1 files changed, 50 insertions, 6 deletions

diff --git a/analysis/countermeasures/simulation.ipynb b/analysis/countermeasures/simulation.ipynb
index ef64493..5d3affc 100644
--- a/analysis/countermeasures/simulation.ipynb
+++ b/analysis/countermeasures/simulation.ipynb
@@ -5,12 +5,19 @@
    "id": "bafc2f4e-05a3-4120-bcd6-5d1f5fb91cd9",
    "metadata": {},
    "source": [
-    "# Distinguishing countermeasures by output"
+    "# Distinguishing countermeasures by output\n",
+    "\n",
+    "This notebook contains simulations of scalar randomization countermeasures acting under the five tests:\n",
+    " - [The 3n test](#3n-test)\n",
+    " - [The $n + \\epsilon$ test](#Mask-recovery-(n+ϵ-test)) including mask recovery\n",
+    " - [The $k = 10$ test](#k=10-test)\n",
+    " - [The composite test](#Composite-test)\n",
+    " - [The EPA test](#EPA-test)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 97,
    "id": "33ee6084-2ac3-4f95-9610-0fbc06026538",
    "metadata": {},
    "outputs": [],
@@ -42,6 +49,14 @@
    ]
   },
   {
+   "cell_type": "markdown",
+   "id": "73e5efc6-b5ea-474f-9c71-8b54561d4ec1",
+   "metadata": {},
+   "source": [
+    "Let's first initialize some useful objects. We will be working with projective coordinates and the `add-2007-bl` and `dbl-2007-bl` formulas, though any formulas would work. However, one obtains different results if working with complete formulas."
+   ]
+  },
+  {
    "cell_type": "code",
    "execution_count": 3,
    "id": "b1b9596c-1eba-4ace-af84-8cb279d84cc2",
@@ -85,7 +100,9 @@
    "id": "27626337-dcbc-497c-a54e-02d50e2b8f34",
    "metadata": {},
    "source": [
-    "## 3n test"
+    "## 3n test\n",
+    "\n",
+    "In the 3n test the target is given domain parameters of order $3n$ but claimed order $n$. The target is then given a point of order $3n$ for scalar multiplication and the results are observed."
    ]
   },
   {
@@ -2324,7 +2341,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 103,
+   "execution_count": 93,
    "id": "7fdd24cc-7c52-4222-b473-79b09c0df810",
    "metadata": {},
    "outputs": [],
@@ -2342,7 +2359,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 104,
+   "execution_count": 94,
    "id": "9db677c5-34e3-4b5e-93dc-11b9b7e2cf3a",
    "metadata": {},
    "outputs": [
@@ -2377,7 +2394,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 120,
+   "execution_count": 95,
    "id": "db1e4115-d0cf-4558-93e5-d60781407548",
    "metadata": {},
    "outputs": [],
@@ -2702,6 +2719,33 @@
   },
   {
    "cell_type": "markdown",
+   "id": "843ce251-4454-4902-add5-262d5d3c02ed",
+   "metadata": {},
+   "source": [
+    "### Brumley and Tuveri bit-length fixing\n",
+    "Brumley and Tuveri has no issues computing over composite order curves."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 96,
+   "id": "7f9b4fd2-b85f-4fe8-916c-68c239140748",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0 errors, 0 wrong results\n"
+     ]
+    }
+   ],
+   "source": [
+    "test_composite(bt, 100)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
    "id": "38ce47d6-e9ee-47d9-bb0d-6a182261e422",
    "metadata": {},
    "source": [