Add ZVP notebook.

1 files changed, 243 insertions, 0 deletions

diff --git a/re/zvp.ipynb b/re/zvp.ipynb
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "3ff024c8-7e90-4094-ab07-a051a601d9cd",
+   "metadata": {},
+   "source": [
+    "# ZVP-based reverse-engineering"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "17a9e580-5f1e-45c9-8afd-fc35e833b0b0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import sympy\n",
+    "from sympy import FF, sympify, symbols\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\n",
+    "from pyecsca.ec.point import Point\n",
+    "from pyecsca.ec.mod import Mod, SymbolicMod\n",
+    "from pyecsca.ec.context import DefaultContext, local\n",
+    "from pyecsca.misc.cfg import getconfig"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "d8ea0c4d-86e1-46af-ac20-569e6ef5439d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cfg = getconfig()\n",
+    "cfg.ec.mod_implementation = \"python\""
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "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",
+    "\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",
+    "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)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "e91d81b6-a3ce-4b1f-8ace-3e55e0d6fadf",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# add\n",
+    "# TODO: this is wrooooong, needs to have X1 and X2...\n",
+    "P1 = Point(coords, **{str(var): SymbolicMod(symbols(var + \"1\"), p) for var in coords.variables})\n",
+    "P2 = Point(coords, **{str(var): SymbolicMod(symbols(var + \"2\"), p) for var in coords.variables})\n",
+    "parameters = {str(var): SymbolicMod(var, p) for var in symbols(model.parameter_names)}\n",
+    "with local(DefaultContext()) as ctx:\n",
+    "    res = add(p, P1, P2, **parameters)[0]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "7f4c7416-49a9-4fe5-a1ff-38f2cb6c5815",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle 2 Z_{1} Z_{2} \\left(Y_{1} Z_{2} + Y_{2} Z_{1}\\right) \\left(Z_{1}^{2} Z_{2}^{2} \\left(Y_{1} Z_{2} + Y_{2} Z_{1}\\right)^{4} + \\left(X_{1} Z_{2} + X_{2} Z_{1}\\right)^{2} - \\left(X_{1} Z_{2} + X_{2} Z_{1} + Z_{1} Z_{2} \\left(Y_{1} Z_{2} + Y_{2} Z_{1}\\right)^{2}\\right)^{2} + 2 \\left(- X_{1} X_{2} Z_{1} Z_{2} + Z_{1}^{2} Z_{2}^{2} a + \\left(X_{1} Z_{2} + X_{2} Z_{1}\\right)^{2}\\right)^{2}\\right)$"
+      ],
+      "text/plain": [
+       "2*Z1*Z2*(Y1*Z2 + Y2*Z1)*(Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4 + (X1*Z2 + X2*Z1)**2 - (X1*Z2 + X2*Z1 + Z1*Z2*(Y1*Z2 + Y2*Z1)**2)**2 + 2*(-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)**2)"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "res.X.x"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "89a34db8-81d2-4741-ae0a-5268b46d0974",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle - 2 Z_{1}^{2} Z_{2}^{2} \\left(Y_{1} Z_{2} + Y_{2} Z_{1}\\right)^{4} + \\left(- X_{1} X_{2} Z_{1} Z_{2} + Z_{1}^{2} Z_{2}^{2} a + \\left(X_{1} Z_{2} + X_{2} Z_{1}\\right)^{2}\\right) \\left(- 3 Z_{1}^{2} Z_{2}^{2} \\left(Y_{1} Z_{2} + Y_{2} Z_{1}\\right)^{4} - 3 \\left(X_{1} Z_{2} + X_{2} Z_{1}\\right)^{2} + 3 \\left(X_{1} Z_{2} + X_{2} Z_{1} + Z_{1} Z_{2} \\left(Y_{1} Z_{2} + Y_{2} Z_{1}\\right)^{2}\\right)^{2} - 4 \\left(- X_{1} X_{2} Z_{1} Z_{2} + Z_{1}^{2} Z_{2}^{2} a + \\left(X_{1} Z_{2} + X_{2} Z_{1}\\right)^{2}\\right)^{2}\\right)$"
+      ],
+      "text/plain": [
+       "-2*Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4 + (-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)*(-3*Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4 - 3*(X1*Z2 + X2*Z1)**2 + 3*(X1*Z2 + X2*Z1 + Z1*Z2*(Y1*Z2 + Y2*Z1)**2)**2 - 4*(-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)**2)"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "res.Y.x"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "8d3db4ac-95fb-4483-a572-265744461daf",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle 4 Z_{1}^{3} Z_{2}^{3} \\left(Y_{1} Z_{2} + Y_{2} Z_{1}\\right)^{3}$"
+      ],
+      "text/plain": [
+       "4*Z1**3*Z2**3*(Y1*Z2 + Y2*Z1)**3"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "res.Z.x"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "645ca07a-8d47-446d-93ca-eab4de26dfff",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "U1 = X1*Z2 \t X1*Z2\n",
+      "U2 = X2*Z1 \t X2*Z1\n",
+      "S1 = Y1*Z2 \t Y1*Z2\n",
+      "S2 = Y2*Z1 \t Y2*Z1\n",
+      "ZZ = Z1*Z2 \t Z1*Z2\n",
+      "T = U1+U2 \t X1*Z2 + X2*Z1\n",
+      "TT = T \t (X1*Z2 + X2*Z1)**2\n",
+      "M = S1+S2 \t Y1*Z2 + Y2*Z1\n",
+      "t0 = ZZ \t Z1**2*Z2**2\n",
+      "t1 = a*t0 \t Z1**2*Z2**2*a\n",
+      "t2 = U1*U2 \t X1*X2*Z1*Z2\n",
+      "t3 = TT-t2 \t -X1*X2*Z1*Z2 + (X1*Z2 + X2*Z1)**2\n",
+      "R = t3+t1 \t -X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2\n",
+      "F = ZZ*M \t Z1*Z2*(Y1*Z2 + Y2*Z1)\n",
+      "L = M*F \t Z1*Z2*(Y1*Z2 + Y2*Z1)**2\n",
+      "LL = L \t Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4\n",
+      "t4 = T+L \t X1*Z2 + X2*Z1 + Z1*Z2*(Y1*Z2 + Y2*Z1)**2\n",
+      "t5 = t4 \t (X1*Z2 + X2*Z1 + Z1*Z2*(Y1*Z2 + Y2*Z1)**2)**2\n",
+      "t6 = t5-TT \t -(X1*Z2 + X2*Z1)**2 + (X1*Z2 + X2*Z1 + Z1*Z2*(Y1*Z2 + Y2*Z1)**2)**2\n",
+      "G = t6-LL \t -Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4 - (X1*Z2 + X2*Z1)**2 + (X1*Z2 + X2*Z1 + Z1*Z2*(Y1*Z2 + Y2*Z1)**2)**2\n",
+      "t7 = R \t (-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)**2\n",
+      "t8 = 2*t7 \t 2*(-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)**2\n",
+      "W = t8-G \t Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4 + (X1*Z2 + X2*Z1)**2 - (X1*Z2 + X2*Z1 + Z1*Z2*(Y1*Z2 + Y2*Z1)**2)**2 + 2*(-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)**2\n",
+      "t9 = F*W \t Z1*Z2*(Y1*Z2 + Y2*Z1)*(Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4 + (X1*Z2 + X2*Z1)**2 - (X1*Z2 + X2*Z1 + Z1*Z2*(Y1*Z2 + Y2*Z1)**2)**2 + 2*(-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)**2)\n",
+      "X3 = 2*t9 \t 2*Z1*Z2*(Y1*Z2 + Y2*Z1)*(Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4 + (X1*Z2 + X2*Z1)**2 - (X1*Z2 + X2*Z1 + Z1*Z2*(Y1*Z2 + Y2*Z1)**2)**2 + 2*(-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)**2)\n",
+      "t10 = 2*W \t 2*Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4 + 2*(X1*Z2 + X2*Z1)**2 - 2*(X1*Z2 + X2*Z1 + Z1*Z2*(Y1*Z2 + Y2*Z1)**2)**2 + 4*(-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)**2\n",
+      "t11 = G-t10 \t -3*Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4 - 3*(X1*Z2 + X2*Z1)**2 + 3*(X1*Z2 + X2*Z1 + Z1*Z2*(Y1*Z2 + Y2*Z1)**2)**2 - 4*(-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)**2\n",
+      "t12 = 2*LL \t 2*Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4\n",
+      "t13 = R*t11 \t (-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)*(-3*Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4 - 3*(X1*Z2 + X2*Z1)**2 + 3*(X1*Z2 + X2*Z1 + Z1*Z2*(Y1*Z2 + Y2*Z1)**2)**2 - 4*(-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)**2)\n",
+      "Y3 = t13-t12 \t -2*Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4 + (-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)*(-3*Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**4 - 3*(X1*Z2 + X2*Z1)**2 + 3*(X1*Z2 + X2*Z1 + Z1*Z2*(Y1*Z2 + Y2*Z1)**2)**2 - 4*(-X1*X2*Z1*Z2 + Z1**2*Z2**2*a + (X1*Z2 + X2*Z1)**2)**2)\n",
+      "t14 = F \t Z1**2*Z2**2*(Y1*Z2 + Y2*Z1)**2\n",
+      "t15 = F*t14 \t Z1**3*Z2**3*(Y1*Z2 + Y2*Z1)**3\n",
+      "Z3 = 4*t15 \t 4*Z1**3*Z2**3*(Y1*Z2 + Y2*Z1)**3\n"
+     ]
+    }
+   ],
+   "source": [
+    "for op_result in ctx.actions.get_by_index([0])[0].op_results:\n",
+    "    print(repr(op_result), \"\\t\", op_result.value.x)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "08e17876-331a-445a-8fbc-1990a0b5f69d",
+   "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
+}