5 files changed, 1227 insertions, 49 deletions

diff --git a/analysis/scalarmults/README.md b/analysis/scalarmults/README.md
index d66b113..6dd71fc 100644
--- a/analysis/scalarmults/README.md
+++ b/analysis/scalarmults/README.md
@@ -1,2 +1,9 @@
 # Unravelling scalar multipliers
-![](unravelling.svg)
+
+## Simulation
+
+![](unravelling_simulate.svg)
+
+## Distinguishing
+
+![](unravelling_distinguish.svg)
diff --git a/analysis/scalarmults/distinguish.ipynb b/analysis/scalarmults/distinguish.ipynb
index 4165d87..3a77c4c 100644
--- a/analysis/scalarmults/distinguish.ipynb
+++ b/analysis/scalarmults/distinguish.ipynb
@@ -5,12 +5,16 @@
    "id": "e76983df-053b-450b-976c-295826248978",
    "metadata": {},
    "source": [
-    "# Unraveling scalar mults and countermeasures"
+    "# Unraveling scalar multiplications and countermeasures\n",
+    "\n",
+    "This notebook explores using error probability maps (as computed by the [simulate](simulate.ipynb) notebook). \n",
+    "\n",
+    "![](unravelling_distinguish.svg)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "id": "bc1528b8-61cd-4219-993f-e3f1ac79e801",
    "metadata": {},
    "outputs": [],
@@ -41,8 +45,17 @@
    ]
   },
   {
+   "cell_type": "markdown",
+   "id": "4868c083-8073-453d-b508-704fcb6d6f2a",
+   "metadata": {},
+   "source": [
+    "## Prepare\n",
+    "We need to silence some warnings."
+   ]
+  },
+  {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "id": "119b1e18-eeb0-4b70-bec3-ff277641403f",
    "metadata": {},
    "outputs": [],
@@ -58,17 +71,8 @@
    ]
   },
   {
-   "cell_type": "markdown",
-   "id": "4868c083-8073-453d-b508-704fcb6d6f2a",
-   "metadata": {},
-   "source": [
-    "## Prepare\n",
-    "Select *divisor name* to restrict the features. Select *kind* to pick the probmap source."
-   ]
-  },
-  {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "id": "ccb00342-3c48-49c9-bedf-2341e5eae3a2",
    "metadata": {},
    "outputs": [],
@@ -78,37 +82,92 @@
    ]
   },
   {
+   "cell_type": "markdown",
+   "id": "8a10e546-1d29-4145-b3e9-2d5724828ecb",
+   "metadata": {},
+   "source": [
+    "Now we can load the probmaps."
+   ]
+  },
+  {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "id": "3dbac9be-d098-479a-8ca2-f531f6668f7c",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "1e5c7654ba8c4e559d1e100a334a3331",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "  0%|          | 0/12480 [00:00<?, ?it/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
-    "# Load\n",
     "with open(f\"merged.pickle\", \"rb\") as f:\n",
     "    distributions_mults = pickle.load(f)\n",
-    "for probmap in tqdm(distributions_mults.values()):\n",
+    "for probmap in tqdm(distributions_mults.values(), desc=f\"Narrowing probmaps to {divisor_name}.\"):\n",
     "    probmap.narrow(allfeats)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 8,
    "id": "38c81e38-a37c-4e58-ac9e-927d14dad458",
    "metadata": {},
    "outputs": [],
    "source": [
     "allmults = list(distributions_mults.keys())\n",
+    "basemults = list(all_mults_with_ctr)\n",
+    "nbase = len(basemults)\n",
     "nmults = len(allmults)\n",
     "nallfeats = len(allfeats)"
    ]
   },
   {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "206b385a-bb98-47e7-9312-94a864794faa",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Have 12480 configurations (scalar multiplier x countermeasure x error model).\n",
+      "Have 390 base configurations (scalar multiplier x countermeasure).\n",
+      "Have 3215 base point orders (features).\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(f\"Have {nmults} configurations (scalar multiplier x countermeasure x error model).\")\n",
+    "print(f\"Have {nbase} base configurations (scalar multiplier x countermeasure).\")\n",
+    "print(f\"Have {nallfeats} base point orders (features).\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "437bcd9c-1da5-428a-a979-0835326777f3",
+   "metadata": {},
+   "source": [
+    "## Simulate distinguishing using a tree\n",
+    "We can follow the approach of the [**pyecsca**](https://pyecsca.org/papers.html#pyecsca-reverse-engineering-black-box-elliptic-curve-cryptography-via-side-channel-analysis) paper and use the probability maps to build a decision table (called dmap in code) and from that build a decision tree to use for reverse-engineering."
+   ]
+  },
+  {
    "cell_type": "markdown",
    "id": "1f783baf-bc81-40c1-9282-e2dfdacfd17c",
    "metadata": {},
    "source": [
-    "## Build dmap and tree"
+    "### Build dmap and tree"
    ]
   },
   {
@@ -196,7 +255,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "# deduplicate dmap\n",
+    "# deduplicate the dmap\n",
     "dmap.deduplicate()"
    ]
   },
@@ -213,6 +272,18 @@
   {
    "cell_type": "code",
    "execution_count": null,
+   "id": "5f261f61-fc41-494c-8465-18ecc8c9a525",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# save the dmap\n",
+    "with open(\"dmap.pickle\", \"wb\") as f:\n",
+    "    pickle.dump(dmap, f)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
    "id": "5735e7d4-149c-4184-96f7-dcfd6017fbad",
    "metadata": {},
    "outputs": [],
@@ -245,11 +316,22 @@
    ]
   },
   {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fb68df68-7976-4d46-9e50-94a65ae492c7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# save a tree\n",
+    "with open(\"tree.pickle\", \"wb\") as f:\n",
+    "    pickle.dump(tree, f)"
+   ]
+  },
+  {
    "cell_type": "markdown",
-   "id": "437bcd9c-1da5-428a-a979-0835326777f3",
+   "id": "b57fa09b-16de-43d5-bc25-c66849d0c18a",
    "metadata": {},
    "source": [
-    "## Simulate distinguishing using a tree\n",
     "We can now simulate distinguishing using the tree and how it behaves with increasing the number of samples per divisor collected."
    ]
   },
diff --git a/analysis/scalarmults/simulate.ipynb b/analysis/scalarmults/simulate.ipynb
index 3db4307..9177390 100644
--- a/analysis/scalarmults/simulate.ipynb
+++ b/analysis/scalarmults/simulate.ipynb
@@ -20,12 +20,12 @@
     "properties, i.e.: For random scalars, how probable is an error for a point of low order, for example, 5?\n",
     "\n",
     "Examine the figure below that shows the big picture.\n",
-    "![](unravelling.svg)"
+    "![](unravelling_simulate.svg)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "id": "b4386513-cc14-434b-a748-2863f8657452",
    "metadata": {},
    "outputs": [],
@@ -80,7 +80,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "id": "3463a7bd-34d8-458b-8ceb-dddf99de21dc",
    "metadata": {},
    "outputs": [],
@@ -97,21 +97,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": null,
    "id": "170c11fc-86cf-4eb1-bf4e-b2e44b2d7ac5",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Scalar multipliers considered:  65\n",
-      "Scalar multipliers (with a single countermeasure) considered:  390\n",
-      "Error models considered:  32\n",
-      "Total configurations considered:  12480\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "nmults = len(all_mults)\n",
     "nmults_ctr = len(all_mults_with_ctr)\n",
@@ -406,14 +395,13 @@
     "                                             evaluate_multiples_direct,\n",
     "                                             full, in_fname, start, divisor_map[\"all\"])\n",
     "                    gc.collect()\n",
-    "                    if len(pool.tasks) > 1000:\n",
-    "                        for full, future in pool.as_completed():\n",
-    "                            processing_bar.update(1)\n",
-    "                            if error := future.exception():\n",
-    "                                print(\"Error!\", full, error)\n",
-    "                                continue\n",
-    "                            res = future.result()\n",
-    "                            pickle.dump((full, res), h)\n",
+    "                    for full, future in pool.as_completed(wait=False):\n",
+    "                        processing_bar.update(1)\n",
+    "                        if error := future.exception():\n",
+    "                            print(\"Error!\", full, error)\n",
+    "                            continue\n",
+    "                        res = future.result()\n",
+    "                        pickle.dump((full, res), h)\n",
     "                except EOFError:\n",
     "                    break\n",
     "                except pickle.UnpicklingError:\n",
@@ -451,7 +439,7 @@
     "for in_fname in tqdm(glob.glob(f\"probs_{bits}_{'init' if use_init else 'noinit'}_{'mult' if use_multiply else 'nomult'}_chunk*.pickle\"), desc=\"Processing chunks\", smoothing=0):\n",
     "    \n",
     "    match = re.match(\"probs_(?P<bits>[0-9]+)_(?P<init>(?:no)?init)_(?P<mult>(?:no)?mult)_chunk(?P<id>[0-9a-f]+).pickle\", in_fname)\n",
-    "    chunk_id = match.group(\"id\")    \n",
+    "    chunk_id = match.group(\"id\")\n",
     "    \n",
     "    with open(in_fname, \"rb\") as f:\n",
     "        loading_bar = tqdm(total=ncfgs, desc=f\"Loading chunk {chunk_id}.\", smoothing=0)\n",
@@ -523,7 +511,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "daba5215-fef8-4c8a-8d7d-1af49edffa7b",
+   "id": "a07cf1d0-14d8-4c9b-a86c-6a7437d4e9dc",
    "metadata": {},
    "outputs": [],
    "source": []
diff --git a/analysis/scalarmults/unravelling_distinguish.svg b/analysis/scalarmults/unravelling_distinguish.svg
new file mode 100644
index 0000000..05cb77f
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@@ -0,0 +1,1101 @@
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diff --git a/analysis/scalarmults/unravelling.svg b/analysis/scalarmults/unravelling_simulate.svg
index f548719..f548719 100644
--- a/analysis/scalarmults/unravelling.svg
+++ b/analysis/scalarmults/unravelling_simulate.svg