m in \u001b[0;36m_handle_rsa_enc_dec_error\u001b[1;34m(backend, key)\u001b[0m\n\u001b[0;32m    151\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    152\u001b[0m         \u001b[0mbackend\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mopenssl_assert\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0merrors\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mreason\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mdecoding_errors\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 153\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Decryption failed.\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    154\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    155\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: Decryption failed."
     ]
    }
   ],
   "source": [
    "# TODO: объясните, почему данные не расшифровываются\n",
    "mult_plain_texts = private_key.decrypt(int_to_bytes(mult_cipher_texts), padding.PKCS1v15())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# \"Чистый\" RSA (без padding)\n",
    "m1=58\n",
    "m2=8\n",
    "e=5\n",
    "n=289301\n",
    "d=57641"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = pow(m1,e) % n\n",
    "c2 = pow(m2,e) % n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "464 == 464\n"
     ]
    }
   ],
   "source": [
    "# Проверка гомоморфизма для умножения\n",
    "mult_c1c2 = (c1*c2) % n\n",
    "print(pow(mult_c1c2,d)% n,'==',m1*m2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "259859 == 66\n"
     ]
    }
   ],
   "source": [
    "# Проверка гомоморфизма для сложения\n",
    "sum_c1c2 = (c1+c2) % n\n",
    "print(pow(sum_c1c2,d)% n,'==',m1+m2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}