diff --git a/concrete/common/tracing/base_tracer.py b/concrete/common/tracing/base_tracer.py
index 6bfcd410f..4b183e882 100644
--- a/concrete/common/tracing/base_tracer.py
+++ b/concrete/common/tracing/base_tracer.py
@@ -302,6 +302,66 @@ class BaseTracer(ABC):
             self, other, lambda x, y: x != y, "ne"
         )
 
+    def __pow__(self, other: Union["BaseTracer", Any]):
+        # x ** cst
+        return self._helper_for_binary_functions_with_one_cst_input(
+            self, other, lambda x, y: x ** y, "pow"
+        )
+
+    def __rpow__(self, other: Union["BaseTracer", Any]):
+        # cst ** x
+        return self._helper_for_binary_functions_with_one_cst_input(
+            other, self, lambda x, y: x ** y, "pow"
+        )
+
+    def __mod__(self, other: Union["BaseTracer", Any]):
+        # x % cst
+        return self._helper_for_binary_functions_with_one_cst_input(
+            self, other, lambda x, y: x % y, "mod"
+        )
+
+    def __rmod__(self, other: Union["BaseTracer", Any]):
+        # cst % x
+        return self._helper_for_binary_functions_with_one_cst_input(
+            other, self, lambda x, y: x % y, "mod"
+        )
+
+    def __and__(self, other: Union["BaseTracer", Any]):
+        # x & cst
+        return self._helper_for_binary_functions_with_one_cst_input(
+            self, other, lambda x, y: x & y, "and"
+        )
+
+    def __rand__(self, other: Union["BaseTracer", Any]):
+        # cst & x
+        return self._helper_for_binary_functions_with_one_cst_input(
+            other, self, lambda x, y: x & y, "and"
+        )
+
+    def __or__(self, other: Union["BaseTracer", Any]):
+        # x | cst
+        return self._helper_for_binary_functions_with_one_cst_input(
+            self, other, lambda x, y: x | y, "or"
+        )
+
+    def __ror__(self, other: Union["BaseTracer", Any]):
+        # cst | x
+        return self._helper_for_binary_functions_with_one_cst_input(
+            other, self, lambda x, y: x | y, "or"
+        )
+
+    def __xor__(self, other: Union["BaseTracer", Any]):
+        # x ^ cst
+        return self._helper_for_binary_functions_with_one_cst_input(
+            self, other, lambda x, y: x ^ y, "xor"
+        )
+
+    def __rxor__(self, other: Union["BaseTracer", Any]):
+        # cst ^ x
+        return self._helper_for_binary_functions_with_one_cst_input(
+            other, self, lambda x, y: x ^ y, "xor"
+        )
+
     def __sub__(self, other: Union["BaseTracer", Any]) -> "BaseTracer":
         if not self._supports_other_operand(other):
             return NotImplemented
diff --git a/tests/numpy/test_tracing.py b/tests/numpy/test_tracing.py
index df2daaa12..32403c6d5 100644
--- a/tests/numpy/test_tracing.py
+++ b/tests/numpy/test_tracing.py
@@ -859,6 +859,106 @@ def test_tracing_numpy_calls(
             ],
         ),
         # pylint: enable=misplaced-comparison-constant
+        (
+            lambda x: x & 11,
+            [
+                (
+                    EncryptedTensor(Integer(32, is_signed=False), shape=(3, 5)),
+                    numpy.arange(15).reshape(3, 5),
+                    numpy.array([i & 11 for i in range(15)]).reshape(3, 5),
+                ),
+            ],
+        ),
+        (
+            lambda x: 13 & x,
+            [
+                (
+                    EncryptedTensor(Integer(32, is_signed=False), shape=(3, 5)),
+                    numpy.arange(15).reshape(3, 5),
+                    numpy.array([i & 13 for i in range(15)]).reshape(3, 5),
+                ),
+            ],
+        ),
+        (
+            lambda x: x | 6,
+            [
+                (
+                    EncryptedTensor(Integer(32, is_signed=False), shape=(3, 5)),
+                    numpy.arange(15).reshape(3, 5),
+                    numpy.array([i | 6 for i in range(15)]).reshape(3, 5),
+                ),
+            ],
+        ),
+        (
+            lambda x: 30 | x,
+            [
+                (
+                    EncryptedTensor(Integer(32, is_signed=False), shape=(3, 5)),
+                    numpy.arange(15).reshape(3, 5),
+                    numpy.array([i | 30 for i in range(15)]).reshape(3, 5),
+                ),
+            ],
+        ),
+        (
+            lambda x: x ^ 91,
+            [
+                (
+                    EncryptedTensor(Integer(32, is_signed=False), shape=(3, 5)),
+                    numpy.arange(15).reshape(3, 5),
+                    numpy.array([i ^ 91 for i in range(15)]).reshape(3, 5),
+                ),
+            ],
+        ),
+        (
+            lambda x: 115 ^ x,
+            [
+                (
+                    EncryptedTensor(Integer(32, is_signed=False), shape=(3, 5)),
+                    numpy.arange(15).reshape(3, 5),
+                    numpy.array([i ^ 115 for i in range(15)]).reshape(3, 5),
+                ),
+            ],
+        ),
+        (
+            lambda x: x % 11,
+            [
+                (
+                    EncryptedTensor(Integer(32, is_signed=False), shape=(3, 5)),
+                    numpy.arange(15).reshape(3, 5),
+                    numpy.array([i % 11 for i in range(15)]).reshape(3, 5),
+                ),
+            ],
+        ),
+        (
+            lambda x: 150 % (x + 1),
+            [
+                (
+                    EncryptedTensor(Integer(32, is_signed=False), shape=(3, 5)),
+                    numpy.arange(15).reshape(3, 5),
+                    numpy.array([150 % (i + 1) for i in range(15)]).reshape(3, 5),
+                ),
+            ],
+        ),
+        (
+            lambda x: x ** 2,
+            [
+                (
+                    EncryptedTensor(Integer(32, is_signed=False), shape=(3, 5)),
+                    numpy.arange(15).reshape(3, 5),
+                    numpy.array([i ** 2 for i in range(15)]).reshape(3, 5),
+                ),
+            ],
+        ),
+        (
+            lambda x: 2 ** x,
+            [
+                (
+                    EncryptedTensor(Integer(32, is_signed=False), shape=(3, 5)),
+                    numpy.arange(15).reshape(3, 5) % 7,
+                    numpy.array([2 ** (i % 7) for i in range(15)]).reshape(3, 5),
+                ),
+            ],
+        ),
     ],
 )
 def test_tracing_ndarray_calls(