Almost finished ZVP.

1 files changed, 301 insertions, 2420 deletions

diff --git a/re/zvp.ipynb b/re/zvp.ipynb
index fc633f8..fedb688 100644
--- a/re/zvp.ipynb
+++ b/re/zvp.ipynb
@@ -10,7 +10,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": null,
    "id": "17a9e580-5f1e-45c9-8afd-fc35e833b0b0",
    "metadata": {},
    "outputs": [],
@@ -25,76 +25,126 @@
     "from IPython.display import HTML, display\n",
     "from tqdm.notebook import tqdm\n",
     "from anytree import RenderTree\n",
+    "from concurrent.futures import ProcessPoolExecutor, as_completed\n",
     "\n",
     "from pyecsca.ec.model import ShortWeierstrassModel\n",
     "from pyecsca.ec.coordinates import AffineCoordinateModel\n",
     "from pyecsca.ec.curve import EllipticCurve\n",
     "from pyecsca.ec.params import DomainParameters, load_params_ecgen\n",
-    "from pyecsca.ec.formula import FormulaAction\n",
-    "from pyecsca.ec.formula.fake import FakeAdditionFormula, FakeDoublingFormula, FakePoint\n",
+    "from pyecsca.ec.formula import FormulaAction, AdditionFormula, DoublingFormula\n",
     "from pyecsca.ec.point import Point\n",
-    "from pyecsca.ec.mod import Mod, gcd\n",
+    "from pyecsca.ec.mod import Mod, gcd, SymbolicMod\n",
     "from pyecsca.sca.re.tree import build_distinguishing_tree\n",
     "from pyecsca.sca.re.rpa import MultipleContext\n",
     "from pyecsca.sca.re.zvp import zvp_points, compute_factor_set\n",
     "from pyecsca.ec.context import DefaultContext, local\n",
     "from pyecsca.ec.mult import LTRMultiplier, AccumulationOrder\n",
     "from pyecsca.misc.cfg import getconfig\n",
-    "from pyecsca.ec.error import NonInvertibleError\n",
-    "from pyecsca.sca.re.zvp import unroll_formula, compute_factor_set, zvp_points"
+    "from pyecsca.ec.error import NonInvertibleError, UnsatisfiedAssumptionError\n",
+    "from pyecsca.sca.re.zvp import unroll_formula, compute_factor_set, zvp_points, addition_chain, precomp_zvp_points"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
-   "id": "d8ea0c4d-86e1-46af-ac20-569e6ef5439d",
+   "execution_count": null,
+   "id": "c2240ed4-5279-487a-ad90-f6a6798f403c",
    "metadata": {},
    "outputs": [],
    "source": [
-    "cfg = getconfig()\n",
-    "cfg.ec.mod_implementation = \"gmp\""
+    "# TODO: Maybe combine with EPA?\n",
+    "# TODO: Maybe extend oracle with number or position?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "60547b40-9b8e-409b-8b7e-b3dc266c01d4",
+   "metadata": {},
+   "source": [
+    "## Exploration\n",
+    "First lets explore the behavior of addition formulas. The following two cells pick a coordinate model along with some formulas and symbolically unroll a scalar multiplication."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "id": "8de124f1-9498-4e55-8b7f-1bd291ccf3fe",
    "metadata": {},
    "outputs": [],
    "source": [
     "model = ShortWeierstrassModel()\n",
     "coordsaff = AffineCoordinateModel(model)\n",
-    "coords = model.coordinates[\"projective\"]\n",
-    "add = coords.formulas[\"add-2007-bl\"]\n",
-    "dbl = coords.formulas[\"dbl-2007-bl\"]\n",
-    "neg = coords.formulas[\"neg\"]\n",
+    "which = \"jacobian\"\n",
+    "coords = model.coordinates[which]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2193ab53-9dc9-4ba4-89d3-e331e5cc20de",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "getconfig().ec.mod_implementation = \"symbolic\"\n",
+    "x, y, z = symbols(\"x y z\")\n",
     "\n",
     "# A 64-bit prime order curve for testing things out\n",
     "p = 0xc50de883f0e7b167\n",
-    "a = Mod(0x4833d7aa73fa6694, p)\n",
-    "b = Mod(0xa6c44a61c5323f6a, p)\n",
-    "gx = Mod(0x5fd1f7d38d4f2333, p)\n",
-    "gy = Mod(0x21f43957d7e20ceb, p)\n",
+    "field = FF(p)\n",
+    "a = SymbolicMod(Poly(0x4833d7aa73fa6694, x, y, z, domain=field), p)\n",
+    "b = SymbolicMod(Poly(0xa6c44a61c5323f6a, x, y, z, domain=field), p)\n",
+    "gx = SymbolicMod(Poly(0x5fd1f7d38d4f2333, x, y, z, domain=field), p)\n",
+    "gy = SymbolicMod(Poly(0x21f43957d7e20ceb, x, y, z, domain=field), p)\n",
     "n = 0xc50de885003b80eb\n",
     "h = 1\n",
     "\n",
-    "field = FF(p)\n",
-    "\n",
     "infty = Point(coords, X=Mod(0, p), Y=Mod(1, p), Z=Mod(0, p))\n",
     "g = Point(coords, X=gx, Y=gy, Z=Mod(1, p))\n",
     "\n",
     "curve = EllipticCurve(model, coords, p, infty, dict(a=a,b=b))\n",
-    "params = DomainParameters(curve, g, n, h)"
+    "params = DomainParameters(curve, g, n, h)\n",
+    "\n",
+    "\n",
+    "add = coords.formulas[\"add-2007-bl\"]\n",
+    "dbl = coords.formulas[\"dbl-2007-bl\"]\n",
+    "mult = LTRMultiplier(add, dbl, None, False, AccumulationOrder.PeqRP, True, True)\n",
+    "\n",
+    "\n",
+    "point = Point(coords,\n",
+    "              X=SymbolicMod(Poly(x, x, y, z, domain=field), params.curve.prime),\n",
+    "              Y=SymbolicMod(Poly(y, x, y, z, domain=field), params.curve.prime),\n",
+    "              Z=SymbolicMod(Poly(z, x, y, z, domain=field), params.curve.prime))\n",
+    "mult.init(params, point)\n",
+    "res = mult.multiply(5)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": null,
+   "id": "d8ea0c4d-86e1-46af-ac20-569e6ef5439d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cfg = getconfig()\n",
+    "cfg.ec.mod_implementation = \"gmp\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c3b3ae94-242b-4f36-81e3-e8a64b5af33c",
+   "metadata": {},
+   "source": [
+    "## Reverse-engineering\n",
+    "Now, lets look at using the ZVP attack for reverse-engineering. First pick 10 random curves and one curve with `a = 0`. These curves are not special in any way and just serve to randomize the process, as the existence of ZVP points for a given intermediate value polynomial depends on the curve."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
    "id": "0252f8fa-012c-453c-ba23-b40f9686fcce",
    "metadata": {},
    "outputs": [],
    "source": [
-    "curves = list(map(lambda spec: load_params_ecgen(io.BytesIO(spec.encode()), \"projective\"), [\n",
+    "curves = list(map(lambda spec: load_params_ecgen(io.BytesIO(spec.encode()), \"affine\"), [\n",
     "    \"\"\"[{\"field\":{\"p\":\"0xa7ec3617d4166b2d\"},\"a\":\"0x372994d9d680a83b\",\"b\":\"0xa0a2bf719d8e68c5\",\"order\":\"0xa7ec3618be1dab55\",\"subgroups\":[{\"x\":\"0x1ef15756946a5b6d\",\"y\":\"0x2ca9658f7ab9a558\",\"order\":\"0xa7ec3618be1dab55\",\"cofactor\":\"0x1\",\"points\":[{\"x\":\"0x1ef15756946a5b6d\",\"y\":\"0x2ca9658f7ab9a558\",\"order\":\"0xa7ec3618be1dab55\"}]}]}]\"\"\",\n",
     "    \"\"\"[{\"field\":{\"p\":\"0xa42c1467a1ed04f3\"},\"a\":\"0x55d07340a4572f2d\",\"b\":\"0x0a938c37dfb0b6d5\",\"order\":\"0xa42c14689284d3a7\",\"subgroups\":[{\"x\":\"0x8633981c83ed43a2\",\"y\":\"0x7b5374e9d7997199\",\"order\":\"0xa42c14689284d3a7\",\"cofactor\":\"0x1\",\"points\":[{\"x\":\"0x8633981c83ed43a2\",\"y\":\"0x7b5374e9d7997199\",\"order\":\"0xa42c14689284d3a7\"}]}]}]\"\"\",\n",
     "    \"\"\"[{\"field\":{\"p\":\"0xea0d9cead19016ab\"},\"a\":\"0xcbbfe501c4ef6d92\",\"b\":\"0x5762de777a6d9178\",\"order\":\"0xea0d9cea8cd2c857\",\"subgroups\":[{\"x\":\"0xe7daa3e061c3111b\",\"y\":\"0x56ee59a6845c5e93\",\"order\":\"0xea0d9cea8cd2c857\",\"cofactor\":\"0x1\",\"points\":[{\"x\":\"0xe7daa3e061c3111b\",\"y\":\"0x56ee59a6845c5e93\",\"order\":\"0xea0d9cea8cd2c857\"}]}]}]\"\"\",\n",
@@ -105,2470 +155,301 @@
     "    \"\"\"[{\"field\":{\"p\":\"0xd47ec1d03a62686d\"},\"a\":\"0xd00a3ee0f5c86b02\",\"b\":\"0x457a5b6c47db38d8\",\"order\":\"0xd47ec1d107db7d6f\",\"subgroups\":[{\"x\":\"0x41ebc3b763f3cd1b\",\"y\":\"0x3d6925f214620e0c\",\"order\":\"0xd47ec1d107db7d6f\",\"cofactor\":\"0x1\",\"points\":[{\"x\":\"0x41ebc3b763f3cd1b\",\"y\":\"0x3d6925f214620e0c\",\"order\":\"0xd47ec1d107db7d6f\"}]}]}]\"\"\",\n",
     "    \"\"\"[{\"field\":{\"p\":\"0xb1c9115c6f40d755\"},\"a\":\"0x79d3ceefafc44ce9\",\"b\":\"0x8316af84264df42b\",\"order\":\"0xb1c9115d17f84a45\",\"subgroups\":[{\"x\":\"0x8b0a274089b53fe5\",\"y\":\"0x3508d33c4beba5ad\",\"order\":\"0xb1c9115d17f84a45\",\"cofactor\":\"0x1\",\"points\":[{\"x\":\"0x8b0a274089b53fe5\",\"y\":\"0x3508d33c4beba5ad\",\"order\":\"0xb1c9115d17f84a45\"}]}]}]\"\"\",\n",
     "    \"\"\"[{\"field\":{\"p\":\"0x8f738fda18cd5dff\"},\"a\":\"0x4747f2f9b8628cbf\",\"b\":\"0x586cdb9378a1389f\",\"order\":\"0x8f738fd8fc7ebed3\",\"subgroups\":[{\"x\":\"0x7ad306c73b64c1b5\",\"y\":\"0x69e3ca555190da4b\",\"order\":\"0x8f738fd8fc7ebed3\",\"cofactor\":\"0x1\",\"points\":[{\"x\":\"0x7ad306c73b64c1b5\",\"y\":\"0x69e3ca555190da4b\",\"order\":\"0x8f738fd8fc7ebed3\"}]}]}]\"\"\",\n",
+    "    \"\"\"[{\"field\":{\"p\":\"0xcfef393139c3007f\"},\"a\":\"0xcfef393139c3007e\",\"b\":\"0x950312812acb155f\",\"order\":\"0xcfef39320179387b\",\"subgroups\":[{\"x\":\"0xae2d2f58ca5b5cf7\",\"y\":\"0xc3a4bf3a1dc10005\",\"order\":\"0xcfef39320179387b\",\"cofactor\":\"0x1\",\"points\":[{\"x\":\"0xae2d2f58ca5b5cf7\",\"y\":\"0xc3a4bf3a1dc10005\",\"order\":\"0xcfef39320179387b\"}]}]}]\"\"\",\n",
+    "    \"\"\"[{\"field\":{\"p\":\"0x8d79ca36cee026a7\"},\"a\":\"0x8d79ca36cee026a4\",\"b\":\"0x0478c1f80ce2c9c6\",\"order\":\"0x8d79ca35a428c76f\",\"subgroups\":[{\"x\":\"0x2e94a3e38f8b345e\",\"y\":\"0x83e6c6f0cb8f69c4\",\"order\":\"0x8d79ca35a428c76f\",\"cofactor\":\"0x1\",\"points\":[{\"x\":\"0x2e94a3e38f8b345e\",\"y\":\"0x83e6c6f0cb8f69c4\",\"order\":\"0x8d79ca35a428c76f\"}]}]}]\"\"\",\n",
     "    \"\"\"[{\"field\":{\"p\":\"0xceaf446a53f14bc1\"},\"a\":\"0x0000000000000000\",\"b\":\"0x326539376260f173\",\"order\":\"0xceaf446aae275419\",\"subgroups\":[{\"x\":\"0x98fe44948c3f8678\",\"y\":\"0x3d440ee959a912d7\",\"order\":\"0xceaf446aae275419\",\"cofactor\":\"0x1\",\"points\":[{\"x\":\"0x98fe44948c3f8678\",\"y\":\"0x3d440ee959a912d7\",\"order\":\"0xceaf446aae275419\"}]}]}]\"\"\",\n",
-    "    \"\"\"[{\"field\":{\"p\":\"0x9d9119957f02fe3f\"},\"a\":\"0x0106903196d88df9\",\"b\":\"0x0000000000000000\",\"order\":\"0x9d9119957f02fe40\",\"subgroups\":[{\"x\":\"0x191a36b9cd81de96\",\"y\":\"0x10f2c6bded391aa9\",\"order\":\"0x9d9119957f02fe40\",\"cofactor\":\"0x1\",\"points\":[{\"x\":\"0x0000000000000000\",\"y\":\"0x0000000000000000\",\"order\":\"0x2\"},{\"x\":\"0x95913fae9065da0f\",\"y\":\"0x5eeddeee7152d6fb\",\"order\":\"0x276446655fc0bf9\"}]}]}]\"\"\"\n",
+    "    #\"\"\"[{\"field\":{\"p\":\"0x9d9119957f02fe3f\"},\"a\":\"0x0106903196d88df9\",\"b\":\"0x0000000000000000\",\"order\":\"0x9d9119957f02fe40\",\"subgroups\":[{\"x\":\"0x191a36b9cd81de96\",\"y\":\"0x10f2c6bded391aa9\",\"order\":\"0x9d9119957f02fe40\",\"cofactor\":\"0x1\",\"points\":[{\"x\":\"0x0000000000000000\",\"y\":\"0x0000000000000000\",\"order\":\"0x2\"},{\"x\":\"0x95913fae9065da0f\",\"y\":\"0x5eeddeee7152d6fb\",\"order\":\"0x276446655fc0bf9\"}]}]}]\"\"\"\n",
     "]))"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": 5,
-   "id": "e65c4ab0-a9fa-479b-b109-67968fd67c1c",
+   "cell_type": "markdown",
+   "id": "4276de4c-78f4-4cdb-b60e-8c24eabfa00d",
    "metadata": {},
-   "outputs": [],
    "source": [
-    "def simulated_oracle(scalar, affine_point, real_coord_name=\"projective\", real_add_name=\"add-2007-bl\", real_dbl_name=\"dbl-2007-bl\"):\n",
-    "    real_coords = model.coordinates[real_coord_name]\n",
-    "    real_add = real_coords.formulas[real_add_name]\n",
-    "    real_dbl = real_coords.formulas[real_dbl_name]\n",
-    "    real_mult = LTRMultiplier(real_add, real_dbl, None, False, AccumulationOrder.PeqPR, True, True)\n",
-    "    point = affine_point.to_model(params.curve.coordinate_model, params.curve)\n",
-    "    with local(DefaultContext()) as ctx:\n",
-    "        real_mult.init(params, point)\n",
-    "        real_mult.multiply(scalar)\n",
-    "\n",
-    "    trace = []\n",
-    "\n",
-    "    def callback(action):\n",
-    "        if isinstance(action, FormulaAction):\n",
-    "            for intermediate in action.op_results:\n",
-    "                trace.append(intermediate.value)\n",
-    "    ctx.actions.walk(callback)\n",
-    "    return any(int(value) == 0 for value in trace)"
+    "First lets fix a scalar, go over the curves and compute the addition chain to obtain information about which multiples of the input point will go into the formulas."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
-   "id": "d0ef1628-3d87-40be-95a0-3045bb1ee4aa",
+   "execution_count": null,
+   "id": "7ab00a5c-2873-40c0-a81c-873350897e46",
    "metadata": {},
    "outputs": [],
    "source": [
-    "adds = list(filter(lambda formula: formula.name.startswith(\"add\"), coords.formulas.values()))\n",
-    "dbls = list(filter(lambda formula: formula.name.startswith(\"dbl\"), coords.formulas.values()))\n",
-    "formula_pairs = list(product(adds, dbls))\n",
+    "scalar = 123456789\n",
     "\n",
-    "# Compute all of the factor sets, and adjust those for dbl to the right index.\n",
-    "add_fsets = {add: compute_factor_set(add) for add in adds}\n",
-    "dbl_fsets = {}\n",
-    "for dbl in dbls:\n",
-    "    fset = compute_factor_set(dbl)\n",
-    "    dbl2_fset = set()\n",
-    "    for poly in fset:\n",
-    "        pl = poly.copy()\n",
-    "        for symbol in poly.free_symbols:\n",
-    "            original = str(symbol)\n",
-    "            if original.endswith(\"1\"):\n",
-    "                new = original.replace(\"1\", \"2\")\n",
-    "                pl = pl.subs(original, new)\n",
-    "        dbl2_fset.add(pl)\n",
-    "    dbl_fsets[dbl] = dbl2_fset"
+    "chains = []\n",
+    "for i, params in enumerate(curves):\n",
+    "    chain = addition_chain(scalar, params, LTRMultiplier, lambda add,dbl: LTRMultiplier(add, dbl, None, False, AccumulationOrder.PeqRP, True, True))\n",
+    "    chains.append(chain)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "12646534-8ca5-48c1-a4ae-1ad62575821f",
+   "metadata": {},
+   "source": [
+    "Now, lets compute the sets of ZVP points, going over all coordinate systems and all of their formulas (that fit the scalar multiplier) and store them into the `point_chains`. These items form individual distinct entries of the distinguishing table."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
-   "id": "b7c7b341-5b15-44fb-b9cf-462b64e7536e",
+   "execution_count": null,
+   "id": "91bc36bb-80e8-41d8-8612-7f9e24bdf278",
    "metadata": {},
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-       "Compute ZVP points:   0%|          | 0/12 [00:00<?, ?it/s]"
-      ]
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-      ]
-     },
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-       "Compute ZVP points for dbls:   0%|          | 0/4 [00:00<?, ?it/s]"
-      ]
-     },
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-   ],
+   "outputs": [],
    "source": [
-    "scalar = 123456789\n",
     "bound = 25\n",
+    "chain_bound = 20\n",
     "\n",
-    "chains = []\n",
-    "for i, params in enumerate(curves):\n",
-    "    fake_add = FakeAdditionFormula(params.curve.coordinate_model)\n",
-    "    fake_dbl = FakeDoublingFormula(params.curve.coordinate_model)\n",
-    "    fake_mult = LTRMultiplier(fake_add, fake_dbl, None, False, AccumulationOrder.PeqPR, True, True)\n",
-    "    fake_mult.init(params, FakePoint(params.curve.coordinate_model))\n",
-    "    \n",
-    "    with local(MultipleContext()) as mctx:\n",
-    "        fake_mult.multiply(scalar)\n",
-    "\n",
-    "    chain = []\n",
-    "\n",
-    "    for point, parents in mctx.parents.items():\n",
-    "        if not parents:\n",
-    "            continue\n",
-    "        k = mctx.points[parents[0]]\n",
-    "        # TODO: look at this k computation\n",
-    "        if len(parents) == 2:\n",
-    "            if k > bound:\n",
+    "formula_classes = [AdditionFormula, DoublingFormula]\n",
+    "point_chains = {}\n",
+    "with ProcessPoolExecutor(max_workers=10) as pool:\n",
+    "    futures = []\n",
+    "    args = []\n",
+    "    for coord_name, coords in model.coordinates.items():\n",
+    "        for chain, affine_params in zip(chains, curves):\n",
+    "            try:\n",
+    "                params = affine_params.to_coords(coords)\n",
+    "            except UnsatisfiedAssumptionError:\n",
     "                continue\n",
-    "            chain.append((\"add\", k))\n",
-    "        else:\n",
-    "            chain.append((\"dbl\", k))\n",
-    "    chains.append(chain)\n",
+    "            formula_groups = [list(filter(lambda formula: isinstance(formula, formula_class), coords.formulas.values())) for formula_class in formula_classes]\n",
     "\n",
-    "point_sets = {}\n",
-    "for chain, params in tqdm(zip(chains, curves), desc=\"Compute ZVP points\", total=len(chains)):\n",
-    "    for add in tqdm(adds, desc=\"Compute ZVP points for adds\", leave=False):\n",
-    "        add_fset = add_fsets[add]\n",
-    "        for op, k in tqdm(chain, leave=False):\n",
-    "            if op == \"add\" and (add, k, params) not in point_sets:\n",
-    "                points = set()\n",
-    "                for poly in add_fset:\n",
-    "                    try:\n",
-    "                        points.update(zvp_points(poly, params.curve, k, params.order))\n",
-    "                    except NonInvertibleError:\n",
-    "                        pass\n",
-    "                point_sets[(add, k, params)] = points\n",
-    "    for dbl in tqdm(dbls, desc=\"Compute ZVP points for dbls\", leave=False):\n",
-    "        dbl_fset = dbl_fsets[dbl]\n",
-    "        for op, k in tqdm(chain, leave=False):\n",
-    "            if op == \"dbl\" and (dbl, k, params) not in point_sets:\n",
-    "                points = set()\n",
-    "                for poly in dbl_fset:\n",
-    "                    try:\n",
-    "                        points.update(zvp_points(poly, params.curve, k, params.order))\n",
-    "                    except NonInvertibleError:\n",
-    "                        pass\n",
-    "                point_sets[(dbl, k, params)] = points"
+    "            for formula_group, formula_class in zip(formula_groups, formula_classes):\n",
+    "                for formula in formula_group:\n",
+    "                    futures.append(pool.submit(precomp_zvp_points, chain[:chain_bound], {formula_class.shortname: formula}, params, bound))\n",
+    "                    args.append((coords, formula, affine_params))\n",
+    "    for future in tqdm(as_completed(futures), desc=\"Compute\", total=len(futures)):\n",
+    "        j = futures.index(future)\n",
+    "        point_chains[args[j]] = future.result()\n",
+    "            "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "55cb5e3c-b1f1-443f-9d5f-269de6eb59ec",
+   "metadata": {},
+   "source": [
+    "Now, accumulate the rows of the distinguishing table to create the distinguishing map `point_map`."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 63,
-   "id": "f95909c9-8595-4d2d-8963-0c6fcb5728dd",
+   "execution_count": null,
+   "id": "b7c7b341-5b15-44fb-b9cf-462b64e7536e",
    "metadata": {},
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+   "outputs": [],
    "source": [
     "point_map = {}\n",
-    "for add, dbl in formula_pairs:\n",
-    "    points = set()\n",
-    "    for chain, params in zip(chains, curves):\n",
-    "        \n",
-    "        for op, k in chain:\n",
-    "            if op == \"add\" and (add, k, params) in point_sets:\n",
-    "                point_set = point_sets[(add, k, params)]\n",
-    "            elif op == \"dbl\" and (dbl, k, params) in point_sets:\n",
-    "                point_set = point_sets[(dbl, k, params)]\n",
-    "            for point in point_set:\n",
-    "                points.add((point, params, k))\n",
-    "    point_map[(add, dbl)] = points\n",
-    "all_points = set().union(*point_map.values())\n",
-    "\n",
-    "remapped_point_map = {}\n",
-    "for add, dbl in tqdm(formula_pairs, desc=\"Remapping\"):\n",
-    "    mult = LTRMultiplier(add, dbl, None, False, AccumulationOrder.PeqPR, True, True)\n",
+    "for coord_name, coords in tqdm(model.coordinates.items(), desc=\"Accumulate for coord systems\"):\n",
+    "    formula_groups = [list(filter(lambda formula: isinstance(formula, formula_class), coords.formulas.values())) for formula_class in formula_classes]\n",
+    "    formula_combinations = list(product(*formula_groups))\n",
+    "    for formulas in formula_combinations:\n",
+    "        points = set()\n",
+    "        for formula in formulas:\n",
+    "            for chain, affine_params in zip(chains, curves):\n",
+    "                try:\n",
+    "                    params = affine_params.to_coords(coords)\n",
+    "                except UnsatisfiedAssumptionError:\n",
+    "                    continue\n",
+    "                point_chain = point_chains[(coords, formula, affine_params)]\n",
+    "                for step in point_chain:\n",
+    "                    for poly, poly_points in step.items():\n",
+    "                        for point in poly_points:\n",
+    "                            points.add((point, affine_params))\n",
+    "        point_map[formulas] = points\n",
+    "all_points = set().union(*point_map.values())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2718285c-913c-4d46-b3bc-db8c7ef1f9ee",
+   "metadata": {},
+   "source": [
+    "We now have a distinguishing map so we can build the tree and visualize it."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8afea2a8-49a1-4969-a19e-9e17e26fb1e8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "tree = build_distinguishing_tree(point_map)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ab09b767-71ca-4d28-abf0-532307efefbd",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "print(RenderTree(tree).by_attr(lambda n: n.name if n.name is not None else \"\\n\".join((\", \".join(str(formula) for formula in cfg) for cfg in n.cfgs))))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ed2d4b51-573f-4fef-b1a4-d30b3be07423",
+   "metadata": {},
+   "source": [
+    "Our ZVP points might (due to the bounds above thus the incompleteness of our analysis) lead to more zeros than we attribute to then (in more configurations), thus we perform a remapping step where we execute the scalar multiplication with given points and trace whether they introduce the zeros. This gives us a new distinguishing map `remapped_point_map`, now without \"false negatives\"."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ca932717-2b0a-4dea-ae84-988b7d9af233",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def remap(coords, formulas, points, scalar):\n",
+    "    mult = LTRMultiplier(*formulas, None, False, AccumulationOrder.PeqRP, True, True)\n",
     "    new_points = set()\n",
-    "    for point, params, k in tqdm(all_points, leave=False):\n",
-    "        mult.init(params, point.to_model(params.curve.coordinate_model, params.curve))\n",
+    "    param_map = {}\n",
+    "    for point, params in points:\n",
+    "        if params not in param_map:\n",
+    "            try:\n",
+    "                param_map[params] = params.to_coords(coords)\n",
+    "            except UnsatisfiedAssumptionError:\n",
+    "                param_map[params] = None\n",
+    "                continue\n",
+    "        elif param_map[params] is None:\n",
+    "            continue\n",
+    "        mult.init(param_map[params], point.to_model(param_map[params], param_map[params].curve))\n",
     "        with local(DefaultContext()) as ctx:\n",
     "            mult.multiply(scalar)\n",
     "        trace = []\n",
-    "\n",
     "        def callback(action):\n",
     "            if isinstance(action, FormulaAction):\n",
     "                for intermediate in action.op_results:\n",
     "                    trace.append(intermediate.value)\n",
-    "        # TODO: What is going on? And where is it going on?\n",
-    "        # TODO: Run through all coord systems at once.\n",
-    "        # TODO: Maybe combine with EPA?\n",
-    "        # TODO: Maybe extend oracle with number or position?\n",
-    "        # TODO: k in map? why?\n",
     "        ctx.actions.walk(callback)\n",
     "        hit_zero = any(int(value) == 0 for value in trace)\n",
-    "        should_hit_zero = (point, params, k) in point_map[(add, dbl)]\n",
     "        if hit_zero:\n",
-    "            new_points.add((point, params, k))\n",
-    "        #if hit_zero != should_hit_zero:\n",
-    "        #    print(add, dbl, hit_zero, should_hit_zero, point, params, k)\n",
-    "        #else:\n",
-    "        #    print(\"ok\", hit_zero, should_hit_zero)\n",
-    "    remapped_point_map[(add, dbl)] = new_points"
+    "            new_points.add((point, params))\n",
+    "    return new_points\n",
+    "\n",
+    "remapped_point_map = {}\n",
+    "with ProcessPoolExecutor(max_workers=10) as pool:\n",
+    "    futures = []\n",
+    "    pairs = []\n",
+    "    for coord_name, coords in model.coordinates.items():\n",
+    "        formula_groups = [list(filter(lambda formula: isinstance(formula, formula_class), coords.formulas.values())) for formula_class in formula_classes]\n",
+    "        formula_combinations = list(product(*formula_groups))\n",
+    "        for formulas in formula_combinations:\n",
+    "            futures.append(pool.submit(remap, coords, formulas, all_points, scalar))\n",
+    "            pairs.append(formulas)\n",
+    "    results = [None for _ in futures]\n",
+    "    for future in tqdm(as_completed(futures), total=len(futures), desc=\"Remap\"):\n",
+    "        j = futures.index(future)\n",
+    "        remapped_point_map[pairs[j]] = future.result()"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": 64,
-   "id": "8afea2a8-49a1-4969-a19e-9e17e26fb1e8",
+   "cell_type": "markdown",
+   "id": "8a909b33-5c4d-450b-ad97-dee3615d8462",
    "metadata": {},
+   "source": [
+    "We can compare the remapped distinguishing map to the original one and see the changes."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "cc87dfd1-f058-4338-aaca-fc05105fc9f1",
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [],
    "source": [
-    "tree = build_distinguishing_tree(remapped_point_map)"
+    "for pair in point_map.keys():\n",
+    "    print(pair[0], pair[1],\n",
+    "          len(point_map[pair]),\n",
+    "          len(remapped_point_map[pair]),\n",
+    "          -len(point_map[pair].difference(remapped_point_map[pair])),\n",
+    "          len(remapped_point_map[pair].difference(point_map[pair])))\n",
+    "    crvs = set()\n",
+    "    for point, params in remapped_point_map[pair].difference(point_map[pair]):\n",
+    "        crvs.add(params)\n",
+    "    print(repr(crvs))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3c0d710b-19fd-4ff7-a39f-f38b1b8856f8",
+   "metadata": {},
+   "source": [
+    "Finally, we can build a tree using the remapped distinguishing map."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 65,
-   "id": "ab09b767-71ca-4d28-abf0-532307efefbd",
+   "execution_count": null,
+   "id": "5ffc5564-a42b-4837-94bb-4ecb890b38b2",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[x=3034406243747257516, y=11482511777964072902]\n",
-      "DomainParameters(EllipticCurve)\n",
-      "6\n",
-      "├── [x=6126421359781338627, y=9772906831073546368]\n",
-      "│   DomainParameters(EllipticCurve)\n",
-      "│   1\n",
-      "│   ├── [x=9219828953749013321, y=2141216720201514772]\n",
-      "│   │   DomainParameters(EllipticCurve)\n",
-      "│   │   3858024\n",
-      "│   │   ├── [x=5047606674150175385, y=1956997826490032405]\n",
-      "│   │   │   DomainParameters(EllipticCurve)\n",
-      "│   │   │   6\n",
-      "│   │   │   ├── (AdditionEFDFormula(add-2007-bl for shortw/projective), DoublingEFDFormula(dbl-2015-rcb for shortw/projective))\n",
-      "│   │   │   │   (AdditionEFDFormula(add-2002-bj for shortw/projective), DoublingEFDFormula(dbl-2015-rcb for shortw/projective))\n",
-      "│   │   │   └── (AdditionEFDFormula(add-2015-rcb for shortw/projective), DoublingEFDFormula(dbl-2015-rcb for shortw/projective))\n",
-      "│   │   └── (AdditionEFDFormula(add-2015-rcb for shortw/projective), DoublingEFDFormula(dbl-2007-bl for shortw/projective))\n",
-      "│   │       (AdditionEFDFormula(add-2015-rcb for shortw/projective), DoublingEFDFormula(dbl-1998-cmo for shortw/projective))\n",
-      "│   │       (AdditionEFDFormula(add-2015-rcb for shortw/projective), DoublingEFDFormula(dbl-1998-cmo-2 for shortw/projective))\n",
-      "│   └── (AdditionEFDFormula(add-2007-bl for shortw/projective), DoublingEFDFormula(dbl-2007-bl for shortw/projective))\n",
-      "│       (AdditionEFDFormula(add-2007-bl for shortw/projective), DoublingEFDFormula(dbl-1998-cmo for shortw/projective))\n",
-      "│       (AdditionEFDFormula(add-2007-bl for shortw/projective), DoublingEFDFormula(dbl-1998-cmo-2 for shortw/projective))\n",
-      "│       (AdditionEFDFormula(add-2002-bj for shortw/projective), DoublingEFDFormula(dbl-2007-bl for shortw/projective))\n",
-      "│       (AdditionEFDFormula(add-2002-bj for shortw/projective), DoublingEFDFormula(dbl-1998-cmo for shortw/projective))\n",
-      "│       (AdditionEFDFormula(add-2002-bj for shortw/projective), DoublingEFDFormula(dbl-1998-cmo-2 for shortw/projective))\n",
-      "└── [x=9219828953749013321, y=2141216720201514772]\n",
-      "    DomainParameters(EllipticCurve)\n",
-      "    3858024\n",
-      "    ├── (AdditionEFDFormula(add-1998-cmo for shortw/projective), DoublingEFDFormula(dbl-2015-rcb for shortw/projective))\n",
-      "    │   (AdditionEFDFormula(add-1998-cmo-2 for shortw/projective), DoublingEFDFormula(dbl-2015-rcb for shortw/projective))\n",
-      "    └── (AdditionEFDFormula(add-1998-cmo for shortw/projective), DoublingEFDFormula(dbl-2007-bl for shortw/projective))\n",
-      "        (AdditionEFDFormula(add-1998-cmo for shortw/projective), DoublingEFDFormula(dbl-1998-cmo for shortw/projective))\n",
-      "        (AdditionEFDFormula(add-1998-cmo for shortw/projective), DoublingEFDFormula(dbl-1998-cmo-2 for shortw/projective))\n",
-      "        (AdditionEFDFormula(add-1998-cmo-2 for shortw/projective), DoublingEFDFormula(dbl-2007-bl for shortw/projective))\n",
-      "        (AdditionEFDFormula(add-1998-cmo-2 for shortw/projective), DoublingEFDFormula(dbl-1998-cmo for shortw/projective))\n",
-      "        (AdditionEFDFormula(add-1998-cmo-2 for shortw/projective), DoublingEFDFormula(dbl-1998-cmo-2 for shortw/projective))\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "print(RenderTree(tree).by_attr(lambda n: n.name if n.name is not None else n.cfgs))"
+    "remapped_tree = build_distinguishing_tree(remapped_point_map)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 77,
-   "id": "cc87dfd1-f058-4338-aaca-fc05105fc9f1",
+   "execution_count": null,
+   "id": "5d2bbf5b-76e6-4137-9c32-cbd09a5c3600",
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "print(RenderTree(remapped_tree).by_attr(lambda n: n.name if n.name is not None else n.cfgs))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6db4910f-c492-462b-9d0e-effe3e7bfed9",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "shortw/projective/add-2007-bl shortw/projective/dbl-2007-bl 462 518 0 56\n",
-      "set()\n",
-      "shortw/projective/add-2007-bl shortw/projective/dbl-1998-cmo 462 518 0 56\n",
-      "set()\n",
-      "shortw/projective/add-2007-bl shortw/projective/dbl-2015-rcb 1716 1784 0 68\n",
-      "set()\n",
-      "shortw/projective/add-2007-bl shortw/projective/dbl-1998-cmo-2 462 518 0 56\n",
-      "set()\n",
-      "shortw/projective/add-2015-rcb shortw/projective/dbl-2007-bl 850 870 0 20\n",
-      "set()\n",
-      "shortw/projective/add-2015-rcb shortw/projective/dbl-1998-cmo 850 870 0 20\n",
-      "set()\n",
-      "shortw/projective/add-2015-rcb shortw/projective/dbl-2015-rcb 2104 2108 0 4\n",
-      "set()\n",
-      "shortw/projective/add-2015-rcb shortw/projective/dbl-1998-cmo-2 850 870 0 20\n",
-      "set()\n",
-      "shortw/projective/add-2002-bj shortw/projective/dbl-2007-bl 462 518 0 56\n",
-      "set()\n",
-      "shortw/projective/add-2002-bj shortw/projective/dbl-1998-cmo 462 518 0 56\n",
-      "set()\n",
-      "shortw/projective/add-2002-bj shortw/projective/dbl-2015-rcb 1716 1784 0 68\n",
-      "set()\n",
-      "shortw/projective/add-2002-bj shortw/projective/dbl-1998-cmo-2 462 518 0 56\n",
-      "set()\n",
-      "shortw/projective/add-1998-cmo shortw/projective/dbl-2007-bl 400 440 -30 70\n",
-      "{(Point([[x=3506583871477322073, y=6741142221818933028]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=6266750213032352783, y=2572643933633910467]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=10266451081742949860, y=6375395324081956250]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 6), (Point([[x=6266750213032352783, y=8359538538250281626]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=518029702578685213]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=11860202707452705321, y=2052542901066170704]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 2), (Point([[x=9819149482471069087, y=5440687058305090757]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=4173724707785958223, y=4699325755562909213]] in shortw/affine), DomainParameters(EllipticCurve([a=3625103617301682823, b=4388462454794354946] on ShortWeierstrass using shortw/projective), Point([[X=3776323442245452173, Y=3498331799874979092, Z=1]] in shortw/projective), 11276575961681749769, 1), 2), (Point([[x=9819149482471069087, y=5491495413579101336]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=10431270994884570551, y=3130627042319158740]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=7585529656491369468, y=4693648949403847510]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=5135606693713390464, y=10464898676446924539]] in shortw/affine), DomainParameters(EllipticCurve([a=2601366152990292210, b=16667361733373129443] on ShortWeierstrass using shortw/projective), Point([[X=4281839768736361216, Y=3013285706496074176, Z=1]] in shortw/projective), 16958157002496852713, 1), 6), (Point([[x=11104973634291672093, y=6542585482520847060]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=5135606693713390464, y=6493258320292274272]] in shortw/affine), DomainParameters(EllipticCurve([a=2601366152990292210, b=16667361733373129443] on ShortWeierstrass using shortw/projective), Point([[X=4281839768736361216, Y=3013285706496074176, Z=1]] in shortw/projective), 16958157002496852713, 1), 6), (Point([[x=10266451081742949860, y=5454457432444346201]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 6), (Point([[x=10312946530826786949, y=6471666721643547004]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=1138105631230065649, y=10185298079248308414]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10312946530826786949, y=6339122982089723353]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5897106082088403986]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=2579783466931099474, y=2102965590089588720]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=11860202707452705321, y=10758246802667099653]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 2), (Point([[x=2579783466931099474, y=8829216881794603373]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=4173724707785958223, y=6577250203972113290]] in shortw/affine), DomainParameters(EllipticCurve([a=3625103617301682823, b=4388462454794354946] on ShortWeierstrass using shortw/projective), Point([[X=3776323442245452173, Y=3498331799874979092, Z=1]] in shortw/projective), 11276575961681749769, 1), 2), (Point([[x=3506583871477322073, y=8570746661364218185]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=1138105631230065649, y=1644554677277994037]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10431270994884570551, y=13734681669605378263]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=7585529656491369468, y=6238533522480344583]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=11104973634291672093, y=6268204221212423297]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5035076389795788107]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=16347279009345851790]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2)}\n",
-      "shortw/projective/add-1998-cmo shortw/projective/dbl-1998-cmo 400 440 -30 70\n",
-      "{(Point([[x=3506583871477322073, y=6741142221818933028]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=6266750213032352783, y=2572643933633910467]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=10266451081742949860, y=6375395324081956250]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 6), (Point([[x=6266750213032352783, y=8359538538250281626]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=518029702578685213]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=11860202707452705321, y=2052542901066170704]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 2), (Point([[x=9819149482471069087, y=5440687058305090757]] in shortw/affine), 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Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=1138105631230065649, y=10185298079248308414]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10312946530826786949, y=6339122982089723353]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5897106082088403986]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=2579783466931099474, y=2102965590089588720]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=11860202707452705321, y=10758246802667099653]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 2), (Point([[x=2579783466931099474, y=8829216881794603373]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=4173724707785958223, y=6577250203972113290]] in shortw/affine), DomainParameters(EllipticCurve([a=3625103617301682823, b=4388462454794354946] on ShortWeierstrass using shortw/projective), Point([[X=3776323442245452173, Y=3498331799874979092, Z=1]] in shortw/projective), 11276575961681749769, 1), 2), (Point([[x=3506583871477322073, y=8570746661364218185]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=1138105631230065649, y=1644554677277994037]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10431270994884570551, y=13734681669605378263]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=7585529656491369468, y=6238533522480344583]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=11104973634291672093, y=6268204221212423297]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5035076389795788107]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=16347279009345851790]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2)}\n",
-      "shortw/projective/add-1998-cmo shortw/projective/dbl-2015-rcb 1654 1712 -30 88\n",
-      "{(Point([[x=3506583871477322073, y=6741142221818933028]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=10266451081742949860, y=6375395324081956250]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 6), (Point([[x=6266750213032352783, y=2572643933633910467]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=6266750213032352783, y=8359538538250281626]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=518029702578685213]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=11860202707452705321, y=2052542901066170704]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 2), (Point([[x=9819149482471069087, y=5440687058305090757]] in shortw/affine), 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b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=7585529656491369468, y=4693648949403847510]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=5135606693713390464, y=10464898676446924539]] in shortw/affine), DomainParameters(EllipticCurve([a=2601366152990292210, b=16667361733373129443] on ShortWeierstrass using shortw/projective), Point([[X=4281839768736361216, Y=3013285706496074176, Z=1]] in shortw/projective), 16958157002496852713, 1), 6), (Point([[x=11104973634291672093, y=6542585482520847060]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using 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Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=1138105631230065649, y=10185298079248308414]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10312946530826786949, y=6339122982089723353]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5897106082088403986]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=2579783466931099474, y=2102965590089588720]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=11860202707452705321, y=10758246802667099653]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 2), (Point([[x=4173724707785958223, y=6577250203972113290]] in shortw/affine), DomainParameters(EllipticCurve([a=3625103617301682823, b=4388462454794354946] on ShortWeierstrass using shortw/projective), Point([[X=3776323442245452173, Y=3498331799874979092, Z=1]] in shortw/projective), 11276575961681749769, 1), 2), (Point([[x=2579783466931099474, y=8829216881794603373]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=3506583871477322073, y=8570746661364218185]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=1138105631230065649, y=1644554677277994037]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10431270994884570551, y=13734681669605378263]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=7585529656491369468, y=6238533522480344583]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=11104973634291672093, y=6268204221212423297]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5035076389795788107]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=16347279009345851790]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2)}\n",
-      "shortw/projective/add-1998-cmo shortw/projective/dbl-1998-cmo-2 400 440 -30 70\n",
-      "{(Point([[x=3506583871477322073, y=6741142221818933028]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=6266750213032352783, y=2572643933633910467]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=10266451081742949860, y=6375395324081956250]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 6), (Point([[x=6266750213032352783, y=8359538538250281626]] 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y=6577250203972113290]] in shortw/affine), DomainParameters(EllipticCurve([a=3625103617301682823, b=4388462454794354946] on ShortWeierstrass using shortw/projective), Point([[X=3776323442245452173, Y=3498331799874979092, Z=1]] in shortw/projective), 11276575961681749769, 1), 2), (Point([[x=3506583871477322073, y=8570746661364218185]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=1138105631230065649, y=1644554677277994037]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10431270994884570551, y=13734681669605378263]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=7585529656491369468, y=6238533522480344583]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=11104973634291672093, y=6268204221212423297]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5035076389795788107]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=16347279009345851790]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2)}\n",
-      "shortw/projective/add-1998-cmo-2 shortw/projective/dbl-2007-bl 400 440 -30 70\n",
-      "{(Point([[x=3506583871477322073, y=6741142221818933028]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=6266750213032352783, y=2572643933633910467]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=10266451081742949860, y=6375395324081956250]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 6), (Point([[x=6266750213032352783, y=8359538538250281626]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=518029702578685213]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=11860202707452705321, y=2052542901066170704]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 2), (Point([[x=9819149482471069087, y=5440687058305090757]] in shortw/affine), 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Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=1138105631230065649, y=10185298079248308414]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10312946530826786949, y=6339122982089723353]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5897106082088403986]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 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y=6577250203972113290]] in shortw/affine), DomainParameters(EllipticCurve([a=3625103617301682823, b=4388462454794354946] on ShortWeierstrass using shortw/projective), Point([[X=3776323442245452173, Y=3498331799874979092, Z=1]] in shortw/projective), 11276575961681749769, 1), 2), (Point([[x=3506583871477322073, y=8570746661364218185]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=1138105631230065649, y=1644554677277994037]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10431270994884570551, y=13734681669605378263]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=7585529656491369468, y=6238533522480344583]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=11104973634291672093, y=6268204221212423297]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5035076389795788107]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=16347279009345851790]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2)}\n",
-      "shortw/projective/add-1998-cmo-2 shortw/projective/dbl-1998-cmo 400 440 -30 70\n",
-      "{(Point([[x=3506583871477322073, y=6741142221818933028]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=6266750213032352783, y=2572643933633910467]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=10266451081742949860, y=6375395324081956250]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 6), (Point([[x=6266750213032352783, y=8359538538250281626]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=518029702578685213]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=11860202707452705321, y=2052542901066170704]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 2), (Point([[x=9819149482471069087, y=5440687058305090757]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=4173724707785958223, y=4699325755562909213]] in shortw/affine), DomainParameters(EllipticCurve([a=3625103617301682823, b=4388462454794354946] on ShortWeierstrass using shortw/projective), Point([[X=3776323442245452173, Y=3498331799874979092, Z=1]] in shortw/projective), 11276575961681749769, 1), 2), (Point([[x=9819149482471069087, y=5491495413579101336]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=10431270994884570551, y=3130627042319158740]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=7585529656491369468, y=4693648949403847510]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=5135606693713390464, y=10464898676446924539]] in shortw/affine), DomainParameters(EllipticCurve([a=2601366152990292210, b=16667361733373129443] on ShortWeierstrass using shortw/projective), Point([[X=4281839768736361216, Y=3013285706496074176, Z=1]] in shortw/projective), 16958157002496852713, 1), 6), (Point([[x=11104973634291672093, y=6542585482520847060]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=5135606693713390464, y=6493258320292274272]] in shortw/affine), DomainParameters(EllipticCurve([a=2601366152990292210, b=16667361733373129443] on ShortWeierstrass using shortw/projective), Point([[X=4281839768736361216, Y=3013285706496074176, Z=1]] in shortw/projective), 16958157002496852713, 1), 6), (Point([[x=10266451081742949860, y=5454457432444346201]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 6), (Point([[x=10312946530826786949, y=6471666721643547004]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=1138105631230065649, y=10185298079248308414]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10312946530826786949, y=6339122982089723353]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5897106082088403986]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=2579783466931099474, y=2102965590089588720]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=11860202707452705321, y=10758246802667099653]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 2), (Point([[x=2579783466931099474, y=8829216881794603373]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=4173724707785958223, y=6577250203972113290]] in shortw/affine), DomainParameters(EllipticCurve([a=3625103617301682823, b=4388462454794354946] on ShortWeierstrass using shortw/projective), Point([[X=3776323442245452173, Y=3498331799874979092, Z=1]] in shortw/projective), 11276575961681749769, 1), 2), (Point([[x=3506583871477322073, y=8570746661364218185]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=1138105631230065649, y=1644554677277994037]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10431270994884570551, y=13734681669605378263]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=7585529656491369468, y=6238533522480344583]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=11104973634291672093, y=6268204221212423297]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5035076389795788107]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=16347279009345851790]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2)}\n",
-      "shortw/projective/add-1998-cmo-2 shortw/projective/dbl-2015-rcb 1654 1712 -30 88\n",
-      "{(Point([[x=3506583871477322073, y=6741142221818933028]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=10266451081742949860, y=6375395324081956250]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 6), (Point([[x=6266750213032352783, y=2572643933633910467]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=6266750213032352783, y=8359538538250281626]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=518029702578685213]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=11860202707452705321, y=2052542901066170704]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 2), (Point([[x=9819149482471069087, y=5440687058305090757]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=4173724707785958223, y=4699325755562909213]] in shortw/affine), DomainParameters(EllipticCurve([a=3625103617301682823, b=4388462454794354946] on ShortWeierstrass using shortw/projective), Point([[X=3776323442245452173, Y=3498331799874979092, Z=1]] in shortw/projective), 11276575961681749769, 1), 2), (Point([[x=9819149482471069087, y=5491495413579101336]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=10431270994884570551, y=3130627042319158740]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=7585529656491369468, y=4693648949403847510]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=5135606693713390464, y=10464898676446924539]] in shortw/affine), DomainParameters(EllipticCurve([a=2601366152990292210, b=16667361733373129443] on ShortWeierstrass using shortw/projective), Point([[X=4281839768736361216, Y=3013285706496074176, Z=1]] in shortw/projective), 16958157002496852713, 1), 6), (Point([[x=11104973634291672093, y=6542585482520847060]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using 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Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=1138105631230065649, y=10185298079248308414]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10312946530826786949, y=6339122982089723353]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5897106082088403986]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=2579783466931099474, y=2102965590089588720]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=11860202707452705321, y=10758246802667099653]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 2), (Point([[x=4173724707785958223, y=6577250203972113290]] in shortw/affine), DomainParameters(EllipticCurve([a=3625103617301682823, b=4388462454794354946] on ShortWeierstrass using shortw/projective), Point([[X=3776323442245452173, Y=3498331799874979092, Z=1]] in shortw/projective), 11276575961681749769, 1), 2), (Point([[x=2579783466931099474, y=8829216881794603373]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=3506583871477322073, y=8570746661364218185]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=1138105631230065649, y=1644554677277994037]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10431270994884570551, y=13734681669605378263]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=7585529656491369468, y=6238533522480344583]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=11104973634291672093, y=6268204221212423297]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5035076389795788107]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=16347279009345851790]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2)}\n",
-      "shortw/projective/add-1998-cmo-2 shortw/projective/dbl-1998-cmo-2 400 440 -30 70\n",
-      "{(Point([[x=3506583871477322073, y=6741142221818933028]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=6266750213032352783, y=2572643933633910467]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=10266451081742949860, y=6375395324081956250]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 6), (Point([[x=6266750213032352783, y=8359538538250281626]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=518029702578685213]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=11860202707452705321, y=2052542901066170704]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 2), (Point([[x=9819149482471069087, y=5440687058305090757]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=4173724707785958223, y=4699325755562909213]] in shortw/affine), DomainParameters(EllipticCurve([a=3625103617301682823, b=4388462454794354946] on ShortWeierstrass using shortw/projective), Point([[X=3776323442245452173, Y=3498331799874979092, Z=1]] in shortw/projective), 11276575961681749769, 1), 2), (Point([[x=9819149482471069087, y=5491495413579101336]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=10431270994884570551, y=3130627042319158740]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=7585529656491369468, y=4693648949403847510]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=5135606693713390464, y=10464898676446924539]] in shortw/affine), DomainParameters(EllipticCurve([a=2601366152990292210, b=16667361733373129443] on ShortWeierstrass using shortw/projective), Point([[X=4281839768736361216, Y=3013285706496074176, Z=1]] in shortw/projective), 16958157002496852713, 1), 6), (Point([[x=11104973634291672093, y=6542585482520847060]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=5135606693713390464, y=6493258320292274272]] in shortw/affine), DomainParameters(EllipticCurve([a=2601366152990292210, b=16667361733373129443] on ShortWeierstrass using shortw/projective), Point([[X=4281839768736361216, Y=3013285706496074176, Z=1]] in shortw/projective), 16958157002496852713, 1), 6), (Point([[x=10266451081742949860, y=5454457432444346201]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 6), (Point([[x=10312946530826786949, y=6471666721643547004]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=1138105631230065649, y=10185298079248308414]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10312946530826786949, y=6339122982089723353]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5897106082088403986]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=2579783466931099474, y=2102965590089588720]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=11860202707452705321, y=10758246802667099653]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 2), (Point([[x=2579783466931099474, y=8829216881794603373]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=4173724707785958223, y=6577250203972113290]] in shortw/affine), DomainParameters(EllipticCurve([a=3625103617301682823, b=4388462454794354946] on ShortWeierstrass using shortw/projective), Point([[X=3776323442245452173, Y=3498331799874979092, Z=1]] in shortw/projective), 11276575961681749769, 1), 2), (Point([[x=3506583871477322073, y=8570746661364218185]] in shortw/affine), DomainParameters(EllipticCurve([a=14990863445573266178, b=5006414456395872472] on ShortWeierstrass using shortw/projective), Point([[X=4750105424415673627, Y=4425109830522506764, Z=1]] in shortw/projective), 15311888886630415727, 1), 6), (Point([[x=1138105631230065649, y=1644554677277994037]] in shortw/affine), DomainParameters(EllipticCurve([a=6183569009851969325, b=762106933559736021] on ShortWeierstrass using shortw/projective), Point([[X=9670240073134457762, Y=8886575037425480089, Z=1]] in shortw/projective), 11829852760562783143, 1), 2), (Point([[x=10431270994884570551, y=13734681669605378263]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2), (Point([[x=7585529656491369468, y=6238533522480344583]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 6), (Point([[x=11104973634291672093, y=6268204221212423297]] in shortw/affine), DomainParameters(EllipticCurve([a=8778587627516611817, b=9445930250569380907] on ShortWeierstrass using shortw/projective), Point([[X=10018863479180836837, Y=3821536539749098925, Z=1]] in shortw/projective), 12810789706563865157, 1), 6), (Point([[x=6317967938476284435, y=5035076389795788107]] in shortw/affine), DomainParameters(EllipticCurve([a=6127782631951813907, b=5171791703060456988] on ShortWeierstrass using shortw/projective), Point([[X=2190614060104834009, Y=407219013830067215, Z=1]] in shortw/projective), 10932182471093495659, 1), 2), (Point([[x=5063489076477151910, y=16347279009345851790]] in shortw/affine), DomainParameters(EllipticCurve([a=14681705106012859794, b=6296839833753850232] on ShortWeierstrass using shortw/projective), Point([[X=16706845951792451867, Y=6264042703439027859, Z=1]] in shortw/projective), 16865308710771279959, 1), 2)}\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "for pair in point_map.keys():\n",
-    "    print(pair[0], pair[1],\n",
-    "          len(point_map[pair]),\n",
-    "          len(remapped_point_map[pair]),\n",
-    "          -len(point_map[pair].difference(remapped_point_map[pair])),\n",
-    "          len(remapped_point_map[pair].difference(point_map[pair])))\n",
-    "    print(point_map[pair].difference(remapped_point_map[pair]))"
+    "for filter_nonhomo in (True, False):\n",
+    "    for affine in (True, False):\n",
+    "        print(f\"-------------- filter_nonhomo={filter_nonhomo} affine={affine} --------------\")\n",
+    "        fset_map = {dbl: compute_factor_set(dbl, filter_nonhomo=filter_nonhomo, affine=affine) for dbl in dbls}\n",
+    "        fset_tree = build_distinguishing_tree(fset_map)\n",
+    "        print(RenderTree(fset_tree).by_attr(lambda n: n.name if n.name is not None else n.cfgs))"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b0181494-ca94-46cc-8572-c142eaf0abdb",
+   "id": "42b5f4cc-c327-4f6c-9d41-357593ef1799",
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "def simulated_oracle(scalar, affine_point, real_coord_name=\"projective\", real_add_name=\"add-2007-bl\", real_dbl_name=\"dbl-2007-bl\"):\n",
+    "    real_coords = model.coordinates[real_coord_name]\n",
+    "    real_add = real_coords.formulas[real_add_name]\n",
+    "    real_dbl = real_coords.formulas[real_dbl_name]\n",
+    "    real_mult = LTRMultiplier(real_add, real_dbl, None, False, AccumulationOrder.PeqRP, True, True)\n",
+    "    point = affine_point.to_model(params.curve.coordinate_model, params.curve)\n",
+    "    with local(DefaultContext()) as ctx:\n",
+    "        real_mult.init(params, point)\n",
+    "        real_mult.multiply(scalar)\n",
+    "\n",
+    "    result = {\"result\": False}\n",
+    "\n",
+    "    def callback(action):\n",
+    "        if isinstance(action, FormulaAction):\n",
+    "            for intermediate in action.op_results:\n",
+    "                if int(value) == 0:\n",
+    "                    result[\"result\"] = True\n",
+    "                trace.append(intermediate.value)\n",
+    "    ctx.actions.walk(callback)\n",
+    "    return result[\"result\"]"
+   ]
   }
  ],
  "metadata": {