Sage.ECDSA.ipynb

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    {
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     "text": [
      "2.7.15 (default, Jul 10 2018, 10:33:10) \n",
      "[GCC 7.2.0]\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "print(sys.version)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 2,
     "metadata": {},
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    }
   ],
   "source": [
    "# https://github.com/TheBlueMatt/bitcoinninja/blob/master/secp256k1.ecdsa.sage\n",
    "# Parameters for secp256k1\n",
    "# https://en.bitcoin.it/wiki/Secp256k1\n",
    "F = FiniteField(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)\n",
    "C = EllipticCurve([F(0), F(7)])                                # y^2=x^3+ax+b\n",
    "G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)\n",
    "N = FiniteField(C.order())                                     # how many points on the curve\n",
    "\n",
    "# primitive\n",
    "d = int(F.random_element())                                    # privkey\n",
    "pd = G*d                                                       # pubkey\n",
    "e = int(''.join(i.encode('hex') for i in 'hello'), 16)         # message('hello')\n",
    "\n",
    "# sign\n",
    "k = N.random_element()                                         # nonce\n",
    "r = (int(k)*G).xy()[0]                                         # r = kG.x\n",
    "s = (1/k)*(e+N(r)*d)                                           # s = k^-1(e+dr)\n",
    "\n",
    "# verify\n",
    "w = 1/N(s)                                                     # w = s^-1\n",
    "r == (int(w*e)*G + int(N(r)*w)*pd).xy()[0]                     # r == (we*G+wr*pd).x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sage.rings.finite_rings.finite_field_constructor import is_PrimeFiniteField\n",
    "is_PrimeFiniteField(F)"
   ]
  }
 ],
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   "display_name": "SageMath 8.3",
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