{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8bd03ae1",
   "metadata": {},
   "source": [
    "# LFSR\n",
    "\n",
    "https://en.wikipedia.org/wiki/Linear-feedback_shift_register"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "413e9cd6",
   "metadata": {},
   "source": [
    "## Theoretical\n",
    "\n",
    "$a_{i+4} = a_{i+2}+a_{i}, IV = [1, 0, 1, 0]$\n",
    "\n",
    "* next bits?\n",
    "\n",
    "$a_{i+4} = a_{i+2}+a_{i}, IV = [1, 1, 0, 1]$\n",
    "\n",
    "* next bits?\n",
    "\n",
    "    0100011010101110101010111110101 (32bit)\n",
    "\n",
    "* 32 bit LFSR generating sequence above?\n",
    "* 31 bit LFSR generating sequence above?\n",
    "* What can be the smallest degree of LFSR?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07018c2d",
   "metadata": {},
   "source": [
    "## LFSR generation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62aa14cd",
   "metadata": {},
   "source": [
    " $s_{i+4} = s_i + s_{i+1} + s_{i+3}$\n",
    " \n",
    " inicialized with vector [1, 1, 0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9cdc9240",
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import dot\n",
    "\n",
    "state = [1, 1, 0, 0]\n",
    "coef = [1, 1, 0, 1]\n",
    "\n",
    "int(dot(state, coef) % 2) #next bit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e317627",
   "metadata": {},
   "source": [
    "    [1, 1, 0, 0] => [1, 0, 0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6978dc3b",
   "metadata": {},
   "outputs": [],
   "source": [
    "state = state[1:]+[int(dot(state, coef)) % 2]\n",
    "state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a73cc7e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "state = state[1:]+[int(dot(state, coef)) % 2]\n",
    "state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b008e6f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "state = [1, 1, 0, 0]\n",
    "coef = [1, 1, 0, 1]\n",
    "\n",
    "stream = state.copy()\n",
    "for _ in range(46):\n",
    "    bit = int(dot(state, coef) % 2) #calculate next bit\n",
    "#    print(bit)\n",
    "    stream.append(bit) #append to the strean\n",
    "    state = state[1:]+[bit]  # change state (omit first bit and append new calculated at the end\n",
    "#    print(state)\n",
    "print(*stream)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6f7a6846",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Python iterator\n",
    "def lfsr(seed, coef):\n",
    "    \"\"\"\n",
    "        generates bits of LFSR with the given seed and coefficients\n",
    "        seed and coef can be list/tuple of int or string of digits 0/1\n",
    "    \"\"\"    \n",
    "    assert len(seed) == len(coef), \"Lengths of SEED and COEF differ\"\n",
    "    state = list(map(int, seed))\n",
    "    coef = list(map(int, coef))\n",
    "    while True:\n",
    "        yield state[0] #next value from list\n",
    "        state = state[1:]+[int(dot(state, coef) % 2)] #next state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31611af2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import islice\n",
    "\n",
    "islice(lfsr([1, 1, 0, 0], [1, 1, 0, 1]), 30) #creates new iterator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c4036a6f",
   "metadata": {},
   "outputs": [],
   "source": [
    "list(islice(lfsr(\"1100\", \"1101\"), 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5258b916",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(*islice(lfsr([1, 1, 0, 0], [1, 1, 0, 1]), 30))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ef0657e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "\" \".join(map(str, islice(lfsr([1, 1, 0, 0], [1, 1, 0, 1]), 30)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "affca7fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(*islice(lfsr([1, 1, 0, 0], [1, 1, 0, 1]), 30), sep=\",\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa11ba40",
   "metadata": {},
   "source": [
    "# Sum\n",
    "\n",
    "Compute the sequence, which you get by modular sum of two LFSRs. What is the period of resulting sequence?\n",
    "\n",
    "$$c_i = a_i + b_i $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "99db5a3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = [0,1,0]\n",
    "b = [1,1,1]\n",
    "\n",
    "c = a+b\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cff33bf",
   "metadata": {},
   "source": [
    "### using indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4e0f10a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "[ (a[i]+b[i]) % 2 for i in range(len(a))] #by index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "446c844d",
   "metadata": {},
   "outputs": [],
   "source": [
    "[ (a[i] ^ b[i]) for i in range(len(a))] #using XOR"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "121ecbd2",
   "metadata": {},
   "source": [
    "### list comprehension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "993dd555",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(a)\n",
    "print(b)\n",
    "print(*zip(a,b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f9854347",
   "metadata": {},
   "outputs": [],
   "source": [
    "[ (x+y) % 2 for x, y in zip(a,b) ] #list comprehension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a722577f",
   "metadata": {},
   "outputs": [],
   "source": [
    "[ (x ^ y) for x, y in zip(a,b) ] #list comprehension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9811299a",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = [0, 1, 0]\n",
    "b = [1, 1, 1]\n",
    "c = [1, 1, 0]\n",
    "\n",
    "[ sum(vals) % 2 for vals in zip(a,b,c) ] #a+b+c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c3a8956",
   "metadata": {},
   "source": [
    "## Using stream cipher for encoding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0e55db7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "plain = 'AHOJ'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1d1cb712",
   "metadata": {},
   "outputs": [],
   "source": [
    "plain.encode('ascii')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e2af24cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "plain_bytes = plain.encode('ascii')\n",
    "print(*plain_bytes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "da3dbfd8",
   "metadata": {},
   "outputs": [],
   "source": [
    "text1 = 'AHOJ'.encode('ascii')\n",
    "text2 = 'TEXT'.encode('ascii')\n",
    "print([ a ^ b for a,b in zip(text1, text2)]) #ascii XOR\n",
    "for a, b in zip(text1, text2):\n",
    "    print(f'{a:08b}')\n",
    "    print(f'{b:08b}')\n",
    "    print('-'*8)\n",
    "    print(f'{a ^ b:08b}')\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d16688bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import zip_longest\n",
    "stream = [1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1]\n",
    "stream = \"110001110001110001110001110001\"\n",
    "\n",
    "#convert input to list of bytes\n",
    "[int(\"\".join([str(bit) for bit in x]),2) for x in zip_longest(*([iter(stream)] * 8), fillvalue=\"\")] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9146863a",
   "metadata": {},
   "outputs": [],
   "source": [
    "bin(28)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0e0f4d37",
   "metadata": {},
   "outputs": [],
   "source": [
    "bin(28)[2:].zfill(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3adce189",
   "metadata": {},
   "outputs": [],
   "source": [
    "'{:08b}'.format(28)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecb01b78",
   "metadata": {},
   "outputs": [],
   "source": [
    "f'{28:08b}' #Python 3.6+"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "faf350dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\".join(f'{value:08b}' for value in [199, 28, 113, 49])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b44846e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\".join(chr(value) for value in [199, 28, 113, 49])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0f3c727a",
   "metadata": {},
   "outputs": [],
   "source": [
    "plain = 'Rastislav (KRS2026) Krivos-Bellus' #use YOUR names"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1261b928",
   "metadata": {},
   "source": [
    "## Berlekamp-Massey algorithm\n",
    "\n",
    "https://crypto.stanford.edu/~mironov/cs359/massey.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c8a8eed0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def berlekamp_massey(sequence):\n",
    "    ...\n",
    "    return (IV, coef) #minimal LFSR"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
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"
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    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "6f5562d9",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)\n",
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "accb8a36",
   "metadata": {},
   "outputs": [],
   "source": [
    "for n in range(len(s)): #Step 2\n",
    "    ..."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "b47cf7b1",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4baf2b38",
   "metadata": {},
   "outputs": [],
   "source": [
    "d = s[n]\n",
    "for i in range(1, l+1):\n",
    "    d ^= c[i] & s[n-i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5f120dad",
   "metadata": {},
   "outputs": [],
   "source": [
    "def berlekamp_massey(sequence):\n",
    "    \"\"\"\n",
    "    Run Berlekamp-Maddey algorithm over GF(2) on the given binary sequence.\n",
    "\n",
    "    Returns:\n",
    "        (IV, taps)\n",
    "        - IV: list of the first L bits (initial state of the LFSR)\n",
    "        - taps: list of length L with coefficients c1..cL\n",
    "                (s_t = sum_{i=1..L} c_i * s_{i} mod 2)\n",
    "    \"\"\"\n",
    "    s = list(map(int, sequence))\n",
    "\n",
    "    # Polynomial c(x) (connection), initialized to 1\n",
    "    c = [1]  # coefficients, c[0] corresponds to x^0\n",
    "    # Previous c for potential replacement\n",
    "    b = [1]\n",
    "\n",
    "    l = 0        # current LFSR length\n",
    "    m = 1        # spacing since last update of L\n",
    "    # Note: in GF(2), discrepancies d are either 0 or 1; we don't need 'b' explicitly\n",
    "\n",
    "    for n in range(len(s)):\n",
    "        # Compute discrepancy d at position n\n",
    "        d = s[n]\n",
    "        for i in range(1, l + 1):\n",
    "            d ^= c[i] & s[n-i]\n",
    "        if d == 0:\n",
    "            m += 1\n",
    "        else:\n",
    "            t = c.copy()\n",
    "            # Ensure c has enough length to XOR with b shifted by m\n",
    "            c += [0] * (len(b) + m - len(c))\n",
    "            # c = c XOR (b shifted by m)\n",
    "            for i in range(len(b)):\n",
    "                c[i + m] ^= b[i]\n",
    "\n",
    "            if 2 * l <= n:\n",
    "                l = n + 1 - l\n",
    "                b = t\n",
    "                m = 1\n",
    "            else:\n",
    "                m += 1\n",
    "\n",
    "    #IV, coefficients (in reversed order)\n",
    "    return s[:l], c[-1:0:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6c6df412",
   "metadata": {},
   "outputs": [],
   "source": [
    "berlekamp_massey([1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ee59c785",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(list(islice(lfsr(*berlekamp_massey([1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1])), 30)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd262b05",
   "metadata": {},
   "source": [
    "## hex string"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ed4695ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "str_hex = \"5398\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "868ca0de",
   "metadata": {},
   "outputs": [],
   "source": [
    "bytes.fromhex(str_hex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bb95327c",
   "metadata": {},
   "outputs": [],
   "source": [
    "[x for x in bytes.fromhex(str_hex)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b8f242bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import binascii\n",
    "\n",
    "binascii.unhexlify(str_hex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b1318221",
   "metadata": {},
   "outputs": [],
   "source": [
    "[int(str_hex[i:i+2], 16) for i in range(0, len(str_hex), 2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "48ed731e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.5"
  }
 },
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}