Add non-working EPA notebook.

1 files changed, 162 insertions, 0 deletions

diff --git a/re/epa.ipynb b/re/epa.ipynb
new file mode 100644
index 0000000..2ed690b
--- /dev/null
+++ b/re/epa.ipynb
@@ -0,0 +1,162 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "18343664-ebec-4e95-88f2-0231082b6b6e",
+   "metadata": {},
+   "source": [
+    "# EPA-based reverse engineering"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "dac3b016-508b-4e63-897a-8ab46cb4f6ed",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from pyecsca.ec.model import ShortWeierstrassModel\n",
+    "from pyecsca.ec.curve import EllipticCurve\n",
+    "from pyecsca.ec.params import DomainParameters\n",
+    "from pyecsca.ec.mod import Mod, miller_rabin\n",
+    "from pyecsca.ec.point import Point\n",
+    "from pyecsca.ec.error import NonInvertibleError\n",
+    "from pyecsca.ec.mult import LTRMultiplier"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6e92cdd8-9040-4c6d-9700-f992d09195ee",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "model = ShortWeierstrassModel()\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",
+    "\n",
+    "p = 0xdb49063db56b7783fa01dd62077c5a88dfa28009  # such that phi(p)/p ~ 0.5\n",
+    "a = Mod(0xaee572fdd4790bcd4729bb3b612b52a573df46e9, p)\n",
+    "b = Mod(0xdab9e68366a593ca1df9cb2f20890a578729d6ef, p)\n",
+    "\n",
+    "n = 0x34a9fbe62b272f930b2e5027780a32300feb0dd8f\n",
+    "h = 1\n",
+    "gx = Mod(0xd4a3aaf43bdb25be7c308b69ae54f639e6e32e8c, p)\n",
+    "gy = Mod(0x7b6c82140bb427ac6e2a64507f60775949b2c8ce, p)\n",
+    "\n",
+    "g = Point(coords, X=gx, Y=gy, Z=Mod(1, p))\n",
+    "infty = Point(coords, X=Mod(0, p), Y=Mod(1, p), Z=Mod(0, p))\n",
+    "\n",
+    "curve = EllipticCurve(model, coords, p, infty, dict(a=a, b=b))\n",
+    "params = DomainParameters(curve, g, n, h)\n",
+    "print(miller_rabin(p))\n",
+    "print(curve.is_on_curve(g))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ffce5b71-3029-4219-a45a-1c8d78748fee",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "mult = LTRMultiplier(add, dbl, None, False, True, True)\n",
+    "mult.init(params, g)\n",
+    "non = 0\n",
+    "for _ in range(1000):\n",
+    "    scalar = int(Mod.random(n*5))\n",
+    "    \n",
+    "    res = mult.multiply(scalar)\n",
+    "    #print(res)\n",
+    "    try:\n",
+    "        res.Z.inverse()\n",
+    "        print(\"yay\", scalar, res)\n",
+    "        break\n",
+    "    except NonInvertibleError as e:\n",
+    "        non += 1\n",
+    "print(non)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7611348f-ac20-402f-8791-6f4eb6d681af",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "b.inverse()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4108fce0-28a9-4c28-a8d4-6051b86ce534",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "b"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ba9e5177-ca8f-488d-af4c-f3261e6563ef",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dbl(p, g, a=a, b=b)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9b42e209-5185-4121-b756-7f8c3374da5c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Mod(753921130225168876277183530034689476795287082245, p).inverse()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "dff4a049-2cad-40d8-9c49-98dcd9f93231",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "curve.affine_random()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4ebc3535-737f-4ed6-8df5-d0629795ce8f",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}