{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SSIS - Spread Spectrum Image Steganography\n",
    "\n",
    "In the 1990's and early 2000's, Lisa Marvel (my graduate student), Charles Retter, and I developed a fundamental steganography method we called SSIS (Spread Spectrum Image Steganography).  Lisa and Charles work for the US Army Research Laboratory.  Lisa has become one of the world's experts in steganography and steganalysis.  Charles is an expert in error correcting codes, especially for low signal to noise ratios.\n",
    "\n",
    "Some quick definitions:\n",
    "\n",
    "**cryptography**: system for translating a message into a language known only to sender and receiver, that language is determined by a cryptographic method, e.g., AES, and a secret key.\n",
    "    \n",
    "**cryptoanalysis**: attempt to break cryptosystems, can use any technique that works\n",
    "    \n",
    "**steganography**: system for hiding a message, typically by embedding the message inside a larger message, called the \"envelope\". Like cryptography, steganography also requires the  sender and receiver to agree on a method and to share a secret key.\n",
    "    \n",
    "**steganalysis**: attempt to detect steganography, usually by a third party.  \n",
    "    \n",
    "Cryptography and steganography are separate goals, but can be combined: anyone paranoid to hide the fact they are communicating is also likely to encrypt their messages."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SSIS Basics\n",
    "\n",
    "The basic idea is we encode the hidden message as Gaussian noise and add the message to the envelope (e.g., an image).  \n",
    "\n",
    "Let me emphasize this: the encoded message is statistically indistinguishable from IID Gaussian noise (assuming the random number generator is strong). The best a steganalyst can say is the image has some Gaussian noise.  Many images naturally have Gaussian noise.  Our embedded noise looks no different from naturally occurring noise.\n",
    "\n",
    "To explain the process, let's start with an old cryptographic idea: XOR'ing the data with a pseudo-random bit sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'%.3f'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.random import rand, randint\n",
    "%matplotlib inline\n",
    "%precision 3\n",
    "\n",
    "#for my macbook, feel free to comment this line away\n",
    "#%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In actual practice, the `crypt` pseudo-random sequence below is chosen with a cryptographically secure pseudo-random number generator keyed by a secret key known only to sender and receiver.  For the purposes of this notebook, however, we use the standard pseudo-random number generator and ignore the secret key."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0, 0, 0, 1, 1, 0, 1, 0, 1, 1]),\n",
       " array([1, 1, 0, 1, 1, 0, 1, 1, 1, 0]),\n",
       " array([1, 1, 0, 0, 0, 0, 0, 1, 0, 1]))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Message = randint(0,2,10)\n",
    "Crypt = randint(0,2,10)\n",
    "Encrypted = Message ^ Crypt #XOR\n",
    "Message, Crypt, Encrypted"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `encrypted` sequence looks like a random sequence (looks like a duck, walks like a duck, quacks like a duck, so ...).  Even if we assume the `message` sequence is non-random, the `encrypted` sequence inherits the statistical properties of the `crypt` sequence.\n",
    "\n",
    "Assuming each value of the `crypt` sequence is equally likely, each value of the `encrypted` sequence is equally likely regardless of the value of the `message` sequence.\n",
    "\n",
    "Aside: This argument is surprisingly subtle.  It is considered improper to speak of the message as random.  It is what it is.  We have no control over that.  What we can control is the `crypt` sequence.  As long as the `crypt` sequence is random, the `encrypted` sequence is random."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part Way Home: Encoding Message as Uniforms\n",
    "\n",
    "The core SSIS idea: For each bit in the message, generate a uniform random variable, U.  If the bit = 1, let $Y=U$; if the bit = 0, let $Y=g(U)$ where \n",
    "\n",
    "$$\n",
    "g(U) = \\begin{cases} U+0.5 & \\text{for $0<U<0.5$}\\\\ U-0.5 & \\text{for $0.5<U<1$} \\end{cases}\n",
    "$$\n",
    "\n",
    "Note $\\big|U-G(U)\\big| = 0.5$ for all $0<U<1$. That this difference is bounded from below (i.e., greater than 0) allows us to decode the message.\n",
    "\n",
    "The two functions are shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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YAGAEgWkekQk4UGFhoZKTk2VZlrp27Vrj/rt27VJCQoIsy1JCQoJ27dplw5R18+2332ri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\nAAAAAPAZkkwAAAAAgM+QZAIAAAAAfOZv0Fym5wLGF7wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1156cef60>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 450,
       "width": 460
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5,5))\n",
    "plt.plot([0,1],[0,1],'b',label='X=1')\n",
    "plt.plot([0.5,1],[0,0.5],'r')\n",
    "plt.plot([0,0.5],[0.5,1],'r',label='$X=0$')\n",
    "plt.plot([0.5,0.5],[1,0],':r')\n",
    "plt.axis([-0.1,1.1,-0.1,1.1])\n",
    "plt.axis('equal')\n",
    "plt.xlabel('Uniform Input')\n",
    "plt.ylabel('Uniform Output')\n",
    "_ = plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.   ,  0.111,  0.222,  0.333,  0.444,  0.556,  0.667,  0.778,\n",
       "         0.889,  1.   ]),\n",
       " array([ 0.5  ,  0.611,  0.722,  0.833,  0.944,  0.056,  0.167,  0.278,\n",
       "         0.389,  0.5  ]),\n",
       " array([ 0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5]))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def g(u):\n",
    "    \"\"\"transformation of Uniforms\"\"\"\n",
    "    return (u+0.5)*(u<0.5)+(u-0.5)*(u>=0.5)\n",
    "\n",
    "#test it\n",
    "u = np.linspace(0,1,10)\n",
    "u, g(u), np.abs(u-g(u))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modulate the pseudo-random uniform sequence by the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0, 0, 1, 0, 0, 1, 1, 1, 0, 1]),\n",
       " array([ 0.043,  0.129,  0.308,  0.141,  0.543,  0.87 ,  0.522,  0.543,\n",
       "         0.033,  0.178]),\n",
       " array([ 0.543,  0.629,  0.308,  0.641,  0.043,  0.87 ,  0.522,  0.543,\n",
       "         0.533,  0.178]))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Message = randint(0,2,10)\n",
    "Unifs = rand(10)\n",
    "Encoded = Message*Unifs + (1-Message)*g(Unifs) \n",
    "Message, Unifs, Encoded"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note when message = 1, the uniform is changed; when the message = 0, the uniform is unchanged. The resulting sequence is statistically indistinguishable from pseudo-random uniform noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generation of Pseudo-random Gaussian Noise\n",
    "\n",
    "There are many techniques for generating pseudo-random Gaussian noise.  Here we focus on inverting the distribution function.  \n",
    "\n",
    "Let $Z \\sim N(0,1)$ and $U \\sim U(0,1)$.  Let $F_Z(z) = Pr(Z\\le z) = \\Phi(z)$ and let $F_U(u) = Pr(U \\le u) = u$ for $0<u<1$.  \n",
    "\n",
    "We can generate Gaussians from uniforms by inverting the Gaussian distribution function.\n",
    "\n",
    "$$ \\begin{align}\n",
    "Z &= \\Phi^{-1}(U)\\\\\n",
    "Pr(Z \\le z) &= Pr(\\Phi^{-1}(U) \\le z) = Pr(U\\le \\Phi(z)) = \\Phi(z)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "So we can generate Gaussians from Uniforms by applying the inverse distribution transformation.\n",
    "\n",
    "Note, there are faster ways to generate Gaussian random variables than inverting the distribution function, but this is the simplest method to describe and it works well in SSIS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.132, -1.16 ,  0.405,  1.172, -0.265, -0.507,  0.684,  0.385,\n",
       "        0.56 ,  2.439])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "Phi_inv = norm.ppf\n",
    "U = rand(10)\n",
    "G = Phi_inv(U)\n",
    "G"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using the Message to Modulate a Gaussian noise sequence\n",
    "\n",
    "Now that the encoded message is a modulated uniform sequence, we generate a modulated Gaussian sequence by applying the inverse of the distribution function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.109,  0.33 , -0.5  ,  0.361, -1.713,  1.129,  0.056,  0.108,\n",
       "        0.084, -0.922])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gaussians = Phi_inv(Encoded) #gaussian noise\n",
    "Gaussians"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some Properties of the Gaussian Embedding\n",
    "\n",
    "First, look at the transformation for $X=0$ and $X=1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11aee0240>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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MAAACSlqW9bUpVlABVIhHHnlEwf///MJx48ZZrr377ruaNGmSJOmqq67S22+/bXu+M7V6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bOmQUHS8OHSM89IZcpY3hoAnA4BFQggZ5o1DQ7yaNiVcfpnlwYKDw22oTsAgCWys6UXXvDNmmb7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\n9sAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11aec1390>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 453,
       "width": 468
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = np.linspace(0,1,201)\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.plot(u,Phi_inv(u),label='$X=1$')\n",
    "plt.plot(u,Phi_inv(g(u)),'r', label='$X=0$')\n",
    "plt.axis([0,1,-3,3])\n",
    "plt.legend(loc=2)\n",
    "plt.xlabel('Uniform Input')\n",
    "plt.ylabel('Gaussian Output')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are interested in the minimum vertical distance between the red and blue curves.  This occurs when $u=0.25$ and $u=0.75$ and has value 1.349."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum vertical distance = 1.349\n"
     ]
    },
    {
     "data": {
      "image/png": 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Xrl1qaWnRM888o6OOOipyz4cffqiqqioVFxfri1/8YqqHiAxmnslsbAuqtT1E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D2imwpZEdmnuHAfrJg5CH6KBs2p+ZWYtGgv8srrVMqMiC5HlmUs2Jp5YdMRRRvKKQOj8Hcu1yIb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\nTJs2WW14f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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b364be0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 315,
       "width": 573
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,2.5))\n",
    "ax = fig.add_axes([0,0,1,1])\n",
    "plt.plot(u,np.abs(Phi_inv(u)-Phi_inv(g(u))))\n",
    "plt.xlabel(r'$u$')\n",
    "plt.ylabel(r'Vertical Distance')\n",
    "\n",
    "#other ylabels I tried\n",
    "#ax.text(-0.12,2.1,r'$\\left|\\Phi^{-1}(u)-\\Phi^{-1}(g(u))\\right|$',\n",
    "#       horizontalalignment='right',\n",
    "#       fontsize=12)\n",
    "#plt.ylabel(r'$\\left|\\Phi^{-1}(u)-\\Phi^{-1}(g(u))\\right|$',\n",
    "#           rotation='horizontal', horizontalalignment='right')\n",
    "\n",
    "print('Minimum vertical distance = %.3f' % (Phi_inv(0.75)-Phi_inv(0.25)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test the process and verify the output sequence actually has a Gaussian distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HxsZKksrKylr1uStWrFBFRYUsy9KJEye0ceNGvfrqq3rmmWe0b98+vfLKKxct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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11aefe0f0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 415,
       "width": 558
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 10000\n",
    "Mn = randint(0,2,n)\n",
    "Un = rand(n)\n",
    "En = Mn*Un + (1-Mn)*g(Un)\n",
    "GNn = Phi_inv(En)\n",
    "\n",
    "plt.hist(GNn,bins=51, normed=True)\n",
    "x = np.linspace(-4,4,101)\n",
    "_ = plt.plot(x, norm.pdf(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look at the difference between $M=0$ and $M=1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6AfusX78+w4YNy5tvvpmOHTtmwYIFGTRoUOmy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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bd68fd0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 415,
       "width": 562
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "GN_diff = Phi_inv(g(Un[Mn==0])) - Phi_inv(Un[Mn==0])\n",
    "\n",
    "_ = plt.hist(GN_diff,bins=51)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the clear separation between the two groups."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Embed the Message Into the Image\n",
    "\n",
    "Image pixels are typically 8 bit integer values from 0 to 255 (per color).  Gaussian noise is continuous.  We need to assure the resulting image is quantized and clipped.\n",
    "\n",
    "Create fake image data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([104, 234, 119, 175,  57, 140, 187,  33, 115, 113])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image = randint(0,256,10)\n",
    "Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.109,  0.33 , -0.5  ,  0.361, -1.713,  1.129,  0.056,  0.108,\n",
       "         0.084, -0.922]),\n",
       " array([104, 234, 119, 175,  57, 140, 187,  33, 115, 113]),\n",
       " array([ 104.218,  234.66 ,  117.999,  175.722,   53.573,  142.257,\n",
       "         187.112,   33.215,  115.168,  111.155]),\n",
       " array([104, 235, 118, 176,  54, 142, 187,  33, 115, 111]))"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scale = 2.0\n",
    "StegoImage_f = Image + scale*Gaussians\n",
    "StegoImage = np.clip(np.round(StegoImage_f).astype('int'),0,255)\n",
    "Gaussians, Image, StegoImage_f, StegoImage"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decode\n",
    "\n",
    "We assume the Image data is known to both the sender and the receiver.  This is known as \"non-blind\" decoding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0. ,  0.5, -0.5,  0.5, -1.5,  1. ,  0. ,  0. ,  0. , -1. ])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gaussians_hat = (StegoImage - Image)/scale\n",
    "Gaussians_hat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate Gaussians corresponding to $X=0$ and $X=1$.  Then see which is closer to `Gaussians_hat`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.109,  0.33 ,  0.872,  0.361, -1.713, -0.331, -2.006, -1.719,\n",
       "         0.084,  0.463]),\n",
       " array([-1.713, -1.13 , -0.5  , -1.076,  0.109,  1.129,  0.056,  0.108,\n",
       "        -1.833, -0.922]))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G0 = Phi_inv(g(Unifs))\n",
    "G1 = Phi_inv(Unifs)\n",
    "G0, G1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0, 0, 1, 0, 0, 1, 1, 1, 0, 1]), array([0, 0, 1, 0, 0, 1, 1, 1, 0, 1]))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X0 = np.abs(G0-Gaussians_hat)\n",
    "X1 = np.abs(G1-Gaussians_hat)\n",
    "Message_hat = np.where(X0<X1, 0, 1)\n",
    "Message_hat, Message"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errors = np.sum(np.abs(Message-Message_hat))\n",
    "errors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "Here is a quick summary of the steps:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "221"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 100000\n",
    "scale = 1.0 \n",
    "Message = randint(0,2,n)\n",
    "Image = randint(0,256,n)\n",
    "Unifs = rand(n)\n",
    "Encoded = Message*Unifs + (1-Message)*g(Unifs)\n",
    "Gaussians = Phi_inv(Encoded)\n",
    "StegoImage_f = Image + scale*Gaussians\n",
    "StegoImage = np.clip(np.round(StegoImage_f).astype('int'),0,255)\n",
    "Gaussians_hat = (StegoImage - Image)/scale\n",
    "G0 = Phi_inv(g(Unifs))\n",
    "G1 = Phi_inv(Unifs)\n",
    "X0 = np.abs(G0-Gaussians_hat)\n",
    "X1 = np.abs(G1-Gaussians_hat)\n",
    "Message_hat = np.where(X0<X1, 0, 1)\n",
    "errors = np.sum(np.abs(Message-Message_hat))\n",
    "errors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rounding (especially when `scale` is small) and clipping to 0 and 255 causes the errors. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Rest of the Story\n",
    "\n",
    "We have explained how the message we intend to hide is modulated as Gaussian noise and embedded into the image.  There are a few other considerations:\n",
    "\n",
    "1. The sender usually adds error correction bits and may interleave the bits, so adjacent bits are far apart.\n",
    "2. The `scale` parameter is important.  Making it too small results in many errors; too large and the embedded noise significantly reduces image quality.\n",
    "3. Above we assumed the receiver knows the original image.  If this is not the case (\"blind\" detection), the receiver needs to estimate the image.  One recommended way is to apply a good noise reduction algorithm to the received image and subtract the resulting *smoothed* image from the received image to obtain an estimate of the embedded Gaussian noise.\n",
    "4. Typically when doing blind detection, the estimate of the embedded Gaussian noise is \"noisy\".  The raw decoded error rate may be high.  It is important to use ECC to lower the error rate to an acceptable level.  E.g., using low rate codes and soft decision decoding."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "1. Marvel, Lisa M., Charles G. Boncelet, and Charles T. Retter. \"Spread spectrum image steganography.\" IEEE Transactions on image processing 8.8 (1999): 1075-1083.\n",
    "\n",
    "2. Boncelet Jr, Charles G., Lisa M. Marvel, and Charles T. Retter. \"Spread spectrum image steganography.\" U.S. Patent No. 6,557,103. 29 Apr. 2003.\n",
    "\n",
    "3. Marvel, Lisa M., Charles G. Boncelet Jr, and Charles T. Retter. \"Reliable blind information hiding for images.\" International Workshop on Information Hiding. Springer Berlin Heidelberg, 1998.\n",
    "\n",
    "4. Marvel, Lisa M., Charles T. Retter, and Charles G. Boncelet. \"A methodology for data hiding using images.\" Military Communications Conference, 1998. MILCOM 98. Proceedings., IEEE. Vol. 3. IEEE, 1998.\n",
    "\n",
    "5. Marvel, Lisa M., Charles T. Retter, and Charles G. Boncelet. \"Hiding information in images.\" Image Processing, 1998. ICIP 98. Proceedings. 1998 International Conference on. Vol. 2. IEEE, 1998."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "Charles Boncelet, <boncelet@udel.edu>, 4/13/17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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