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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "rsa-attack.ipynb",
"provenance": []
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "_a2v4MMrsNq-",
"outputId": "1bc17d8a-56e2-44e4-ee57-6f01f017390b"
},
"source": [
"#https://www.johndcook.com/blog/2019/03/06/rsa-exponent-3/\n",
"from secrets import randbits, randbelow\n",
"from sympy import nextprime\n",
"from sympy.ntheory.modular import crt\n",
" \n",
"def modulus():\n",
" p = nextprime(randbits(6))\n",
" q = nextprime(randbits(6))\n",
" print(\"P,Q =\",p,q)\n",
" return p*q\n",
" \n",
"N = [modulus() for _ in range(3)]\n",
"print(\"N =\", N)\n",
"m = randbelow(min(N))\n",
"print(\"m =\",m)\n",
"c = [pow(m, 3, N[i]) for i in range(3)]\n",
"x = crt(N, c)[0]\n",
"print(\"c =\",c) \n",
"print(\"x =\",x)\n",
"print(\"m =\",x**(1./3.))"
],
"execution_count": 30,
"outputs": [
{
"output_type": "stream",
"text": [
"P,Q = 53 31\n",
"P,Q = 29 47\n",
"P,Q = 23 3\n",
"N = [1643, 1363, 69]\n",
"m = 21\n",
"c = [1046, 1083, 15]\n",
"x = 9261\n",
"m = 20.999999999999996\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "J1OmTmMQsU4a",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "f923697a-1592-4af7-ad69-9c11324ecc26"
},
"source": [
"#https://www.di-mgt.com.au/rsa_factorize_n.html\n",
"import math\n",
"N = 25777 \n",
"e =3\n",
"d=16971 \n",
"\n",
"k = (d * e) -1\n",
"\n",
"for g in range (2,N-1):\n",
" t = k\n",
" print(\"g------------\", g)\n",
" d = 0;\n",
" while (t % 2 == 0):\n",
" t = t/2 \n",
" print(\"t = \",t)\n",
" t = int(t)\n",
" x = pow(g,t) % N\n",
" print(\"x = \",x)\n",
" if(x > 1):\n",
" y = math.gcd(x-1,N)\n",
" if(y > 1):\n",
" print(\"p=\",y)\n",
" print(\"y=\",N/y)\n",
" print(\"True\")\n",
" d = 1;\n",
" break \n",
" else:\n",
" d = 0;\n",
" print(\"False\")\n",
" if(d==1):\n",
" break\n",
" print(\"\\n\")\n"
],
"execution_count": 31,
"outputs": [
{
"output_type": "stream",
"text": [
"g------------ 2\n",
"t = 25456.0\n",
"x = 1\n",
"t = 12728.0\n",
"x = 1\n",
"t = 6364.0\n",
"x = 1\n",
"t = 3182.0\n",
"x = 25776\n",
"False\n",
"t = 1591.0\n",
"x = 12709\n",
"False\n",
"\n",
"\n",
"g------------ 3\n",
"t = 25456.0\n",
"x = 1\n",
"t = 12728.0\n",
"x = 1\n",
"t = 6364.0\n",
"x = 1\n",
"t = 3182.0\n",
"x = 25776\n",
"False\n",
"t = 1591.0\n",
"x = 13068\n",
"False\n",
"\n",
"\n",
"g------------ 4\n",
"t = 25456.0\n",
"x = 1\n",
"t = 12728.0\n",
"x = 1\n",
"t = 6364.0\n",
"x = 1\n",
"t = 3182.0\n",
"x = 1\n",
"t = 1591.0\n",
"x = 25776\n",
"False\n",
"\n",
"\n",
"g------------ 5\n",
"t = 25456.0\n",
"x = 1\n",
"t = 12728.0\n",
"x = 1\n",
"t = 6364.0\n",
"x = 1\n",
"t = 3182.0\n",
"x = 15050\n",
"p= 149\n",
"y= 173.0\n",
"True\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "UpRyYh_9r3Sd",
"outputId": "52a718a6-149a-4815-816d-77b032d1018c"
},
"source": [
"#hashing from geeksforgeeks\n",
"import hashlib\n",
" \n",
"# initializing string\n",
"str = \"GeeksforGeeks\"\n",
" \n",
"result = hashlib.sha256(str.encode())\n",
" \n",
"print(\"The hexadecimal equivalent of SHA256 is : \")\n",
"print(result.hexdigest())"
],
"execution_count": 32,
"outputs": [
{
"output_type": "stream",
"text": [
"The hexadecimal equivalent of SHA256 is : \n",
"f6071725e7ddeb434fb6b32b8ec4a2b14dd7db0d785347b2fb48f9975126178f\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "RoD6lR1tsdha",
"outputId": "043b1ac3-091c-48b6-aa17-ddea6f0d4b3c"
},
"source": [
"!pip install PyCrypto\n",
"#import cartopy\n",
"from Crypto.PublicKey import RSA\n",
"from Crypto.Cipher import PKCS1_OAEP\n",
"from Crypto.Signature import PKCS1_v1_5\n",
"from Crypto.Hash import SHA512, SHA384, SHA256, SHA, MD5\n",
"from Crypto import Random\n",
"from base64 import b64encode, b64decode\n",
"hash = \"SHA-256\"\n",
"\n",
"def newkeys(keysize):\n",
" random_generator = Random.new().read\n",
" key = RSA.generate(keysize, random_generator)\n",
" private, public = key, key.publickey()\n",
" return public, private\n",
"\n",
"def importKey(externKey):\n",
" return RSA.importKey(externKey)\n",
"\n",
"def getpublickey(priv_key):\n",
" return priv_key.publickey()\n",
"\n",
"def decrypt(ciphertext, priv_key):\n",
" cipher = PKCS1_OAEP.new(priv_key)\n",
" return cipher.decrypt(ciphertext)\n",
"\n",
"def encrypt(message, pub_key):\n",
" cipher = PKCS1_OAEP.new(pub_key)\n",
" return cipher.encrypt(message)\n",
"\n",
"public, private = newkeys(1024)\n",
"print(\"publickey = \", public)\n",
"print(\"publickey e= \",private.e)\n",
"print(\"privatekey d= \",private.d)\n",
"print(\"N = \", private.n)\n",
"c = encrypt(b\"hello\",public)\n",
"print(\"cipher text = \", c)\n",
"p = decrypt(c,private)\n",
"print(\"plaintext = \",p)\n",
"\n"
],
"execution_count": 39,
"outputs": [
{
"output_type": "stream",
"text": [
"Requirement already satisfied: PyCrypto in /usr/local/lib/python3.7/dist-packages (2.6.1)\n",
"publickey = <_RSAobj @0x7fd042111f50 n(1024),e>\n",
"publickey e= 65537\n",
"privatekey d= 58177119264142305610042127146837107576819333012193647656535716996944363732356343334378431879978582248844883931022489304127875653017269037040735970776368060244452953536175019865694105876207655266671741820912213081795309663119140529607414070763914976280026992314637845563712885411003341940657911574321278069473\n",
"N = 104933366319364091998495414526551906405999962229809690008707342364902787007773157371822190453231219068186243516923651617576127333749628756860842529703339323249812567797468631158875646153770860481986776046212356637545697706772991399145313898136185193439929683926816582951494228042677550852934831577814540337181\n",
"cipher text = b\"?\\x1d\\xc2V\\xbfw3\\xb7Y\\x86W\\x84\\xb5\\x92\\xf3\\xa4\\xbeC\\x10\\xb7D\\xcfG\\xe9\\xa9-\\xb2b\\x10\\xeb\\x04;\\x82\\x1dr\\x15\\x83M1\\xe2\\xe2\\x0e\\x05\\r\\xdaTr\\xff\\x166p\\x98\\x89\\xac\\rP\\xb4\\xae\\xa2\\x9f$\\x0e\\x06$X\\xba5\\x05\\xb4\\x0b h\\x1b\\\\\\xafr\\xd4\\xb8$\\x83\\xdf\\x0b\\x19\\xc0 yd\\n\\xedR\\xc7n\\xaf~\\xdf\\x96\\x82\\x82\\xd9cR\\x1c\\xe1\\xef-\\xc9\\xc1y#\\xc5qp>\\xf75-\\x84B2\\xff\\x0c:'\\xb5\\x1d\\xd3\\xf9\\x0e\"\n",
"plaintext = b'hello'\n"
],
"name": "stdout"
}
]
}
]
}