Index.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Understanding the parameters of Learning With Errors (LWE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "In this report, I will briefly explain the Learning with Errors (LWE) method, which is a post-quantum public-key cryptography algorithm. We provide the mathematical background then detail our implementation based on Python 3 and `numpy`, and finally, our experiments, whose objective is to understand how changing the parameters of the algorithm affects the expected result. Our experiments are based on the encryption and decryption of a single bit message of value `1`, which are executed ten thousand times for each configuration tested. Graphs are created to visualize the results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# LWE Decription"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "LWE is a post-quantum public-key algorithm, see [this presentation](https://summerschool-croatia.cs.ru.nl/2018/slides/Introduction%20to%20post-quantum%20cryptography%20and%20learning%20with%20errors.pdf) for more information and [the original paper](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.205.2622&rep=rep1&type=pdf). This method can be resumed to the computations described in this section. First, to create a public and private key:\n",
    "\n",
    "$$\n",
    "A_{m}^{n \\times 1} \\times S_{m}^{1 \\times 1} + E_{m}^{n \\times 1} = B_{m}^{n \\times 1}\n",
    "$$\n",
    "\n",
    "$A$ and $B$ are the public keys, $S$ is the private key and $E$ is the random error, and $A,B,S,E \\in \\mathbb{Z}$. The matrixes $A,B,E$ have dimension $n \\times 1$, that is, they are single column because in this report we implement single-bit encryption and decryption.\n",
    "\n",
    "To encrypt a single-bit message $x$ using the public key $A,B$ we obtain the encrypted message composed of $(u,v)$ with:\n",
    "\n",
    "$$\n",
    "u = \\left(\\sum A_{samples}\\right) \\bmod m \\\\\n",
    "v = \\left(\\sum B_{samples}\\right) + \\frac{q}{2}x \\bmod m\n",
    "$$\n",
    "\n",
    "Where $samples$ are randomly chosen samples from $A$ and $B$. Finally, to decrypt the message $(u,v)$ and find the value of bit message $x$:\n",
    "\n",
    "$$\n",
    "x' = \n",
    "\\begin{cases}\n",
    "0 \\text{, if } (v - su \\bmod m) < \\frac{q}{2} \\\\\n",
    "1 \\text{, else}\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# LWE Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "The following `run` function was based on [this material](https://medium.com/asecuritysite-when-bob-met-alice/learning-with-errors-and-ring-learning-with-errors-23516a502406), where LWE is implemented to encrypt and decrypt a single bit of value `1`. All parameters required by the algorithm are passed as parameters for this function. They are:\n",
    "+ `n` and `m`, where $n$ is the number of rows of the single column matrixes $A,B,E$, and $m$ is the modulo for all the operations\n",
    "+ `err` sets the largest value of the interval $[1,err] \\in \\mathbb{Z}$, from which error values are randomly drawn and then added to the result of $A_{m}^{n \\times 1} * S_{m}^{1 \\times 1}$, as described above\n",
    "+ `sample` sets the number of samples drawn from the public key $(A,B)$ to encrypt the single-bit message `1`\n",
    "+ `times` sets how many times the experiment is reproduced to find a statistically relevant result\n",
    "\n",
    "The returned value is in the range $[0,1] \\in \\mathbb{R}$ and represents how many experiments ran successfully, that is, correctly encrypted and decrypted the bit `1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "outputs": [
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def run(n = 20, m = 97, err = 4, sample = 5, times = 10000):\n",
    "    if sample > n: # or m > n:\n",
    "        return None\n",
    "\n",
    "    s = np.reshape(np.repeat(n, times), (times, 1))\n",
    "\n",
    "    A = np.reshape(np.random.choice(range(m), n * times), (times, n))\n",
    "    e = np.reshape(np.random.randint(1, err + 1, n * times), (times, n))\n",
    "    B = (A * s + e) % m\n",
    "\n",
    "    sample = np.reshape(np.random.choice(range(n - 1), sample * times), (times, sample))\n",
    "\n",
    "    message = 1\n",
    "\n",
    "    # this [np.arange(times)[:,None], sample] is used for indexing the 2d array\n",
    "    u = np.sum(A[np.arange(times)[:,None], sample], axis = 1) % m\n",
    "    v = (np.sum(B[np.arange(times)[:,None], sample], axis = 1) + (m // 2) * message) % m\n",
    "\n",
    "    s = np.reshape(s, (1, times))\n",
    "\n",
    "    return np.sum(((v - s * u) % m) > m / 2) / times"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Experiments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Having detailed the mathematical background and how our implementation of LWE works, we now proceed to perform some experiments and discuss their results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## 1.  Exploring how `n` affects the result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {
      "image/png": {
       "height": 411,
       "width": 713
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = list(range(1, 1000))\n",
    "plt.plot(r, [run(n = i) for i in r], 'r+')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Increasing `n` doesn't affect the correctness of the encryption and decryption processes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## 2. Exploring how `err` affects the result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "trusted": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {
      "image/png": {
       "height": 411,
       "width": 706
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = list(range(1, 100))\n",
    "plt.plot(r, [run(err = i) for i in r], 'r+')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Apparently running LWE with the error range upper bound greater than roughly 10% of the modulo `m` affects the correctness of the output. Next, we try a prime modulo of about 10x the current to verify if the 10% threshold holds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "trusted": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {
      "image/png": {
       "height": 411,
       "width": 706
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = list(range(1, 1000))\n",
    "plt.plot(r, [run(m = 997, err = i) for i in r], 'r+')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "That finding is apparently true. Next, let's explore if changing `n` will have any effect. Until now, the experiments ran using `n = 20`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "trusted": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {
      "image/png": {
       "height": 411,
       "width": 706
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {
      "image/png": {
       "height": 411,
       "width": 706
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = list(range(1, 100))\n",
    "\n",
    "plt.plot(r, [run(n=50, err = i) for i in r], 'r+')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(r, [run(n=90, err = i) for i in r], 'r+')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Same behavior. Now let's change the sampling size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "trusted": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {
      "image/png": {
       "height": 411,
       "width": 706
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {
      "image/png": {
       "height": 411,
       "width": 706
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.plot(r, [run(sample=10, err = i) for i in r], 'r+')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(r, [run(sample=20, err = i) for i in r], 'r+')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Increasing the sample size has an impact. Apparently the algorithm fails at roughly half the `err` once we double `samples`.\n",
    "Next, we try with modulo `m = 997` and double the sample on each test to see if the behavior continues."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "trusted": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {
      "image/png": {
       "height": 411,
       "width": 706
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {
      "image/png": {
       "height": 411,
       "width": 706
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = list(range(1, 500))\n",
    "\n",
    "plt.plot(r, [run(sample=5, m = 997, err = i) for i in r], 'r+')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(r, [run(sample=10, m = 997, err = i) for i in r], 'r+')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Empirically testing LWE the parameters seem to have to respect the ratio of $err \\leq \\frac{m}{2 \\times sample}$ to correctly encrypt and decrypt. \n",
    "\n",
    "Let's put this claim to the test. First, we calculate all the prime numbers in the range $[101,100000]$ and select 1 for every 100 primes in the list. Then, for all these primes we select the number of samples at random (limiting at 1% of each prime) and calculate the upper bound value for the error range following the formula $\\frac{m}{2 \\times sample}$. Next, we run the LWE algorithm with the aforementioned parameters and plot the result. If our empirically found relation holds, then we shall see no point off the `1.0` value in the y axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "trusted": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {
      "image/png": {
       "height": 411,
       "width": 713
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "def primes(n):\n",
    "    \"\"\" Returns  a list of primes < n \"\"\"\n",
    "    \"\"\" https://stackoverflow.com/questions/2068372/fastest-way-to-list-all-primes-below-n/3035188#3035188 \"\"\"\n",
    "    sieve = [True] * n\n",
    "    for i in range(3,int(n**0.5)+1,2):\n",
    "        if sieve[i]:\n",
    "            sieve[i*i::2*i]=[False]*((n-i*i-1)//(2*i)+1)\n",
    "    return [2] + [i for i in range(3,n,2) if sieve[i]]\n",
    "\n",
    "#primes from 101 to 99991 from 100 to 100\n",
    "list_of_primes_to_100K = primes(100000)[25:-1:100]\n",
    "\n",
    "#store our randomly selected sample values\n",
    "samples = []\n",
    "\n",
    "#store our calculated error\n",
    "error_upper_bound = []\n",
    "\n",
    "for prime in list_of_primes_to_100K:\n",
    "    #limit sample on 1% of prime (the m parameter)\n",
    "    s = random.randint(5, max(5, int(prime * .01)))\n",
    "    samples.append(s)\n",
    "    \n",
    "    #calculte the error value based on our find described above\n",
    "    error = prime // (2 * s)\n",
    "    \n",
    "    error_upper_bound.append(error)\n",
    "    \n",
    "    #run the tests with the random number of samples and limited errors\n",
    "    results = [run(n = s, sample = s, m = prime, err = error)]\n",
    "    \n",
    "    #plot the results\n",
    "    plt.plot(prime, results, '+')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "No experiment presented any error, our prediction worked well. Next, we use the same values from the last experiment but increase ´err´ passed the threshold $err \\leq \\frac{m}{2 \\times sample}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": true,
    "trusted": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {
      "image/png": {
       "height": 411,
       "width": 719
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def custom_range(start, stop, increase_percentage):\n",
    "    while start < stop:\n",
    "        yield start\n",
    "        \n",
    "        if start == int(start*increase_percentage):\n",
    "            start += 1\n",
    "        else:\n",
    "            start *= increase_percentage\n",
    "            \n",
    "        start = int(start)\n",
    "        \n",
    "    yield int(stop)\n",
    "\n",
    "for index, prime in enumerate(list_of_primes_to_100K):\n",
    "    #calculte the error value based on our find described above\n",
    "    error_upper_bound[index] = [i for i in custom_range(error_upper_bound[index], error_upper_bound[index] * 1.1, 1.01)][::-1]\n",
    "    \n",
    "    #run the tests with the random number of samples and limited errors\n",
    "    results = []\n",
    "    \n",
    "    for i in error_upper_bound[index]:\n",
    "        results.append(run(n = samples[index], sample = samples[index], m = prime, err = i))\n",
    "        \n",
    "        if results[-1] == 1.0:\n",
    "            break\n",
    "    \n",
    "    #plot the results\n",
    "    plt.plot([prime] * len(results), results, '+')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "#restore the list error_upper_bound to its previus state\n",
    "for index, prime in enumerate(list_of_primes_to_100K):\n",
    "    error_upper_bound[index] = error_upper_bound[index][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "The relation we found empirically doesn't seem to hold for larger $m$ values. There are probably more complex relations at play in LWE, our equation $err \\leq \\frac{m}{2 \\times sample}$ is a good start, though."
   ]
  }
 ],
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