diff --git a/kerngen/pisa_generators/manifest.json b/kerngen/pisa_generators/manifest.json
index 5a833a02..00cf2f91 100644
--- a/kerngen/pisa_generators/manifest.json
+++ b/kerngen/pisa_generators/manifest.json
@@ -24,6 +24,8 @@
     "INTT": ["INTT", "ntt.py"],
     "MOD": ["Mod", "mod.py"],
     "MODUP": ["Modup", "mod.py"],
-    "RESCALE": ["Rescale", "rescale.py"]
+    "RELIN": ["Relin", "relin.py"],
+    "RESCALE": ["Rescale", "rescale.py"],
+    "ROTATE": ["Rotate", "rotate.py"]
   }
 }
diff --git a/kerngen/pisa_generators/mod.py b/kerngen/pisa_generators/mod.py
index 8383d250..f99bf20d 100644
--- a/kerngen/pisa_generators/mod.py
+++ b/kerngen/pisa_generators/mod.py
@@ -10,12 +10,15 @@
 
 from .basic import (
     Add,
+    Sub,
     Muli,
     mixed_to_pisa_ops,
     split_last_rns_polys,
     duplicate_polys,
     common_immediates,
     muli_last_half,
+    add_last_half,
+    sub_last_half,
 )
 from .ntt import INTT, NTT
 
@@ -43,6 +46,122 @@ def to_pisa(self) -> list[PIsaOp]:
         temp_input_last_rns = duplicate_polys(input_last_rns, "y")
         temp_input_remaining_rns = duplicate_polys(input_remaining_rns, "x")
 
+        # ckks variable
+        p_half = Polys("pHalf", 1, rns=last_q)
+
+        class Stage:
+            """Stage hold a list of PISA ops, which are used by generate_mod_stages"""
+
+            pisa_ops: list[PIsaOp]
+
+            def __init__(self, pisa_ops: list[PIsaOp]):
+                self.pisa_ops = pisa_ops
+
+        def generate_mod_stages() -> list[Stage]:
+            """Generate stages based on the current scheme (e.g. BGV or CKKS)"""
+            # init empty stages
+            stages = []
+            if self.context.scheme == "BGV":
+                stages.append(
+                    Stage(
+                        [
+                            Comment("Mod Stage 0"),
+                            Muli(
+                                self.context,
+                                temp_input_last_rns,
+                                temp_input_last_rns,
+                                it,
+                            ),
+                        ]
+                    )
+                )
+                stages.append(
+                    Stage(
+                        [
+                            Comment("Mod Stage 1"),
+                            muli_last_half(
+                                self.context,
+                                temp_input_remaining_rns,
+                                temp_input_last_rns,
+                                r2,
+                                input_remaining_rns,
+                                last_q,
+                            ),
+                        ]
+                    )
+                )
+                stages.append(
+                    Stage(
+                        [
+                            Comment("Mod Stage 2"),
+                            Muli(
+                                self.context,
+                                temp_input_remaining_rns,
+                                temp_input_remaining_rns,
+                                t,
+                            ),
+                            Comment("Add the delta correction to mod down polys"),
+                            Add(
+                                self.context,
+                                temp_input_remaining_rns,
+                                temp_input_remaining_rns,
+                                input_remaining_rns,
+                            ),
+                        ]
+                    )
+                )
+            elif self.context.scheme == "CKKS":
+                # stage 1 is empty for CKKS
+                stages.append(Stage([Comment("Mod Stage 0 - Empty")]))
+                stages.append(
+                    Stage(
+                        [
+                            Comment("Mod Stage 1 - add/sub half and muli"),
+                            add_last_half(
+                                self.context,
+                                temp_input_last_rns,
+                                temp_input_last_rns,
+                                p_half,
+                                Polys.from_polys(
+                                    input_remaining_rns, mode="drop_last_rns"
+                                ),
+                                last_q,
+                            ),
+                            sub_last_half(
+                                self.context,
+                                temp_input_remaining_rns,
+                                temp_input_last_rns,
+                                p_half,
+                                input_remaining_rns,
+                                last_q,
+                            ),
+                            Muli(
+                                self.context,
+                                temp_input_remaining_rns,
+                                temp_input_remaining_rns,
+                                r2,
+                            ),
+                        ]
+                    )
+                )
+                stages.append(
+                    Stage(
+                        [
+                            Comment("Mod Stage 2 - Sub"),
+                            Sub(
+                                self.context,
+                                temp_input_remaining_rns,
+                                input_remaining_rns,
+                                temp_input_remaining_rns,
+                            ),
+                        ]
+                    )
+                )
+
+            return stages
+
+        stages = generate_mod_stages()
+
         # Compute the `delta_i = t * [-t^-1 * c_i] mod ql` where `i` are the parts
         # The `one` acts as a select flag as whether or not R2 the Montgomery
         # factor should be applied
@@ -51,29 +170,18 @@ def to_pisa(self) -> list[PIsaOp]:
                 Comment("Start of mod kernel"),
                 Comment("Compute the delta from last rns"),
                 INTT(self.context, temp_input_last_rns, input_last_rns),
-                Muli(self.context, temp_input_last_rns, temp_input_last_rns, it),
+            ]
+            + stages[0].pisa_ops
+            + [
                 Muli(self.context, temp_input_last_rns, temp_input_last_rns, one),
                 Comment("Compute the remaining rns"),
-                # drop down to pisa ops to use correct rns q
-                muli_last_half(
-                    self.context,
-                    temp_input_remaining_rns,
-                    temp_input_last_rns,
-                    r2,
-                    input_remaining_rns,
-                    last_q,
-                ),
+            ]
+            + stages[1].pisa_ops
+            + [
                 NTT(self.context, temp_input_remaining_rns, temp_input_remaining_rns),
-                Muli(
-                    self.context, temp_input_remaining_rns, temp_input_remaining_rns, t
-                ),
-                Comment("Add the delta correction to mod down polys"),
-                Add(
-                    self.context,
-                    temp_input_remaining_rns,
-                    temp_input_remaining_rns,
-                    input_remaining_rns,
-                ),
+            ]
+            + stages[2].pisa_ops
+            + [
                 Muli(self.context, self.output, temp_input_remaining_rns, iq),
                 Comment("End of mod kernel"),
             ]