{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "name": "rsaNk.ipynb", "provenance": [], "collapsed_sections": [], "authorship_tag": "ABX9TyPpT9gQBsvr+52dw80/CCws", "include_colab_link": true }, "kernelspec": { "name": "python3", "display_name": "Python 3" } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "view-in-github", "colab_type": "text" }, "source": [ "\"Open" ] }, { "cell_type": "code", "metadata": { "id": "sbpO6gadYhw3" }, "source": [ "import random\n", "\n", "def n_bit_random(n):\n", " return(random.randrange(2**(n-1)+1, 2**n-1))\n", "\n", "first_primes_list = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, \n", " 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, \n", " 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, \n", " 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, \n", " 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, \n", " 293, 307, 311, 313, 317, 331, 337, 347, 349]\n", "\n", "def check_low_level_prime(n):\n", " while True: \n", " prime_candidate = n_bit_random(n) \n", " for divisor in first_primes_list: \n", " if prime_candidate % divisor == 0 and divisor**2 <= prime_candidate: \n", " break\n", " return prime_candidate \n", "\n", "def check_miller_rabin_primality(mrc):\n", " max_divisions_by_two = 0\n", " ec = mrc-1\n", " while ec % 2 == 0: \n", " ec >>= 1\n", " max_divisions_by_two += 1\n", " assert(2**max_divisions_by_two * ec == mrc-1) # lame\n", " \n", " def trial_composite(round_tester): \n", " if pow(round_tester, ec, mrc) == 1: \n", " return False\n", " for i in range(max_divisions_by_two): \n", " if pow(round_tester, 2**i * ec, mrc) == mrc-1: \n", " return False\n", " return True\n", " \n", " trials_amount = 20 \n", " for i in range(trials_amount): \n", " round_tester = random.randrange(2, mrc) \n", " if trial_composite(round_tester): \n", " return False\n", " return True\n", "\n", "def n_bit_random_prime(n):\n", " while True:\n", " possible_prime = check_low_level_prime(n) \n", " if not check_miller_rabin_primality(possible_prime): \n", " continue\n", " return possible_prime" ], "execution_count": null, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "UKJWDO3Pvqri" }, "source": [ "import math\n", "\n", "import decimal\n", "decimal.getcontext().prec=10000\n", "_d = lambda x: decimal.Decimal(x)\n", "\n", "# Modular exponentiation goes brrrrr \n", "def modular_pow(base, exponent, modulus):\n", " base, modulus = _d(base), _d(modulus)\n", " base %= modulus\n", " result = 1\n", " while exponent > 0:\n", " if int(exponent) & 1:\n", " result = (result * base) % modulus\n", " base = (base * base) % modulus\n", " exponent //= 2\n", " return result\n", "\n", "def encrypt(message, exponent, modulus):\n", " out = []\n", " for c in message:\n", " encv = modular_pow(ord(c), exponent, modulus)\n", " out.append(encv)\n", " return out\n", "\n", "def decrypt(encrypted, pkey, modulus):\n", " out = []\n", " for num in encrypted:\n", " decv = modular_pow(num, pkey, modulus)\n", " out.append(chr(decv))\n", " return \"\".join(out)\n", "\n", "def lcm(a, b):\n", " return abs(a*b) // math.gcd(a, b)\n", "\n", "def choose_e(lcmv):\n", " while 1:\n", " e = random.randrange(3, 2**16+2)\n", " if e < lcmv and math.gcd(e, lcmv) == 1:\n", " return e\n", "\n", "def extended_gcd(a, b):\n", " x, old_x = 0, 1\n", " y, old_y = 1, 0\n", "\n", " while (b != 0):\n", " quotient = a // b\n", " a, b = b, a - quotient * b\n", " old_x, x = x, old_x - quotient * x\n", " old_y, y = y, old_y - quotient * y\n", "\n", " return a, old_x, old_y" ], "execution_count": null, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "bw4RrEVrY5CD", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "faa2c44a-3614-4bdc-9a16-2b82714f9034" }, "source": [ "key_length = 1024\n", "%time P = n_bit_random_prime(key_length)\n", "%time Q = n_bit_random_prime(key_length)" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "CPU times: user 3.67 s, sys: 999 µs, total: 3.67 s\n", "Wall time: 3.69 s\n", "CPU times: user 1.85 s, sys: 0 ns, total: 1.85 s\n", "Wall time: 1.86 s\n" ], "name": "stdout" } ] }, { "cell_type": "code", "metadata": { "id": "jmogw7cUubMA" }, "source": [ "n = P * Q\n", "lcmv = lcm(P-1, Q-1)\n", "e = choose_e(lcmv)\n", "\n", "gcd, x, y = extended_gcd(e, lcmv)\n", "if x < 0:\n", " d = x + lcmv\n", "else:\n", " d = x" ], "execution_count": null, "outputs": [] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "wJr-rgmGCwZg", "outputId": "72707a66-fe1c-4ec0-c682-4cd741a50eee" }, "source": [ "print(e, d, n, sep=\"\\n\")" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "39649\n", "2775085486572169457933031624471639527709572371571563930751706363455686679103931887012786872357300821852072462055701332168753464477069850100477857634950881057962034588705265582670348431618430187943675082038338808823502290083334757934315038640497969786069367822629393372740634217481080439281756759203535191518030611113366713687329262086331416243914608547464393822243234244247787598602422663859280454972323707900579310354345134163802897882709119063046579316638215239586955495026262129316401981036727648176233721051089840544139490182413169518916207283731389315379326286341277949065063422651145928466610428684652315668195\n", "23566779236161770643112862787707714768319744752887788874531340221608793304492584597473313112218174480194085827590012234139629339174956445928785901695962763659830088046458803074421870909628916257832886158798721043310543454720481166030983536298954914657023031763702456252981131493715209010905445417269332126191376334319895522288189118297669317432037971085289460034222690931966559137798412723327254054307131802134542456875495143040890127834885396847838923210976349174614092437902214219214789194798418440795059024409693565307454667852500406186883883445142228234703191640206646086208037120337436442497385687546078418876013\n" ], "name": "stdout" } ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "uKS9PEF0wu0M", "outputId": "0555f9a9-d86a-4063-fed7-1ae8da28b2e8" }, "source": [ "message = \"sosait\"\n", "encrypted_message = encrypt(message, e, n)\n", "decrypted_message = decrypt(encrypted_message, d, n)\n", "\n", "print(message, \"Encrypted message will be really long\", decrypted_message, sep=\"\\n\")" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "sosait\n", "Encrypted message will be really long\n", "sosait\n" ], "name": "stdout" } ] }, { "cell_type": "code", "metadata": { "id": "v9TcbW1b822_" }, "source": [ "import os\n", "import pickle\n", "import IPython\n", "from google.colab import output, files\n", "\n", "def prepare_file(filename, data):\n", " with open(filename, \"wb+\") as f:\n", " pickle.dump(data, f, pickle.HIGHEST_PROTOCOL)\n", " return filename\n", "\n", "def download_public():\n", " files.download(prepare_file(\"public.key\", [e, n]))\n", "\n", "def download_private():\n", " files.download(prepare_file(\"private.key\", [d, n]))\n", "\n", "def download_unlink(filename):\n", " try:\n", " os.remove(filename)\n", " except OSError:\n", " pass\n", "\n", "output.register_callback(\"notebook.download_public\", download_public)\n", "output.register_callback(\"notebook.download_private\", download_private)\n", "output.register_callback(\"notebook.download_unlink\", download_unlink)" ], "execution_count": null, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "bmO9YlMLAjvr" }, "source": [ "import os\n", "import pickle\n", "import IPython\n", "from google.colab import output, files\n", "\n", "def check_correctness():\n", " download_unlink(\"public.key\")\n", " download_unlink(\"private.key\")\n", " \n", " print(\"Select `public.key` and `private.key` files\")\n", " uploaded = files.upload()\n", " \n", " eu, nf = pickle.loads(uploaded[\"public.key\"])\n", " du, ns = pickle.loads(uploaded[\"private.key\"])\n", " \n", " try:\n", " assert(nf == ns)\n", " except AssertionError:\n", " print(\"Keys modules are not equal!\")\n", " return\n", "\n", " nu = nf\n", "\n", " test_message = \"test messages for days\"\n", "\n", " try:\n", " encm = encrypt(test_message, eu, nu)\n", " decm = decrypt(encm, du, nu)\n", " except AssertionError:\n", " print(\"Test message not correctly encrypted\")\n", " else:\n", " print(\"Everything seems correct. Encryption and decryption worked well.\")\n", " \n", "output.register_callback(\"notebook.check_correctness\", check_correctness)" ], "execution_count": null, "outputs": [] }, { "cell_type": "code", "metadata": { "colab": { "resources": { "http://localhost:8080/nbextensions/google.colab/files.js": { "data": 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"ok": true, "headers": [ [ "content-type", "application/javascript" ] ], "status": 200, "status_text": "" } }, "base_uri": "https://localhost:8080/", "height": 161 }, "id": "tKBqI0PV8wQ7", "outputId": "f0dc10d0-fa3b-4b75-a55a-c85b76154e2e" }, "source": [ "%%javascript\n", "(async function() {\n", " let dPublic = document.createElement(\"button\");\n", " let dPrivate = document.createElement(\"button\");\n", " let dCheckC = document.createElement(\"button\");\n", "\n", " dPublic.innerText = \"Download public key\";\n", " dPrivate.innerText = \"Download private key\";\n", " dCheckC.innerText = \"Check Correctness\";\n", "\n", " dPublic.addEventListener('click', async (event) => {\n", " await google.colab.kernel.invokeFunction(\"notebook.download_public\", [], {});\n", " await google.colab.kernel.invokeFunction(\"notebook.download_unlink\", [\"public.key\"], {});\n", " });\n", "\n", " dPrivate.addEventListener('click', async (event) => {\n", " await google.colab.kernel.invokeFunction(\"notebook.download_private\", [], {});\n", " await google.colab.kernel.invokeFunction(\"notebook.download_unlink\", [\"private.key\"], {});\n", " });\n", "\n", " dCheckC.addEventListener('click', async (event) => {\n", " await google.colab.kernel.invokeFunction(\"notebook.check_correctness\", [], {});\n", " });\n", "\n", " document.querySelector(\"#output-area\").appendChild(dPublic);\n", " document.querySelector(\"#output-area\").appendChild(dPrivate);\n", " document.querySelector(\"#output-area\").appendChild(dCheckC);\n", "})();" ], "execution_count": null, "outputs": [ { "output_type": "display_data", "data": { "application/javascript": [ "(async function() {\n", " let dPublic = document.createElement(\"button\");\n", " let dPrivate = document.createElement(\"button\");\n", " let dCheckC = document.createElement(\"button\");\n", "\n", " dPublic.innerText = \"Download public key\";\n", " dPrivate.innerText = \"Download private key\";\n", " dCheckC.innerText = \"Check Correctness\";\n", "\n", " dPublic.addEventListener('click', async (event) => {\n", " await google.colab.kernel.invokeFunction(\"notebook.download_public\", [], {});\n", " await google.colab.kernel.invokeFunction(\"notebook.download_unlink\", [\"public.key\"], {});\n", " });\n", "\n", " dPrivate.addEventListener('click', async (event) => {\n", " await google.colab.kernel.invokeFunction(\"notebook.download_private\", [], {});\n", " await google.colab.kernel.invokeFunction(\"notebook.download_unlink\", [\"private.key\"], {});\n", " });\n", "\n", " dCheckC.addEventListener('click', async (event) => {\n", " await google.colab.kernel.invokeFunction(\"notebook.check_correctness\", [], {});\n", " });\n", "\n", " document.querySelector(\"#output-area\").appendChild(dPublic);\n", " document.querySelector(\"#output-area\").appendChild(dPrivate);\n", " document.querySelector(\"#output-area\").appendChild(dCheckC);\n", "})();" ], "text/plain": [ "" ] }, "metadata": { "tags": [] } }, { "output_type": "stream", "text": [ "Select `public.key` and `private.key` files\n" ], "name": "stdout" }, { "output_type": "display_data", "data": { "text/html": [ "\n", " \n", " \n", " Upload widget is only available when the cell has been executed in the\n", " current browser session. Please rerun this cell to enable.\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": { "tags": [] } }, { "output_type": "stream", "text": [ "Saving private.key to private.key\n", "Saving public.key to public.key\n", "Everything seems correct. Encryption and decryption worked well.\n" ], "name": "stdout" } ] } ] }