Benchmark_of_the_SHA256_hash_function__Python_Cython_Numba.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": "true"
   },
   "source": [
    "# Table of Contents\n",
    " <p><div class=\"lev1 toc-item\"><a href=\"#Benchmark-of-the-SHA256-hash-function,-with-Python,-Cython-and-Numba\" data-toc-modified-id=\"Benchmark-of-the-SHA256-hash-function,-with-Python,-Cython-and-Numba-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Benchmark of the SHA256 hash function, with Python, Cython and Numba</a></div><div class=\"lev2 toc-item\"><a href=\"#What-is-a-hash-function?\" data-toc-modified-id=\"What-is-a-hash-function?-11\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>What is a hash function?</a></div><div class=\"lev2 toc-item\"><a href=\"#Common-API-for-the-different-classes\" data-toc-modified-id=\"Common-API-for-the-different-classes-12\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>Common API for the different classes</a></div><div class=\"lev2 toc-item\"><a href=\"#Checking-the-the-hashlib-module-in-Python-standard-library\" data-toc-modified-id=\"Checking-the-the-hashlib-module-in-Python-standard-library-13\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span>Checking the <a href=\"https://docs.python.org/3/library/hashlib.html\" target=\"_blank\">the <code>hashlib</code> module in Python standard library</a></a></div><div class=\"lev2 toc-item\"><a href=\"#Pure-Python-code-for-the-SHA-2-hashing-function\" data-toc-modified-id=\"Pure-Python-code-for-the-SHA-2-hashing-function-14\"><span class=\"toc-item-num\">1.4&nbsp;&nbsp;</span>Pure Python code for the SHA-2 hashing function</a></div><div class=\"lev3 toc-item\"><a href=\"#Useful-functions-the-SHA-2-algorithm\" data-toc-modified-id=\"Useful-functions-the-SHA-2-algorithm-141\"><span class=\"toc-item-num\">1.4.1&nbsp;&nbsp;</span>Useful functions the SHA-2 algorithm</a></div><div class=\"lev3 toc-item\"><a href=\"#The-SHA2-class\" data-toc-modified-id=\"The-SHA2-class-142\"><span class=\"toc-item-num\">1.4.2&nbsp;&nbsp;</span>The <code>SHA2</code> class</a></div><div class=\"lev3 toc-item\"><a href=\"#Check-on-SHA-2\" data-toc-modified-id=\"Check-on-SHA-2-143\"><span class=\"toc-item-num\">1.4.3&nbsp;&nbsp;</span>Check on SHA-2</a></div><div class=\"lev3 toc-item\"><a href=\"#Trying-1000-random-examples\" data-toc-modified-id=\"Trying-1000-random-examples-144\"><span class=\"toc-item-num\">1.4.4&nbsp;&nbsp;</span>Trying 1000 random examples</a></div><div class=\"lev2 toc-item\"><a href=\"#Numba-powered-code-for-the-SHA-2-hashing-function\" data-toc-modified-id=\"Numba-powered-code-for-the-SHA-2-hashing-function-15\"><span class=\"toc-item-num\">1.5&nbsp;&nbsp;</span>Numba-powered code for the SHA-2 hashing function</a></div><div class=\"lev3 toc-item\"><a href=\"#Requirements\" data-toc-modified-id=\"Requirements-151\"><span class=\"toc-item-num\">1.5.1&nbsp;&nbsp;</span>Requirements</a></div><div class=\"lev3 toc-item\"><a href=\"#Useful-functions-the-SHA-2-algorithm\" data-toc-modified-id=\"Useful-functions-the-SHA-2-algorithm-152\"><span class=\"toc-item-num\">1.5.2&nbsp;&nbsp;</span>Useful functions the SHA-2 algorithm</a></div><div class=\"lev3 toc-item\"><a href=\"#The-SHA2_Numba-class\" data-toc-modified-id=\"The-SHA2_Numba-class-153\"><span class=\"toc-item-num\">1.5.3&nbsp;&nbsp;</span>The <code>SHA2_Numba</code> class</a></div><div class=\"lev3 toc-item\"><a href=\"#Check-on-SHA-2\" data-toc-modified-id=\"Check-on-SHA-2-154\"><span class=\"toc-item-num\">1.5.4&nbsp;&nbsp;</span>Check on SHA-2</a></div><div class=\"lev2 toc-item\"><a href=\"#Cython-power-code-for-the-SHA-2-hashing-function\" data-toc-modified-id=\"Cython-power-code-for-the-SHA-2-hashing-function-16\"><span class=\"toc-item-num\">1.6&nbsp;&nbsp;</span>Cython-power code for the <code>SHA-2</code> hashing function</a></div><div class=\"lev3 toc-item\"><a href=\"#Requirements\" data-toc-modified-id=\"Requirements-161\"><span class=\"toc-item-num\">1.6.1&nbsp;&nbsp;</span>Requirements</a></div><div class=\"lev3 toc-item\"><a href=\"#Useful-functions-the-SHA-2-algorithm\" data-toc-modified-id=\"Useful-functions-the-SHA-2-algorithm-162\"><span class=\"toc-item-num\">1.6.2&nbsp;&nbsp;</span>Useful functions the SHA-2 algorithm</a></div><div class=\"lev3 toc-item\"><a href=\"#The-SHA2_Cython-class\" data-toc-modified-id=\"The-SHA2_Cython-class-163\"><span class=\"toc-item-num\">1.6.3&nbsp;&nbsp;</span>The <code>SHA2_Cython</code> class</a></div><div class=\"lev3 toc-item\"><a href=\"#Check-on-SHA-2\" data-toc-modified-id=\"Check-on-SHA-2-164\"><span class=\"toc-item-num\">1.6.4&nbsp;&nbsp;</span>Check on SHA-2</a></div><div class=\"lev2 toc-item\"><a href=\"#Conclusion\" data-toc-modified-id=\"Conclusion-17\"><span class=\"toc-item-num\">1.7&nbsp;&nbsp;</span>Conclusion</a></div><div class=\"lev3 toc-item\"><a href=\"#Bonus\" data-toc-modified-id=\"Bonus-171\"><span class=\"toc-item-num\">1.7.1&nbsp;&nbsp;</span>Bonus</a></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Benchmark of the SHA256 hash function, with Python, Cython and Numba\n",
    "\n",
    "This small [Jupyter notebook](https://www.Jupyter.org/) is a short experiment, to compare the time complexity of three different implementations of the [SHA-256 hash function](https://en.wikipedia.org/wiki/SHA-2), in pure [Python](https://www.Python.org/), with [Cython](http://Cython.org/), and with [Numba](http://Numba.PyData.org/).\n",
    "\n",
    "- *Reference*: Wikipedia pages on [Hash functions](https://en.wikipedia.org/wiki/Hash_function) and [SHA-2](https://en.wikipedia.org/wiki/SHA-2).\n",
    "- *Date*: 21 June 2017.\n",
    "- *Author*: [Lilian Besson](https://GitHub.com/Naereen/notebooks).\n",
    "- *License*: [MIT Licensed](https://LBesson.MIT-License.org/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## What is a hash function?\n",
    "> TL;DR : [Hash functions](https://en.wikipedia.org/wiki/Hash_function) and [cryptographic hashing functions](https://en.wikipedia.org/wiki/Cryptographic_hash_function) on Wikipedia."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Common API for the different classes\n",
    "\n",
    "I will copy the API proposed by [the `hashlib` module in Python standard library](https://docs.python.org/3/library/hashlib.html), so it will be very easy to compare my implementations with the one provided with your default [Python](https://www.Python.org/) installation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "code_folding": [
     0
    ],
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Hash(object):\n",
    "    \"\"\" Common class for all hash methods.\n",
    "    \n",
    "    It copies the one of the hashlib module (https://docs.python.org/3.5/library/hashlib.html).\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, *args, **kwargs):\n",
    "        \"\"\" Create the Hash object.\"\"\"\n",
    "        self.name = self.__class__.__name__  # https://docs.python.org/3.5/library/hashlib.html#hashlib.hash.name\n",
    "        self.byteorder   = 'little'\n",
    "        self.digest_size = 0                # https://docs.python.org/3.5/library/hashlib.html#hashlib.hash.digest_size\n",
    "        self.block_size  = 0                # https://docs.python.org/3.5/library/hashlib.html#hashlib.hash.block_size\n",
    "\n",
    "    def __str__(self):\n",
    "        return self.name\n",
    "        \n",
    "    def update(self, arg):\n",
    "        \"\"\" Update the hash object with the object arg, which must be interpretable as a buffer of bytes.\"\"\"\n",
    "        pass\n",
    "\n",
    "    def digest(self):\n",
    "        \"\"\" Return the digest of the data passed to the update() method so far. This is a bytes object of size digest_size which may contain bytes in the whole range from 0 to 255.\"\"\"\n",
    "        return b\"\"\n",
    "\n",
    "    def hexdigest(self):\n",
    "        \"\"\" Like digest() except the digest is returned as a string object of double length, containing only hexadecimal digits. This may be used to exchange the value safely in email or other non-binary environments.\"\"\"\n",
    "        digest = self.digest()\n",
    "        raw = digest.to_bytes(self.digest_size, byteorder=self.byteorder)\n",
    "        format_str = '{:0' + str(2 * self.digest_size) + 'x}'\n",
    "        return format_str.format(int.from_bytes(raw, byteorder='big'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Checking the [the `hashlib` module in Python standard library](https://docs.python.org/3/library/hashlib.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import hashlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check [the available algorithms](https://docs.python.org/3.5/library/hashlib.html#hashlib.algorithms_available), some of them being [guaranteed to be on any platform](https://docs.python.org/3.5/library/hashlib.html#hashlib.algorithms_guaranteed), some are not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['SHA',\n",
       " 'dsaWithSHA',\n",
       " 'dsaEncryption',\n",
       " 'md4',\n",
       " 'md5',\n",
       " 'sha512',\n",
       " 'sha256',\n",
       " 'sha1',\n",
       " 'RIPEMD160',\n",
       " 'ecdsa-with-SHA1',\n",
       " 'MD4',\n",
       " 'SHA256',\n",
       " 'MD5',\n",
       " 'SHA224',\n",
       " 'SHA1',\n",
       " 'sha224',\n",
       " 'whirlpool',\n",
       " 'DSA',\n",
       " 'ripemd160',\n",
       " 'sha',\n",
       " 'SHA512',\n",
       " 'SHA384',\n",
       " 'DSA-SHA',\n",
       " 'sha384']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(hashlib.algorithms_available)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I will need at least this one:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "assert 'SHA256' in hashlib.algorithms_available"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets check that they have the block size and digest size announced:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For SHA256   : the block size is 64  and the digest size is 32.\n"
     ]
    }
   ],
   "source": [
    "name = 'SHA256'\n",
    "s = hashlib.sha256()\n",
    "print(\"For {:<8} : the block size is {:<3} and the digest size is {:<2}.\".format(name, s.block_size, s.digest_size))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Pure Python code for the SHA-2 hashing function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let now study and implement a last hashing function, again slightly harder to write but more secure: SHA-2, \"Secure Hash Algorithm, version 2\".\n",
    "See [the SHA-2 hashing function](https://en.wikipedia.org/wiki/SHA-2) on Wikipedia, if needed.\n",
    "\n",
    "<center><span style=\"font-size: large; color: green;\"><i>Remark</i>: it is not (yet) considered broken, and it is the military standard for security and cryptographic hashing. SHA-3 is preferred for security purposes.</span></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Useful functions the SHA-2 algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is exactly like for MD5. But SHA-2 requires right-rotate as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def leftrotate(x, c):\n",
    "    \"\"\" Left rotate the number x by c bytes.\"\"\"\n",
    "    x &= 0xFFFFFFFF\n",
    "    return ((x << c) | (x >> (32 - c))) & 0xFFFFFFFF\n",
    "\n",
    "def rightrotate(x, c):\n",
    "    \"\"\" Right rotate the number x by c bytes.\"\"\"\n",
    "    x &= 0xFFFFFFFF\n",
    "    return ((x >> c) | (x << (32 - c))) & 0xFFFFFFFF"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As SHA-2 plays with big-endian and little-endian integers, and at the end it requires a leftshift to combine the 5 hash pieces into one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def leftshift(x, c):\n",
    "    \"\"\" Left shift the number x by c bytes.\"\"\"\n",
    "    return x << c\n",
    "\n",
    "def rightshift(x, c):\n",
    "    \"\"\" Right shift the number x by c bytes.\"\"\"\n",
    "    return x >> c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The `SHA2` class\n",
    "\n",
    "I will use a simple class, very similar to the class used for the SHA-1 algorithm (see above).\n",
    "It is a direct implementation of the pseudo-code, as given for instance on the Wikipedia page.\n",
    "\n",
    "I will only implement the simpler one, SHA-256, of digest size of 256 bits. Other variants are SHA-224, SHA-384, SHA-512 (and others include SHA-512/224, SHA-512/256)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SHA2(Hash):\n",
    "    \"\"\"SHA256 hashing, see https://en.wikipedia.org/wiki/SHA-2#Pseudocode.\"\"\"\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.name        = \"SHA256\"\n",
    "        self.byteorder   = 'big'\n",
    "        self.block_size  = 64\n",
    "        self.digest_size = 32\n",
    "        # Note 2: For each round, there is one round constant k[i] and one entry in the message schedule array w[i], 0 ≤ i ≤ 63\n",
    "        # Note 3: The compression function uses 8 working variables, a through h\n",
    "        # Note 4: Big-endian convention is used when expressing the constants in this pseudocode,\n",
    "        #         and when parsing message block data from bytes to words, for example,\n",
    "        #         the first word of the input message \"abc\" after padding is 0x61626380\n",
    "\n",
    "        # Initialize hash values:\n",
    "        # (first 32 bits of the fractional parts of the square roots of the first 8 primes 2..19):\n",
    "        h0 = 0x6a09e667\n",
    "        h1 = 0xbb67ae85\n",
    "        h2 = 0x3c6ef372\n",
    "        h3 = 0xa54ff53a\n",
    "        h4 = 0x510e527f\n",
    "        h5 = 0x9b05688c\n",
    "        h6 = 0x1f83d9ab\n",
    "        h7 = 0x5be0cd19\n",
    "        \n",
    "        # Initialize array of round constants:\n",
    "        # (first 32 bits of the fractional parts of the cube roots of the first 64 primes 2..311):\n",
    "        self.k = [\n",
    "            0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,\n",
    "            0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,\n",
    "            0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,\n",
    "            0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,\n",
    "            0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,\n",
    "            0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,\n",
    "            0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,\n",
    "            0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2\n",
    "        ]\n",
    "\n",
    "        # Store them\n",
    "        self.hash_pieces = [h0, h1, h2, h3, h4, h5, h6, h7]\n",
    "    \n",
    "    def update(self, arg):\n",
    "        h0, h1, h2, h3, h4, h5, h6, h7 = self.hash_pieces\n",
    "        # 1. Pre-processing, exactly like MD5\n",
    "        data = bytearray(arg)\n",
    "        orig_len_in_bits = (8 * len(data)) & 0xFFFFFFFFFFFFFFFF\n",
    "        # 1.a. Add a single '1' bit at the end of the input bits\n",
    "        data.append(0x80)\n",
    "        # 1.b. Padding with zeros as long as the input bits length ≡ 448 (mod 512)\n",
    "        while len(data) % 64 != 56:\n",
    "            data.append(0)\n",
    "        # 1.c. append original length in bits mod (2 pow 64) to message\n",
    "        data += orig_len_in_bits.to_bytes(8, byteorder='big')\n",
    "        assert len(data) % 64 == 0, \"Error in padding\"\n",
    "        # 2. Computations\n",
    "        # Process the message in successive 512-bit = 64-bytes chunks:\n",
    "        for offset in range(0, len(data), 64):\n",
    "            # 2.a. 512-bits = 64-bytes chunks\n",
    "            chunks = data[offset : offset + 64]\n",
    "            w = [0 for i in range(64)]\n",
    "            # 2.b. Break chunk into sixteen 32-bit = 4-bytes words w[i], 0 ≤ i ≤ 15\n",
    "            for i in range(16):\n",
    "                w[i] = int.from_bytes(chunks[4*i : 4*i + 4], byteorder='big')\n",
    "            # 2.c.  Extend the first 16 words into the remaining 48\n",
    "            #       words w[16..63] of the message schedule array:\n",
    "            for i in range(16, 64):\n",
    "                s0 = (rightrotate(w[i-15], 7) ^ rightrotate(w[i-15], 18) ^ rightshift(w[i-15], 3)) & 0xFFFFFFFF\n",
    "                s1 = (rightrotate(w[i-2], 17) ^ rightrotate(w[i-2], 19) ^ rightshift(w[i-2], 10)) & 0xFFFFFFFF\n",
    "                w[i] = (w[i-16] + s0 + w[i-7] + s1) & 0xFFFFFFFF\n",
    "            # 2.d. Initialize hash value for this chunk\n",
    "            a, b, c, d, e, f, g, h = h0, h1, h2, h3, h4, h5, h6, h7\n",
    "            # 2.e. Main loop, cf. https://tools.ietf.org/html/rfc6234\n",
    "            for i in range(64):\n",
    "                S1 = (rightrotate(e, 6) ^ rightrotate(e, 11) ^ rightrotate(e, 25)) & 0xFFFFFFFF\n",
    "                ch = ((e & f) ^ ((~e) & g)) & 0xFFFFFFFF\n",
    "                temp1 = (h + S1 + ch + self.k[i] + w[i]) & 0xFFFFFFFF\n",
    "                S0 = (rightrotate(a, 2) ^ rightrotate(a, 13) ^ rightrotate(a, 22)) & 0xFFFFFFFF\n",
    "                maj = ((a & b) ^ (a & c) ^ (b & c)) & 0xFFFFFFFF\n",
    "                temp2 = (S0 + maj) & 0xFFFFFFFF\n",
    "\n",
    "                new_a = (temp1 + temp2) & 0xFFFFFFFF\n",
    "                new_e = (d + temp1) & 0xFFFFFFFF\n",
    "                # Rotate the 8 variables\n",
    "                a, b, c, d, e, f, g, h = new_a, a, b, c, new_e, e, f, g\n",
    "\n",
    "            # Add this chunk's hash to result so far:\n",
    "            h0 = (h0 + a) & 0xFFFFFFFF\n",
    "            h1 = (h1 + b) & 0xFFFFFFFF\n",
    "            h2 = (h2 + c) & 0xFFFFFFFF\n",
    "            h3 = (h3 + d) & 0xFFFFFFFF\n",
    "            h4 = (h4 + e) & 0xFFFFFFFF\n",
    "            h5 = (h5 + f) & 0xFFFFFFFF\n",
    "            h6 = (h6 + g) & 0xFFFFFFFF\n",
    "            h7 = (h7 + h) & 0xFFFFFFFF\n",
    "        # 3. Conclusion\n",
    "        self.hash_pieces = [h0, h1, h2, h3, h4, h5, h6, h7]\n",
    "\n",
    "    def digest(self):\n",
    "        # h0 append h1 append h2 append h3 append h4 append h5 append h6 append h7\n",
    "        return sum(leftshift(x, 32 * i) for i, x in enumerate(self.hash_pieces[::-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also write a function to directly compute the hex digest from some bytes data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def hash_SHA2(data):\n",
    "    \"\"\" Shortcut function to directly receive the hex digest from SHA2(data).\"\"\"\n",
    "    h = SHA2()\n",
    "    if isinstance(data, str):\n",
    "        data = bytes(data, encoding='utf8')\n",
    "    h.update(data)\n",
    "    return h.hexdigest()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Check on SHA-2\n",
    "\n",
    "Let try the example from [SHA-2 Wikipedia page](https://en.wikipedia.org/wiki/SHA-2#Test_vectors) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'d7a8fbb307d7809469ca9abcb0082e4f8d5651e46d3cdb762d02d0bf37c9e592'"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hash_SHA2(\"The quick brown fox jumps over the lazy dog\")\n",
    "assert hash_SHA2(\"The quick brown fox jumps over the lazy dog\") == 'd7a8fbb307d7809469ca9abcb0082e4f8d5651e46d3cdb762d02d0bf37c9e592'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even a small change in the message will (with overwhelming probability) result in a mostly different hash, due to the [**avalanche effect**](https://en.wikipedia.org/wiki/Avalanche_effect). For example, adding a period at the end of the sentence:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ef537f25c895bfa782526529a9b63d97aa631564d5d789c2b765448c8635fb6c'"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hash_SHA2(\"The quick brown fox jumps over the lazy dog.\")\n",
    "assert hash_SHA2(\"The quick brown fox jumps over the lazy dog.\") == 'ef537f25c895bfa782526529a9b63d97aa631564d5d789c2b765448c8635fb6c'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The hash of the zero-length string is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855'"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hash_SHA2(\"\")\n",
    "assert hash_SHA2(\"\") == 'e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\implies$ We obtained the same result, OK our function works!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Trying 1000 random examples\n",
    "On a small sentence:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'10a6dec377c28d2d34001c103760339f8d6ab02660d200d6014329b86253552c'"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hash_SHA2(\"My name is Zorro !\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'10a6dec377c28d2d34001c103760339f8d6ab02660d200d6014329b86253552c'"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h = hashlib.sha256()\n",
    "h.update(b\"My name is Zorro !\")\n",
    "h.hexdigest()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It starts to look good."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def true_hash_SHA2(data):\n",
    "    h = hashlib.sha256()\n",
    "    if isinstance(data, str):\n",
    "        data = bytes(data, encoding='utf8')\n",
    "    h.update(data)\n",
    "    return h.hexdigest()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On some random data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy.random as nr\n",
    "alphabets = \"0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz\"\n",
    "\n",
    "def random_string(size=10000):\n",
    "    return ''.join(alphabets[nr.randint(len(alphabets))] for _ in range(size))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'bXOwDYtUOz'"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_string(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from tqdm import tqdm_notebook as tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b17aa534a4544b7ba4a0c3058c84e880"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "CPU times: user 1min 2s, sys: 88 ms, total: 1min 2s\n",
      "Wall time: 1min 2s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "for _ in tqdm(range(1000)):\n",
    "    x = random_string()\n",
    "    assert hash_SHA2(x) == true_hash_SHA2(x), \"Error: x = {} gave two different SHA2 hashes: my implementation = {} != hashlib implementation = {}...\".format(x, hash_SHA2(x), true_hash_SHA2(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Numba-powered code for the SHA-2 hashing function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Requirements\n",
    "You need [numba](http://numba.pydata.org/) to be installed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numba import jit, jitclass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Useful functions the SHA-2 algorithm\n",
    "\n",
    "Let just add the [`numba.jit`](http://numba.pydata.org/numba-doc/latest/user/jit.html) decorator to every function we defined before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@jit\n",
    "def leftrotate_numba(x, c):\n",
    "    \"\"\" Left rotate the number x by c bytes.\"\"\"\n",
    "    x &= 0xFFFFFFFF\n",
    "    return ((x << c) | (x >> (32 - c))) & 0xFFFFFFFF\n",
    "\n",
    "@jit\n",
    "def rightrotate_numba(x, c):\n",
    "    \"\"\" Right rotate the number x by c bytes.\"\"\"\n",
    "    x &= 0xFFFFFFFF\n",
    "    return ((x >> c) | (x << (32 - c))) & 0xFFFFFFFF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@jit\n",
    "def leftshift_numba(x, c):\n",
    "    \"\"\" Left shift the number x by c bytes.\"\"\"\n",
    "    return x << c\n",
    "\n",
    "@jit\n",
    "def rightshift_numba(x, c):\n",
    "    \"\"\" Right shift the number x by c bytes.\"\"\"\n",
    "    return x >> c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The `SHA2_Numba` class\n",
    "\n",
    "And similarly for the `SHA2` class, with the [`numba.jit`](http://numba.pydata.org/numba-doc/latest/user/jit.html) decorator to the `update` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SHA2_Numba(Hash):\n",
    "    \"\"\"SHA256 hashing, speed-up with Numba.jit, see https://en.wikipedia.org/wiki/SHA-2#Pseudocode.\"\"\"\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.name        = \"SHA256\"\n",
    "        self.byteorder   = 'big'\n",
    "        self.block_size  = 64\n",
    "        self.digest_size = 32\n",
    "        # Note 2: For each round, there is one round constant k[i] and one entry in the message schedule array w[i], 0 ≤ i ≤ 63\n",
    "        # Note 3: The compression function uses 8 working variables, a through h\n",
    "        # Note 4: Big-endian convention is used when expressing the constants in this pseudocode,\n",
    "        #         and when parsing message block data from bytes to words, for example,\n",
    "        #         the first word of the input message \"abc\" after padding is 0x61626380\n",
    "\n",
    "        # Initialize hash values:\n",
    "        # (first 32 bits of the fractional parts of the square roots of the first 8 primes 2..19):\n",
    "        h0 = 0x6a09e667\n",
    "        h1 = 0xbb67ae85\n",
    "        h2 = 0x3c6ef372\n",
    "        h3 = 0xa54ff53a\n",
    "        h4 = 0x510e527f\n",
    "        h5 = 0x9b05688c\n",
    "        h6 = 0x1f83d9ab\n",
    "        h7 = 0x5be0cd19\n",
    "        \n",
    "        # Initialize array of round constants:\n",
    "        # (first 32 bits of the fractional parts of the cube roots of the first 64 primes 2..311):\n",
    "        self.k = [\n",
    "            0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,\n",
    "            0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,\n",
    "            0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,\n",
    "            0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,\n",
    "            0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,\n",
    "            0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,\n",
    "            0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,\n",
    "            0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2\n",
    "        ]\n",
    "\n",
    "        # Store them\n",
    "        self.hash_pieces = [h0, h1, h2, h3, h4, h5, h6, h7]\n",
    "    \n",
    "    @jit\n",
    "    def update(self, arg):\n",
    "        h0, h1, h2, h3, h4, h5, h6, h7 = self.hash_pieces\n",
    "        # 1. Pre-processing, exactly like MD5\n",
    "        data = bytearray(arg)\n",
    "        orig_len_in_bits = (8 * len(data)) & 0xFFFFFFFFFFFFFFFF\n",
    "        # 1.a. Add a single '1' bit at the end of the input bits\n",
    "        data.append(0x80)\n",
    "        # 1.b. Padding with zeros as long as the input bits length ≡ 448 (mod 512)\n",
    "        while len(data) % 64 != 56:\n",
    "            data.append(0)\n",
    "        # 1.c. append original length in bits mod (2 pow 64) to message\n",
    "        data += orig_len_in_bits.to_bytes(8, byteorder='big')\n",
    "        assert len(data) % 64 == 0, \"Error in padding\"\n",
    "        # 2. Computations\n",
    "        # Process the message in successive 512-bit = 64-bytes chunks:\n",
    "        for offset in range(0, len(data), 64):\n",
    "            # 2.a. 512-bits = 64-bytes chunks\n",
    "            chunks = data[offset : offset + 64]\n",
    "            w = [0 for i in range(64)]\n",
    "            # 2.b. Break chunk into sixteen 32-bit = 4-bytes words w[i], 0 ≤ i ≤ 15\n",
    "            for i in range(16):\n",
    "                w[i] = int.from_bytes(chunks[4*i : 4*i + 4], byteorder='big')\n",
    "            # 2.c.  Extend the first 16 words into the remaining 48\n",
    "            #       words w[16..63] of the message schedule array:\n",
    "            for i in range(16, 64):\n",
    "                s0 = (rightrotate(w[i-15], 7) ^ rightrotate(w[i-15], 18) ^ rightshift(w[i-15], 3)) & 0xFFFFFFFF\n",
    "                s1 = (rightrotate(w[i-2], 17) ^ rightrotate(w[i-2], 19) ^ rightshift(w[i-2], 10)) & 0xFFFFFFFF\n",
    "                w[i] = (w[i-16] + s0 + w[i-7] + s1) & 0xFFFFFFFF\n",
    "            # 2.d. Initialize hash value for this chunk\n",
    "            a, b, c, d, e, f, g, h = h0, h1, h2, h3, h4, h5, h6, h7\n",
    "            # 2.e. Main loop, cf. https://tools.ietf.org/html/rfc6234\n",
    "            for i in range(64):\n",
    "                S1 = (rightrotate(e, 6) ^ rightrotate(e, 11) ^ rightrotate(e, 25)) & 0xFFFFFFFF\n",
    "                ch = ((e & f) ^ ((~e) & g)) & 0xFFFFFFFF\n",
    "                temp1 = (h + S1 + ch + self.k[i] + w[i]) & 0xFFFFFFFF\n",
    "                S0 = (rightrotate(a, 2) ^ rightrotate(a, 13) ^ rightrotate(a, 22)) & 0xFFFFFFFF\n",
    "                maj = ((a & b) ^ (a & c) ^ (b & c)) & 0xFFFFFFFF\n",
    "                temp2 = (S0 + maj) & 0xFFFFFFFF\n",
    "\n",
    "                new_a = (temp1 + temp2) & 0xFFFFFFFF\n",
    "                new_e = (d + temp1) & 0xFFFFFFFF\n",
    "                # Rotate the 8 variables\n",
    "                a, b, c, d, e, f, g, h = new_a, a, b, c, new_e, e, f, g\n",
    "\n",
    "            # Add this chunk's hash to result so far:\n",
    "            h0 = (h0 + a) & 0xFFFFFFFF\n",
    "            h1 = (h1 + b) & 0xFFFFFFFF\n",
    "            h2 = (h2 + c) & 0xFFFFFFFF\n",
    "            h3 = (h3 + d) & 0xFFFFFFFF\n",
    "            h4 = (h4 + e) & 0xFFFFFFFF\n",
    "            h5 = (h5 + f) & 0xFFFFFFFF\n",
    "            h6 = (h6 + g) & 0xFFFFFFFF\n",
    "            h7 = (h7 + h) & 0xFFFFFFFF\n",
    "        # 3. Conclusion\n",
    "        self.hash_pieces = [h0, h1, h2, h3, h4, h5, h6, h7]\n",
    "\n",
    "    def digest(self):\n",
    "        # h0 append h1 append h2 append h3 append h4 append h5 append h6 append h7\n",
    "        return sum(leftshift(x, 32 * i) for i, x in enumerate(self.hash_pieces[::-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also write a function to directly compute the hex digest from some bytes data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def hash_SHA2_Numba(data):\n",
    "    \"\"\" Shortcut function to directly receive the hex digest from SHA2_Numba(data).\"\"\"\n",
    "    h = SHA2_Numba()\n",
    "    if isinstance(data, str):\n",
    "        data = bytes(data, encoding='utf8')\n",
    "    h.update(data)\n",
    "    return h.hexdigest()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Check on SHA-2\n",
    "\n",
    "Let try the example from [SHA-2 Wikipedia page](https://en.wikipedia.org/wiki/SHA-2#Test_vectors) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "Failed at object (analyzing bytecode)\n'DataFlowAnalysis' object has no attribute 'op_MAKE_FUNCTION'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-44-12552f1afe46>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mhash_SHA2_Numba\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"The quick brown fox jumps over the lazy dog\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0;32massert\u001b[0m \u001b[0mhash_SHA2_Numba\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"The quick brown fox jumps over the lazy dog\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'd7a8fbb307d7809469ca9abcb0082e4f8d5651e46d3cdb762d02d0bf37c9e592'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-43-57e557bf04d8>\u001b[0m in \u001b[0;36mhash_SHA2_Numba\u001b[0;34m(data)\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m         \u001b[0mdata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbytes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'utf8'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m     \u001b[0mh\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhexdigest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/dispatcher.py\u001b[0m in \u001b[0;36m_compile_for_args\u001b[0;34m(self, *args, **kws)\u001b[0m\n\u001b[1;32m    284\u001b[0m                 \u001b[0margtypes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtypeof_pyval\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    285\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 286\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margtypes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    287\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0merrors\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTypingError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    288\u001b[0m             \u001b[0;31m# Intercept typing error that may be due to an argument\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/dispatcher.py\u001b[0m in \u001b[0;36mcompile\u001b[0;34m(self, sig)\u001b[0m\n\u001b[1;32m    530\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    531\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cache_misses\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0msig\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 532\u001b[0;31m             \u001b[0mcres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compiler\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreturn_type\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    533\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_overload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcres\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    534\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cache\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msave_overload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcres\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/dispatcher.py\u001b[0m in \u001b[0;36mcompile\u001b[0;34m(self, args, return_type)\u001b[0m\n\u001b[1;32m     79\u001b[0m                                       \u001b[0mimpl\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     80\u001b[0m                                       \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreturn_type\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mreturn_type\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 81\u001b[0;31m                                       flags=flags, locals=self.locals)\n\u001b[0m\u001b[1;32m     82\u001b[0m         \u001b[0;31m# Check typing error if object mode is used\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     83\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mcres\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtyping_error\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mflags\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0menable_pyobject\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/compiler.py\u001b[0m in \u001b[0;36mcompile_extra\u001b[0;34m(typingctx, targetctx, func, args, return_type, flags, locals, library)\u001b[0m\n\u001b[1;32m    691\u001b[0m     pipeline = Pipeline(typingctx, targetctx, library,\n\u001b[1;32m    692\u001b[0m                         args, return_type, flags, locals)\n\u001b[0;32m--> 693\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mpipeline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompile_extra\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    694\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    695\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/compiler.py\u001b[0m in \u001b[0;36mcompile_extra\u001b[0;34m(self, func)\u001b[0m\n\u001b[1;32m    348\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlifted\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    349\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlifted_from\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 350\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compile_bytecode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    351\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    352\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mcompile_ir\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunc_ir\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlifted\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlifted_from\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/compiler.py\u001b[0m in \u001b[0;36m_compile_bytecode\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    656\u001b[0m         \"\"\"\n\u001b[1;32m    657\u001b[0m         \u001b[0;32massert\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfunc_ir\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 658\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compile_core\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    659\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    660\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_compile_ir\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/compiler.py\u001b[0m in \u001b[0;36m_compile_core\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    643\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    644\u001b[0m         \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfinalize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 645\u001b[0;31m         \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstatus\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    646\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mres\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    647\u001b[0m             \u001b[0;31m# Early pipeline completion\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/compiler.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, status)\u001b[0m\n\u001b[1;32m    234\u001b[0m                     \u001b[0;31m# No more fallback pipelines?\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    235\u001b[0m                     \u001b[0;32mif\u001b[0m \u001b[0mis_final_pipeline\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 236\u001b[0;31m                         \u001b[0;32mraise\u001b[0m \u001b[0mpatched_exception\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    237\u001b[0m                     \u001b[0;31m# Go to next fallback pipeline\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    238\u001b[0m                     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/compiler.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, status)\u001b[0m\n\u001b[1;32m    226\u001b[0m                 \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    227\u001b[0m                     \u001b[0mevent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstage_name\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 228\u001b[0;31m                     \u001b[0mstage\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    229\u001b[0m                 \u001b[0;32mexcept\u001b[0m \u001b[0m_EarlyPipelineCompletion\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    230\u001b[0m                     \u001b[0;32mreturn\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/compiler.py\u001b[0m in \u001b[0;36mstage_analyze_bytecode\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    362\u001b[0m         \u001b[0mAnalyze\u001b[0m \u001b[0mbytecode\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mtranslating\u001b[0m \u001b[0mto\u001b[0m \u001b[0mNumba\u001b[0m \u001b[0mIR\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    363\u001b[0m         \"\"\"\n\u001b[0;32m--> 364\u001b[0;31m         \u001b[0mfunc_ir\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtranslate_stage\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfunc_id\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    365\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_set_and_check_ir\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc_ir\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    366\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/compiler.py\u001b[0m in \u001b[0;36mtranslate_stage\u001b[0;34m(func_id, bytecode)\u001b[0m\n\u001b[1;32m    754\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mtranslate_stage\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc_id\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbytecode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    755\u001b[0m     \u001b[0minterp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minterpreter\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mInterpreter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc_id\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 756\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0minterp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minterpret\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbytecode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    757\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    758\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/interpreter.py\u001b[0m in \u001b[0;36minterpret\u001b[0;34m(self, bytecode)\u001b[0m\n\u001b[1;32m     95\u001b[0m         \u001b[0;31m# Data flow analysis\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     96\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdfa\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdataflow\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDataFlowAnalysis\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcfa\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 97\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdfa\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     98\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     99\u001b[0m         \u001b[0;31m# Temp states during interpretation\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/dataflow.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     25\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     26\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mblk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcfa\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0miterliveblocks\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 27\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minfos\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mblk\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moffset\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_on_block\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mblk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     28\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     29\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mrun_on_block\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mblk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/dataflow.py\u001b[0m in \u001b[0;36mrun_on_block\u001b[0;34m(self, blk)\u001b[0m\n\u001b[1;32m     69\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0moffset\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mblk\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     70\u001b[0m             \u001b[0minst\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbytecode\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0moffset\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 71\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdispatch\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minfo\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minst\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     72\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0minfo\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     73\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numba/dataflow.py\u001b[0m in \u001b[0;36mdispatch\u001b[0;34m(self, info, inst)\u001b[0m\n\u001b[1;32m     78\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mdispatch\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minfo\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minst\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     79\u001b[0m         \u001b[0mfname\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"op_%s\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0minst\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mopname\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreplace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'+'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'_'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 80\u001b[0;31m         \u001b[0mfn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     81\u001b[0m         \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minfo\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minst\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     82\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: Failed at object (analyzing bytecode)\n'DataFlowAnalysis' object has no attribute 'op_MAKE_FUNCTION'"
     ]
    }
   ],
   "source": [
    "hash_SHA2_Numba(\"The quick brown fox jumps over the lazy dog\")\n",
    "assert hash_SHA2_Numba(\"The quick brown fox jumps over the lazy dog\") == 'd7a8fbb307d7809469ca9abcb0082e4f8d5651e46d3cdb762d02d0bf37c9e592'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I failed to make `numba.jit` work on that function :-("
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Cython-power code for the `SHA-2` hashing function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Requirements\n",
    "You need [cython](http://cython.org/) and the cython Jupyter extension to be installed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "%load_ext cython"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Useful functions the SHA-2 algorithm\n",
    "\n",
    "For the functions defined before, we rewrite them with type annotations in `%%cython` cells.\n",
    "All variables are `int`, i.e., 32-bits integer (64-bits are `long`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%cython\n",
    "\n",
    "cpdef int leftrotate_cython(int x, int c):\n",
    "    \"\"\" Left rotate the number x by c bytes.\"\"\"\n",
    "    return (x << c) | (x >> (32 - c))\n",
    "\n",
    "cpdef int rightrotate_cython(int x, int c):\n",
    "    \"\"\" Right rotate the number x by c bytes.\"\"\"\n",
    "    return (x >> c) | (x << (32 - c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[0;31mDocstring:\u001b[0m Left rotate the number x by c bytes.\n",
      "\u001b[0;31mType:\u001b[0m      builtin_function_or_method\n",
      "\n",
      "\u001b[0;31mDocstring:\u001b[0m Right rotate the number x by c bytes.\n",
      "\u001b[0;31mType:\u001b[0m      builtin_function_or_method\n",
      "\n"
     ]
    }
   ],
   "source": [
    "leftrotate_cython?\n",
    "rightrotate_cython?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On basic functions like this, of course we don't get any speedup with Cython:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.57 µs ± 42.3 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n",
      "1.4 µs ± 60.5 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n",
      "1.63 µs ± 19.2 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n",
      "1.44 µs ± 88.2 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
     ]
    }
   ],
   "source": [
    "from numpy.random import randint\n",
    "\n",
    "%timeit leftrotate(randint(0, 100000), 5)\n",
    "%timeit leftrotate_cython(randint(0, 100000), 5)\n",
    "\n",
    "%timeit rightrotate(randint(0, 100000), 5)\n",
    "%timeit rightrotate_cython(randint(0, 100000), 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%cython\n",
    "\n",
    "cpdef int leftshift_cython(int x, int c):\n",
    "    \"\"\" Left shift the number x by c bytes.\"\"\"\n",
    "    return x << c\n",
    "\n",
    "cpdef int rightshift_cython(int x, int c):\n",
    "    \"\"\" Right shift the number x by c bytes.\"\"\"\n",
    "    return x >> c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[0;31mDocstring:\u001b[0m Left shift the number x by c bytes.\n",
      "\u001b[0;31mType:\u001b[0m      builtin_function_or_method\n",
      "\n",
      "\u001b[0;31mDocstring:\u001b[0m Right shift the number x by c bytes.\n",
      "\u001b[0;31mType:\u001b[0m      builtin_function_or_method\n",
      "\n"
     ]
    }
   ],
   "source": [
    "leftshift_cython?\n",
    "rightshift_cython?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On basic functions like this, of course we don't get any speedup with Cython:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4 µs ± 33.1 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n",
      "1.31 µs ± 24.5 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n",
      "1.36 µs ± 35 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n",
      "1.33 µs ± 51.6 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit leftshift(randint(0, 100000), 5)\n",
    "%timeit leftshift_cython(randint(0, 100000), 5)\n",
    "\n",
    "%timeit rightshift(randint(0, 100000), 5)\n",
    "%timeit rightshift_cython(randint(0, 100000), 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The `SHA2_Cython` class\n",
    "\n",
    "And similarly for the `SHA2` class, we write it in a `%%cython` cell, and we type everything."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "%%cython\n",
    "# cython: c_string_type=unicode, c_string_encoding=utf8\n",
    "\n",
    "cdef int rightrotate_cython(int x, int c):\n",
    "    \"\"\" Right rotate the number x by c bytes.\"\"\"\n",
    "    return (x >> c) | (x << (32 - c))\n",
    "\n",
    "cdef int rightshift_cython(int x, int c):\n",
    "    \"\"\" Right shift the number x by c bytes.\"\"\"\n",
    "    return x >> c\n",
    "\n",
    "# See http://cython.readthedocs.io/en/latest/src/tutorial/array.html\n",
    "from cpython cimport array\n",
    "import array\n",
    "\n",
    "cdef array.array empty_64 = array.array('i', [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])\n",
    "cdef int[:] view_empty_64 = empty_64\n",
    "\n",
    "\n",
    "cpdef void update_cython(int[:] hash_pieces, int[:] k, bytearray arg):\n",
    "    \"\"\" One pass of the SHA-256 algorithm, update hash_pieces on place. \"\"\"\n",
    "    # Extract the 8 variables\n",
    "    cdef int h0 = hash_pieces[0], h1 = hash_pieces[1], h2 = hash_pieces[2], h3 = hash_pieces[3], h4 = hash_pieces[4], h5 = hash_pieces[5], h6 = hash_pieces[6], h7 = hash_pieces[7]\n",
    "    # 1. Pre-processing, exactly like MD5\n",
    "    cdef bytearray data = arg\n",
    "    cdef long orig_len_in_bits = 8 * len(data)\n",
    "    # 1.a. Add a single '1' bit at the end of the input bits\n",
    "    data.append(0x80)\n",
    "    # 1.b. Padding with zeros as long as the input bits length ≡ 448 (mod 512)\n",
    "    while len(data) % 64 != 56:\n",
    "        data.append(0x0)\n",
    "    # 1.c. append original length in bits mod (2 pow 64) to message\n",
    "    data += orig_len_in_bits.to_bytes(8, byteorder='big')\n",
    "    assert len(data) % 64 == 0, \"Error in padding\"\n",
    "\n",
    "    # Declare loop indexes and variables\n",
    "    cdef int offset, i\n",
    "    cdef int a, b, c, d, e, f, g, h\n",
    "    cdef int temp1, temp2\n",
    "\n",
    "    # 2. Computations\n",
    "    # Process the message in successive 512-bit = 64-bytes chunks:\n",
    "    cdef int[:] w = view_empty_64\n",
    "\n",
    "    for offset in range(0, len(data), 64):\n",
    "        # 2.a. 512-bits = 64-bytes chunks\n",
    "        # 2.b. Break chunk into sixteen 32-bit = 4-bytes words w[i], 0 ≤ i ≤ 15\n",
    "        for i in range(16):\n",
    "            w[i] = int.from_bytes(data[offset : offset + 64][4*i : 4*i + 4], byteorder='big')\n",
    "        # 2.c.  Extend the first 16 words into the remaining 48\n",
    "        #       words w[16..63] of the message schedule array:\n",
    "        for i in range(16, 64):\n",
    "            w[i] = w[i-16] + (rightrotate_cython(w[i-15], 7) ^ rightrotate_cython(w[i-15], 18) ^ rightshift_cython(w[i-15], 3)) + w[i-7] + (rightrotate_cython(w[i-2], 17) ^ rightrotate_cython(w[i-2], 19) ^ rightshift_cython(w[i-2], 10))\n",
    "        # 2.d. Initialize hash value for this chunk\n",
    "        a = h0\n",
    "        b = h1\n",
    "        c = h2\n",
    "        d = h3\n",
    "        e = h4\n",
    "        f = h5\n",
    "        g = h6\n",
    "        h = h7\n",
    "        # 2.e. Main loop, cf. https://tools.ietf.org/html/rfc6234\n",
    "        for i in range(64):\n",
    "            temp1 = h + (rightrotate_cython(e, 6) ^ rightrotate_cython(e, 11) ^ rightrotate_cython(e, 25)) + ((e & f) ^ ((~e) & g)) + k[i] + w[i]\n",
    "            temp2 = (rightrotate_cython(a, 2) ^ rightrotate_cython(a, 13) ^ rightrotate_cython(a, 22)) + ((a & b) ^ (a & c) ^ (b & c))\n",
    "\n",
    "            # Rotate the 8 variables\n",
    "            a, b, c, d, e, f, g, h = temp1 + temp2, a, b, c, d + temp1, e, f, g\n",
    "\n",
    "        # Add this chunk's hash to result so far:\n",
    "        h0 += a\n",
    "        h1 += b\n",
    "        h2 += c\n",
    "        h3 += d\n",
    "        h4 += e\n",
    "        h5 += f\n",
    "        h6 += g\n",
    "        h7 += h\n",
    "    # 3. Conclusion\n",
    "    hash_pieces[0] = h0\n",
    "    hash_pieces[1] = h1\n",
    "    hash_pieces[2] = h2\n",
    "    hash_pieces[3] = h3\n",
    "    hash_pieces[4] = h4\n",
    "    hash_pieces[5] = h5\n",
    "    hash_pieces[6] = h6\n",
    "    hash_pieces[7] = h7\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {
    "code_folding": [
     3
    ],
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SHA2_Cython(Hash):\n",
    "    \"\"\"SHA256 hashing, speed-up with Numba.jit, see https://en.wikipedia.org/wiki/SHA-2#Pseudocode.\"\"\"\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.name        = \"SHA256\"\n",
    "        self.byteorder   = 'big'\n",
    "        self.block_size  = 64\n",
    "        self.digest_size = 32\n",
    "        # Note 2: For each round, there is one round constant k[i] and one entry in the message schedule array w[i], 0 ≤ i ≤ 63\n",
    "        # Note 3: The compression function uses 8 working variables, a through h\n",
    "        # Note 4: Big-endian convention is used when expressing the constants in this pseudocode,\n",
    "        #         and when parsing message block data from bytes to words, for example,\n",
    "        #         the first word of the input message \"abc\" after padding is 0x61626380\n",
    "\n",
    "        # Initialize hash values:\n",
    "        # (first 32 bits of the fractional parts of the square roots of the first 8 primes 2..19):\n",
    "        h0 = 0x6a09e667\n",
    "        h1 = 0xbb67ae85\n",
    "        h2 = 0x3c6ef372\n",
    "        h3 = 0xa54ff53a\n",
    "        h4 = 0x510e527f\n",
    "        h5 = 0x9b05688c\n",
    "        h6 = 0x1f83d9ab\n",
    "        h7 = 0x5be0cd19\n",
    "        \n",
    "        # Initialize array of round constants:\n",
    "        # (first 32 bits of the fractional parts of the cube roots of the first 64 primes 2..311):\n",
    "        self.k = [\n",
    "            0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,\n",
    "            0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,\n",
    "            0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,\n",
    "            0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,\n",
    "            0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,\n",
    "            0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,\n",
    "            0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,\n",
    "            0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2\n",
    "        ]\n",
    "\n",
    "        # Store them\n",
    "        self.hash_pieces = [h0, h1, h2, h3, h4, h5, h6, h7]\n",
    "    \n",
    "    def update(self, data):\n",
    "        update_cython(self.hash_pieces, self.k, data)\n",
    "\n",
    "    def digest(self):\n",
    "        # h0 append h1 append h2 append h3 append h4 append h5 append h6 append h7\n",
    "        return sum(leftshift(x, 32 * i) for i, x in enumerate(self.hash_pieces[::-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also write a function to directly compute the hex digest from some bytes data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {
    "code_folding": [
     0
    ],
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def hash_SHA2_Cython(data):\n",
    "    \"\"\" Shortcut function to directly receive the hex digest from SHA2_Cython(data).\"\"\"\n",
    "    h = SHA2_Cython()\n",
    "    if isinstance(data, str):\n",
    "        data = bytes(data, encoding='utf8')\n",
    "    print(\"type(data) =\", type(data))\n",
    "    h.update(data)\n",
    "    return h.hexdigest()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1779033703]"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "list"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[1116352408]"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "list"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "b''"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "bytes"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "ename": "TypeError",
     "evalue": "a bytes-like object is required, not 'list'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-185-38958c7f0f71>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0mtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0mupdate_cython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhash_pieces\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbytearray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m_cython_magic_892b302b9e5d7477154227e427367045.pyx\u001b[0m in \u001b[0;36m_cython_magic_892b302b9e5d7477154227e427367045.update_cython (/home/lilian/.cache/ipython/cython/_cython_magic_892b302b9e5d7477154227e427367045.c:2840)\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m~/.cache/ipython/cython/_cython_magic_892b302b9e5d7477154227e427367045.cpython-35m-x86_64-linux-gnu.so\u001b[0m in \u001b[0;36mView.MemoryView.memoryview_cwrapper (/home/lilian/.cache/ipython/cython/_cython_magic_892b302b9e5d7477154227e427367045.c:9311)\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m~/.cache/ipython/cython/_cython_magic_892b302b9e5d7477154227e427367045.cpython-35m-x86_64-linux-gnu.so\u001b[0m in \u001b[0;36mView.MemoryView.memoryview.__cinit__ (/home/lilian/.cache/ipython/cython/_cython_magic_892b302b9e5d7477154227e427367045.c:5546)\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: a bytes-like object is required, not 'list'"
     ]
    }
   ],
   "source": [
    "data = bytes(\"\", encoding='utf8')\n",
    "h = SHA2_Cython()\n",
    "\n",
    "h.hash_pieces[:1]\n",
    "type(h.hash_pieces)\n",
    "h.k[:1]\n",
    "type(h.k)\n",
    "data\n",
    "type(data)\n",
    "\n",
    "update_cython(h.hash_pieces, h.k, bytearray(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Check on SHA-2\n",
    "\n",
    "Let try the example from [SHA-2 Wikipedia page](https://en.wikipedia.org/wiki/SHA-2#Test_vectors) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "a bytes-like object is required, not 'list'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-90-ef3902a7030b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mhash_SHA2_Cython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"The quick brown fox jumps over the lazy dog\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0;32massert\u001b[0m \u001b[0mhash_SHA2_Cython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"The quick brown fox jumps over the lazy dog\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'd7a8fbb307d7809469ca9abcb0082e4f8d5651e46d3cdb762d02d0bf37c9e592'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-89-7da2f16c435f>\u001b[0m in \u001b[0;36mhash_SHA2_Cython\u001b[0;34m(data)\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m         \u001b[0mdata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbytes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'utf8'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m     \u001b[0mh\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhexdigest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-88-3e4059769092>\u001b[0m in \u001b[0;36mupdate\u001b[0;34m(self, data)\u001b[0m\n\u001b[1;32m     41\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     42\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 43\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mupdate_cython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhash_pieces\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     44\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     45\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mdigest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m_cython_magic_3a51a049b19292c89caa81e80cc99ee0.pyx\u001b[0m in \u001b[0;36m_cython_magic_3a51a049b19292c89caa81e80cc99ee0.update_cython (/home/lilian/.cache/ipython/cython/_cython_magic_3a51a049b19292c89caa81e80cc99ee0.c:3101)\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m~/.cache/ipython/cython/_cython_magic_3a51a049b19292c89caa81e80cc99ee0.cpython-35m-x86_64-linux-gnu.so\u001b[0m in \u001b[0;36mView.MemoryView.memoryview_cwrapper (/home/lilian/.cache/ipython/cython/_cython_magic_3a51a049b19292c89caa81e80cc99ee0.c:9569)\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m~/.cache/ipython/cython/_cython_magic_3a51a049b19292c89caa81e80cc99ee0.cpython-35m-x86_64-linux-gnu.so\u001b[0m in \u001b[0;36mView.MemoryView.memoryview.__cinit__ (/home/lilian/.cache/ipython/cython/_cython_magic_3a51a049b19292c89caa81e80cc99ee0.c:5804)\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: a bytes-like object is required, not 'list'"
     ]
    }
   ],
   "source": [
    "hash_SHA2_Cython(\"The quick brown fox jumps over the lazy dog\")\n",
    "assert hash_SHA2_Cython(\"The quick brown fox jumps over the lazy dog\") == 'd7a8fbb307d7809469ca9abcb0082e4f8d5651e46d3cdb762d02d0bf37c9e592'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I still have to work on that.\n",
    "\n",
    "[![made-with-jupyter](https://img.shields.io/badge/Made%20for-Jupyter%20notebook-1f425f.svg)](https://www.jupyter.org/)\n",
    "[![GitHub license](https://img.shields.io/github/license/Naereen/notebooks.svg)](https://github.com/Naereen/notebooks/blob/master/LICENSE.txt)\n",
    "[![forthebadge made-with-python](http://ForTheBadge.com/images/badges/made-with-python.svg)](https://www.python.org/) \n",
    "[![ForTheBadge built-with-science](http://ForTheBadge.com/images/badges/built-with-science.svg)](https://GitHub.com/Naereen/)\n",
    "[![ForTheBadge powered-by-electricity](http://ForTheBadge.com/images/badges/powered-by-electricity.svg)](http://ForTheBadge.com)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bonus\n",
    "\"SHA\" is pronouced like the French word \"chat\", which means *cat*.\n",
    "\n",
    "![a cat playing on a computer](https://media.giphy.com/media/JIX9t2j0ZTN9S/giphy.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> See [my GitHub `notebooks` project](https://GitHub.com/Naereen/notebooks/) for others notebooks."
   ]
  }
 ],
 "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": "3.5.3"
  },
  "notify_time": "5",
  "toc": {
   "colors": {
    "hover_highlight": "#DAA520",
    "running_highlight": "#FF0000",
    "selected_highlight": "#FFD700"
   },
   "moveMenuLeft": true,
   "nav_menu": {
    "height": "303px",
    "width": "251px"
   },
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": true,
   "threshold": 4,
   "toc_cell": true,
   "toc_position": {
    "height": "552px",
    "left": "0px",
    "right": "1164px",
    "top": "117px",
    "width": "212px"
   },
   "toc_section_display": "block",
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}