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diff --git a/epare/countermeasures.ipynb b/epare/countermeasures.ipynb new file mode 100644 index 0000000..1ee3dea --- /dev/null +++ b/epare/countermeasures.ipynb @@ -0,0 +1,1131 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "bafc2f4e-05a3-4120-bcd6-5d1f5fb91cd9", + "metadata": {}, + "source": [ + "# Distinguishing countermeasures by output" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "33ee6084-2ac3-4f95-9610-0fbc06026538", + "metadata": {}, + "outputs": [], + "source": [ + "import io\n", + "import random\n", + "\n", + "from collections import Counter\n", + "from tqdm.auto import tqdm, trange\n", + "\n", + "from pyecsca.ec.mod import mod\n", + "from pyecsca.ec.point import Point\n", + "from pyecsca.ec.model import ShortWeierstrassModel\n", + "from pyecsca.ec.params import load_params_ectester\n", + "from pyecsca.ec.mult import LTRMultiplier\n", + "from pyecsca.ec.countermeasures import GroupScalarRandomization, AdditiveSplitting, MultiplicativeSplitting, EuclideanSplitting, BrumleyTuveri" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "b1b9596c-1eba-4ace-af84-8cb279d84cc2", + "metadata": {}, + "outputs": [], + "source": [ + "model = ShortWeierstrassModel()\n", + "coords = model.coordinates[\"projective\"]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "b0afb195-8390-44c5-931e-75a70ccd4e9e", + "metadata": {}, + "outputs": [], + "source": [ + "add = coords.formulas[\"add-2015-rcb\"]\n", + "dbl = coords.formulas[\"dbl-2015-rcb\"]\n", + "mult = LTRMultiplier(add, dbl, complete=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "52c877e1-5021-4ec2-9daa-dd20bec6bcb2", + "metadata": {}, + "outputs": [], + "source": [ + "gsr = GroupScalarRandomization(mult)\n", + "asplit = AdditiveSplitting(mult)\n", + "msplit = MultiplicativeSplitting(mult)\n", + "esplit = EuclideanSplitting(mult)\n", + "bt = BrumleyTuveri(mult)" + ] + }, + { + "cell_type": "markdown", + "id": "27626337-dcbc-497c-a54e-02d50e2b8f34", + "metadata": {}, + "source": [ + "## 3n test" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "c3088419-161b-4193-a1b6-6f623f217fcd", + "metadata": {}, + "outputs": [], + "source": [ + "key3n = 0x20959f2b437de1e522baf6d814911938157390d3ea5118660b852ab0d5387006\n", + "params3n = load_params_ectester(io.BytesIO(b\"0xc381bb0394f34b5ed061c9107b66974f4d0a8ec89b9fe73b98b6d1368c7d974d,0x5ca6c5ee0a10097af291a8f125303fb1a3e35e8100411902245d691e0e5cb497,0x385a5a8bb8af94721f6fd10b562606d9b9df931f7fd966e96859bb9bd7c05836,0x4616af1898b92cac0f902a9daee24bbae63571cead270467c6a7886ced421f5e,0x34e896bdb1337e0ae5960fa3389fb59c2c8d6c7dbfd9aac33a844f8f98e433ef,0x412b3e5686fbc3ca4575edb0292232702ae721a7d4a230cc170a5561aa70e00f,0x01\"), \"projective\")\n", + "bits3n = params3n.full_order.bit_length()\n", + "point3n = Point(X=mod(0x4a48addb2e471767b7cd0f6f1d4c27fe46f4a828fc20f950bd1f72c939b36a84, params3n.curve.prime),\n", + " Y=mod(0x13384d38c353f862832c0f067e46a3e510bb6803c20745dfb31929f4a18d890d, params3n.curve.prime),\n", + " Z=mod(1, params3n.curve.prime), model=coords)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "a8dde7e6-cd48-4f99-9677-23a19e4c2e5b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "prime:\t0xc381bb0394f34b5ed061c9107b66974f4d0a8ec89b9fe73b98b6d1368c7d974d\n", + "a:\t0x5ca6c5ee0a10097af291a8f125303fb1a3e35e8100411902245d691e0e5cb497\n", + "b:\t0x385a5a8bb8af94721f6fd10b562606d9b9df931f7fd966e96859bb9bd7c05836\n", + "G:\t[0x4616af1898b92cac0f902a9daee24bbae63571cead270467c6a7886ced421f5e,\n", + "\t 0x34e896bdb1337e0ae5960fa3389fb59c2c8d6c7dbfd9aac33a844f8f98e433ef]\n", + "n:\t0x412b3e5686fbc3ca4575edb0292232702ae721a7d4a230cc170a5561aa70e00f\n", + "3n:\t0xc381bb0394f34b5ed061c9107b66975080b564f77de69264451f0024ff52a02d\n", + "\n", + "P:\t[0x4a48addb2e471767b7cd0f6f1d4c27fe46f4a828fc20f950bd1f72c939b36a84,\n", + "\t 0x13384d38c353f862832c0f067e46a3e510bb6803c20745dfb31929f4a18d890d]\n" + ] + } + ], + "source": [ + "print(f\"prime:\\t0x{params3n.curve.prime:x}\")\n", + "print(f\"a:\\t0x{params3n.curve.parameters['a']:x}\")\n", + "print(f\"b:\\t0x{params3n.curve.parameters['b']:x}\")\n", + "print(f\"G:\\t[0x{params3n.generator.X:x},\\n\\t 0x{params3n.generator.Y:x}]\")\n", + "print(f\"n:\\t0x{params3n.order:x}\")\n", + "print(f\"3n:\\t0x{3 * params3n.order:x}\")\n", + "print(f\"\\nP:\\t[0x{point3n.X:x},\\n\\t 0x{point3n.Y:x}]\")" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "cd6f8500-7509-45b0-8b23-471ee5014f42", + "metadata": {}, + "outputs": [], + "source": [ + "def generate_scalars_mod3(rem, samples):\n", + " scalars = []\n", + " while True:\n", + " scalar = random.randint(0, params3n.full_order)\n", + " if scalar % 3 == rem:\n", + " scalars.append(scalar)\n", + " if len(scalars) == samples:\n", + " break\n", + " return scalars\n", + "\n", + "def test_3n(countermeasure, scalars):\n", + " ctr = Counter()\n", + " for k in tqdm(scalars, leave=False):\n", + " mult.init(params3n, point3n)\n", + " kP = mult.multiply(k).to_affine()\n", + " mult.init(params3n, point3n)\n", + " knP = mult.multiply(k + params3n.full_order).to_affine()\n", + " mult.init(params3n, point3n)\n", + " k2nP = mult.multiply(k + 2 * params3n.full_order).to_affine()\n", + "\n", + " countermeasure.init(params3n, point3n)\n", + " res = countermeasure.multiply(k)\n", + " aff = res.to_affine()\n", + " if aff.equals(kP):\n", + " ctr[\"k\"] += 1\n", + " elif aff.equals(knP):\n", + " ctr[\"k + 1n\"] += 1\n", + " elif aff.equals(k2nP):\n", + " ctr[\"k + 2n\"] += 1\n", + " else:\n", + " ctr[aff] += 1\n", + " for name, count in sorted(ctr.items()):\n", + " print(f\"{name}:\\t{count}\")\n", + "\n", + "def test_3n_fixed_scalar(countermeasure, samples):\n", + " test_3n(countermeasure, [key3n for _ in range(samples)])\n", + "\n", + "def test_3n_random_scalar(countermeasure, samples):\n", + " test_3n(countermeasure, [random.randint(0, params3n.full_order) for _ in range(samples)])\n", + "\n", + "def test_3n_random_scalar_projected(countermeasure, samples):\n", + " print(\"k = 0 mod 3\")\n", + " test_3n(countermeasure, generate_scalars_mod3(0, samples))\n", + " print()\n", + " print(\"k = 1 mod 3\")\n", + " test_3n(countermeasure, generate_scalars_mod3(1, samples))\n", + " print()\n", + " print(\"k = 2 mod 3\")\n", + " test_3n(countermeasure, generate_scalars_mod3(2, samples))" + ] + }, + { + "cell_type": "markdown", + "id": "46b8f74a-433d-48c9-b5b9-6bb7d2731246", + "metadata": {}, + "source": [ + "### Fixed scalar experiments" + ] + }, + { + "cell_type": "markdown", + "id": "fc82d4b9-91cd-423c-83aa-89721efa1ae9", + "metadata": {}, + "source": [ + "#### Group scalar randomization" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "86532d50-2db7-4370-b449-c545b330a852", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "a645f19f86484d3f8154c39c2b851de2", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t343\n", + "k + 1n:\t339\n", + "k + 2n:\t318\n" + ] + } + ], + "source": [ + "test_3n_fixed_scalar(gsr, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "aba3e713-6246-435d-93af-2e8b42ee9582", + "metadata": {}, + "source": [ + "#### Additive splitting" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "ad421630-606f-4666-9bbf-1a446eec1b59", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "1d3be2fca22c468c84b0c6fa179ba46c", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t520\n", + "k + 1n:\t480\n" + ] + } + ], + "source": [ + "test_3n_fixed_scalar(asplit, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "a1284a11-4ace-437d-9826-2035cce36756", + "metadata": {}, + "source": [ + "#### Multiplicative splitting" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "3ed5d7f3-0ba1-4b62-9635-aeb492499175", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "758e44f09b0448ba9cd2e69cf7a16691", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t219\n", + "k + 1n:\t554\n", + "k + 2n:\t227\n" + ] + } + ], + "source": [ + "test_3n_fixed_scalar(msplit, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "5e40f8e9-d26f-41e7-adbf-a0fbdb680677", + "metadata": {}, + "source": [ + "#### Euclidean splitting" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "314447c6-a1fb-4d3a-8988-b34c8912dd5e", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "3eec57b52cd647e7bfc37b577ac7b6b9", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t1000\n" + ] + } + ], + "source": [ + "test_3n_fixed_scalar(esplit, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "ff7185a2-3cd9-44d7-b1a9-982eaed561dc", + "metadata": {}, + "source": [ + "#### Brumley and Tuveri bit-length fixing" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "f41dfc1d-1017-4aa0-bcd4-6569c53bf81e", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "cdb7d64c69f64a62b4b1357f06db1481", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k + 2n:\t1000\n" + ] + } + ], + "source": [ + "test_3n_fixed_scalar(bt, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "28915553-b5e6-4108-bc23-e5844b6a63b8", + "metadata": {}, + "source": [ + "### Random scalar experiments" + ] + }, + { + "cell_type": "markdown", + "id": "566ddd10-2d0e-4b32-9b27-60770ab68155", + "metadata": {}, + "source": [ + "#### Group scalar randomization" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "7255321a-6ad6-4938-8ec9-dd8d977686db", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "828fecbd021a43b4a529e1261b4e5f5b", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t315\n", + "k + 1n:\t330\n", + "k + 2n:\t355\n" + ] + } + ], + "source": [ + "test_3n_random_scalar(gsr, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "376c0da8-b92d-4151-ac30-839ab5c0ceae", + "metadata": {}, + "source": [ + "#### Additive splitting" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "b0146a9a-0803-43c4-ab29-8ba6e15934b5", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "5d9adb2b79254271872bdfe5c38a3983", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t505\n", + "k + 1n:\t495\n" + ] + } + ], + "source": [ + "test_3n_random_scalar(asplit, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "96823352-cd63-4cf8-8ab7-cf6e025837b9", + "metadata": {}, + "source": [ + "#### Multiplicative splitting" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "5645ae6f-f5f4-419d-ba47-248532dc2114", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "e4073f552ae248269ab0785b701bd069", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t345\n", + "k + 1n:\t327\n", + "k + 2n:\t328\n" + ] + } + ], + "source": [ + "test_3n_random_scalar(msplit, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "1784d763-932a-4f66-a1da-d7ef51cbc88a", + "metadata": {}, + "source": [ + "#### Euclidean splitting" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "c9fc4f35-1c25-4cac-bb63-8bd70263db47", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "529938c684364319be7d8ba15f68d79c", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t1000\n" + ] + } + ], + "source": [ + "test_3n_random_scalar(esplit, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "8917dfd5-1548-414b-846a-685857bfb427", + "metadata": {}, + "source": [ + "#### Brumley and Tuveri bit-length fixing" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "4fd6b288-08a9-4dbe-9145-e96401805315", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "19bdafccd4f04b42ba188598567a1e8c", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k + 1n:\t35\n", + "k + 2n:\t965\n" + ] + } + ], + "source": [ + "test_3n_random_scalar(bt, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "ee9e23f6-edd9-4fc2-9e7c-b5c176991071", + "metadata": {}, + "source": [ + "### Random scalar experiments projected to scalar divisor classes mod 3" + ] + }, + { + "cell_type": "markdown", + "id": "e17fcb12-1e02-4bcf-a2b7-785c16c03028", + "metadata": {}, + "source": [ + "#### Group scalar randomization" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "6c46fdbb-2ffb-4169-8e00-6d93b8407ee5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k = 0 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "a65c045d5236432aba76108115266213", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t349\n", + "k + 1n:\t300\n", + "k + 2n:\t351\n", + "\n", + "k = 1 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "475dc945b4624296817e939a7e86ca14", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t358\n", + "k + 1n:\t329\n", + "k + 2n:\t313\n", + "\n", + "k = 2 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "a03a298fe08446b7849d02a2b7b217ca", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t310\n", + "k + 1n:\t324\n", + "k + 2n:\t366\n" + ] + } + ], + "source": [ + "test_3n_random_scalar_projected(gsr, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "b9d635c8-f788-4700-876b-ac48e89557a7", + "metadata": {}, + "source": [ + "#### Additive splitting" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "344a4f90-3470-40e9-a75f-b925a88c2480", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k = 0 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "5c77bfdf86864a76ab849f5379f44248", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t513\n", + "k + 1n:\t487\n", + "\n", + "k = 1 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "e98ab853babf4a3ba962d72e19b69dd3", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t484\n", + "k + 1n:\t516\n", + "\n", + "k = 2 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "6e6ebc6372ad45758f30937a6ac3c291", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t518\n", + "k + 1n:\t482\n" + ] + } + ], + "source": [ + "test_3n_random_scalar_projected(asplit, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "78aaf83f-a689-40ad-ae88-58ab20e5e6f9", + "metadata": {}, + "source": [ + "#### Multiplicative splitting" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "616a7726-01e6-4e9c-b7f2-fe8f14b60071", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k = 0 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "fcc70a8e56bc4e19baac2065827fe431", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t564\n", + "k + 1n:\t213\n", + "k + 2n:\t223\n", + "\n", + "k = 1 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "8401c46897fe47739342c17404fe0774", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t216\n", + "k + 1n:\t209\n", + "k + 2n:\t575\n", + "\n", + "k = 2 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "700a89093d19425d8b8a4d3418af215b", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t231\n", + "k + 1n:\t564\n", + "k + 2n:\t205\n" + ] + } + ], + "source": [ + "test_3n_random_scalar_projected(msplit, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "018c8f31-d7c3-497b-bdaf-580c6465753f", + "metadata": {}, + "source": [ + "#### Euclidean splitting" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "adced4e4-37a7-43ed-97b5-01cb5d274d6b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k = 0 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "c314c4a285634a6eaaabc93bbd7aa60f", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t1000\n", + "\n", + "k = 1 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "7134985a8cdf4d1f8cecce1bbfb31f9a", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t1000\n", + "\n", + "k = 2 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "45bc4b1be69c4d918f821e5c3cfde87f", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k:\t1000\n" + ] + } + ], + "source": [ + "test_3n_random_scalar_projected(esplit, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "8d7b0a42-7be7-464d-932d-8386ad912034", + "metadata": {}, + "source": [ + "#### Brumley and Tuveri bit-length fixing" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "fe8d8295-3e69-4b60-b8c3-5710deaeb0b3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k = 0 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "8a13b1ee1a9e448cbcfc95b94efa4254", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k + 1n:\t51\n", + "k + 2n:\t949\n", + "\n", + "k = 1 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "a7db0f83dcd54e92b9b7e3360e255aec", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k + 1n:\t39\n", + "k + 2n:\t961\n", + "\n", + "k = 2 mod 3\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "63a961fdb65e4223bde808fed8f4abbc", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00<?, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "k + 1n:\t37\n", + "k + 2n:\t963\n" + ] + } + ], + "source": [ + "test_3n_random_scalar_projected(bt, 1000)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b1b0bfd6-70f9-4822-b964-0c6ab097b498", + "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": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} |