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  "signature": "sha256:1d9252a691e4540d14fe065c0882321c174303755e599065246b2436fef55866"
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From [wikipedia](http://en.wikipedia.org/wiki/Luhn_algorithm):\n",
      "\n",
      ">It is not intended to be a cryptographically secure hash function; it was designed to protect against accidental errors, not malicious attacks. Most credit cards and many government identification numbers use the algorithm as a simple method of distinguishing valid numbers from mistyped or otherwise incorrect numbers."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def luhn_checksum(card_number):\n",
      "    def digits_of(n):\n",
      "        return [int(d) for d in str(n)]\n",
      "    digits = digits_of(card_number)\n",
      "    odd_digits = digits[-1::-2]\n",
      "    even_digits = digits[-2::-2]\n",
      "    checksum = 0\n",
      "    checksum += sum(odd_digits)\n",
      "    for d in even_digits:\n",
      "        checksum += sum(digits_of(d*2))\n",
      "    return checksum % 10"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def is_luhn_valid(card_number):\n",
      "    return luhn_checksum(card_number) == 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def calculate_luhn(partial_card_number):\n",
      "    check_digit = luhn_checksum(int(partial_card_number) * 10)\n",
      "    return check_digit if check_digit == 0 else 10 - check_digit"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using the random module, we can write a function that returns Luhn-valid numbers with a given amount of digits."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import random"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def generate_card_number(number_of_digits):\n",
      "    partial_card_number = int(\"\".join([str(random.randrange(10)) for i in range(number_of_digits - 1)]))\n",
      "    checksum = calculate_luhn(partial_card_number)\n",
      "    return int(str(partial_card_number) + str(checksum))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can try out that function on the previous `is_luhn_valid` method:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "generate_card_number(16)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "6979197319948772"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "is_luhn_valid(4083102477600833 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, we can also make a number of random tests of this sort."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "[is_luhn_valid(generate_card_number(16)) for i in range(10000)] == [True]*10000"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 8
    }
   ],
   "metadata": {}
  }
 ]
}