diff --git a/docs/source/example_ecdsa.ipynb b/docs/source/example_ecdsa.ipynb
new file mode 100644
index 00000000..816aed11
--- /dev/null
+++ b/docs/source/example_ecdsa.ipynb
@@ -0,0 +1,92 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Private Key: 1\n",
+      "Public Key: 2\n",
+      "Message: 0\n",
+      "Signature: (2, 2)\n",
+      "Signature valid: True\n"
+     ]
+    }
+   ],
+   "source": [
+    "import random\n",
+    "\n",
+    "# Extremely simplified parameters\n",
+    "P = 3  # Prime field\n",
+    "G = 2  # Generator\n",
+    "N = 3  # Order of generator\n",
+    "\n",
+    "\n",
+    "def mod_inv(a, m):\n",
+    "    return 1 if a == 1 else 2  # Only valid for P = 3\n",
+    "\n",
+    "\n",
+    "def generate_keypair():\n",
+    "    private_key = random.randint(1, 3)  # 2-bit key (1 to 3)\n",
+    "    public_key = pow(G, private_key, P)\n",
+    "    return private_key, public_key\n",
+    "\n",
+    "\n",
+    "def sign(message, private_key):\n",
+    "    z = message % N\n",
+    "    k = random.randint(1, 3)  # 2-bit nonce\n",
+    "    r = pow(G, k, P)\n",
+    "    s = (mod_inv(k, N) * (z + r * private_key)) % N\n",
+    "    return (r, s)\n",
+    "\n",
+    "\n",
+    "def verify(message, signature, public_key):\n",
+    "    r, s = signature\n",
+    "    z = message % N\n",
+    "    w = mod_inv(s, N)\n",
+    "    u1 = (z * w) % N\n",
+    "    u2 = (r * w) % N\n",
+    "    v = (pow(G, u1, P) * pow(public_key, u2, P)) % P\n",
+    "    return v == r\n",
+    "\n",
+    "\n",
+    "# Example usage\n",
+    "private_key, public_key = generate_keypair()\n",
+    "message = int(\"0b0\", 2)  # Single character message\n",
+    "signature = sign(message, private_key)\n",
+    "is_valid = verify(message, signature, public_key)\n",
+    "\n",
+    "print(f\"Private Key: {private_key}\")\n",
+    "print(f\"Public Key: {public_key}\")\n",
+    "print(f\"Message: {message}\")\n",
+    "print(f\"Signature: {signature}\")\n",
+    "print(f\"Signature valid: {is_valid}\")"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "qlasskit_310-env",
+   "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": "3.10.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/qlasskit/compiler/internalcompiler.py b/qlasskit/compiler/internalcompiler.py
index 88a290ba..aa46d0da 100644
--- a/qlasskit/compiler/internalcompiler.py
+++ b/qlasskit/compiler/internalcompiler.py
@@ -12,6 +12,8 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+from copy import deepcopy
+
 from sympy import Symbol
 from sympy.logic import And, Not, Xor
 from sympy.logic.boolalg import Boolean, BooleanFalse, BooleanTrue
@@ -25,11 +27,21 @@
 class InternalCompiler(Compiler):
     """InternalCompiler translating an expression list to quantum circuit"""
 
+    def is_symbol_referenced_in_remaining_exps(self, symbol):
+        """Return True if the symbol is referenced in remaining expressions"""
+        for sym, exp in self.remaining_exps:
+            if sym == symbol:
+                return True
+            if symbol in exp.free_symbols:
+                return True
+        return False
+
     def compile(  # noqa: C901
         self, name, args: Args, returns: Arg, exprs: BoolExpList, uncompute=True
     ) -> QCircuit:
         qc = QCircuitEnhanced(name=name)
         self.expqmap = ExpQMap()
+        # self.remaining_exps = deepcopy(exprs)
 
         # 1. We first add a qubit for every input bit
         self.input_symbols = [arg_b for arg in args for arg_b in arg.bitvec]
@@ -37,6 +49,8 @@ def compile(  # noqa: C901
 
         # 2. Iterate over all expressions; iret contains qubit index for the current exp
         for sym, exp in exprs:
+            # self.remaining_exps.pop(0)
+
             is_temp = sym.name.startswith("__")
             symp_exp = self._symplify_exp(exp)