pwnhub.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 3283820208958447696987943374117448908009765357285654693385347327161990683145362435055078968569512096812028089118865534433123727617331619214412173257331161\n",
    "p = 34387544593670505224894952205499074005031928791959611454481093888481277920639\n",
    "q = 95494466027181231798633086231116363926111790946014452380632032637864163116199\n",
    "e = 65537\n",
    "c = 2152534604028570372634288477962037445130495144236447333908131330331177601915631781056255815304219841064038378099612028528380520661613873180982330559507116"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#https://crypto.stackexchange.com/questions/81949/how-to-compute-m-value-from-rsa-if-phin-is-not-relative-prime-with-the-e/81966#81966\n",
    "lmb = (p-1)*(q-1)/gcd(p-1,q-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25053177662682512908646591803999640722109383686205156578614731580343856776669915872289379410352080265907742753566186968532170785613443597417381233626"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lmb/e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "610603001254786950117204016100094851174682771252096629718770045663657708853546673840012894001567171172542663753238859651358189495264776579202830986736744"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pow(2,_,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = _"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = (e^-1)%(lmb/e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "flag{thanks_so_much_for_helping_me_with_these_primitive_primes}\n"
     ]
    }
   ],
   "source": [
    "from Crypto.Util.number import *\n",
    "for i in range(1,e):\n",
    "#     print(c,d,L,i,n)\n",
    "    flag = (pow(c,d,n)*pow(L,i,n))%n\n",
    "    p = long_to_bytes(flag).decode('latin1')\n",
    "    if \"flag\" in p:\n",
    "        print(p)\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 9.0",
   "language": "sage",
   "name": "sagemath"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}