diff --git a/lib/Dialect/ArithExt/Transforms/BUILD b/lib/Dialect/ArithExt/Transforms/BUILD
new file mode 100644
index 000000000..d2596662d
--- /dev/null
+++ b/lib/Dialect/ArithExt/Transforms/BUILD
@@ -0,0 +1,78 @@
+load("@llvm-project//mlir:tblgen.bzl", "gentbl_cc_library")
+
+package(
+    default_applicable_licenses = ["@heir//:license"],
+    default_visibility = ["//visibility:public"],
+)
+
+cc_library(
+    name = "Transforms",
+    hdrs = [
+        "Passes.h",
+    ],
+    deps = [
+        ":pass_inc_gen",
+        "@heir//lib/Dialect/ArithExt/IR:Dialect",
+        "@llvm-project//mlir:IR",
+    ],
+)
+
+cc_library(
+    name = "RewriteModulo",
+    srcs = ["RewriteModulo.cpp"],
+    hdrs = [
+        "RewriteModulo.h",
+    ],
+    deps = [
+        ":rewrite_modulo_inc_gen",
+        ":pass_inc_gen",
+        "@heir//lib/Dialect/ArithExt/IR:Dialect",
+        "@heir//lib/Dialect/Polynomial/IR:PolynomialAttributes",
+        "@llvm-project//mlir:ArithDialect",
+        "@llvm-project//mlir:IR",
+        "@llvm-project//mlir:Pass",
+        "@llvm-project//mlir:TransformUtils",
+    ],
+)
+
+gentbl_cc_library(
+    name = "pass_inc_gen",
+    tbl_outs = [
+        (
+            [
+                "-gen-pass-decls",
+                "-name=ArithExt",
+            ],
+            "Passes.h.inc",
+        ),
+        (
+            ["-gen-pass-doc"],
+            "ArithExtPasses.md",
+        ),
+    ],
+    tblgen = "@llvm-project//mlir:mlir-tblgen",
+    td_file = "Passes.td",
+    deps = [
+        "@llvm-project//mlir:OpBaseTdFiles",
+        "@llvm-project//mlir:PassBaseTdFiles",
+    ],
+)
+
+gentbl_cc_library(
+    name = "rewrite_modulo_inc_gen",
+    tbl_outs = [
+        (
+            ["-gen-rewriters"],
+            "RewriteModulo.cpp.inc",
+        ),
+    ],
+    tblgen = "@llvm-project//mlir:mlir-tblgen",
+    td_file = "RewriteModulo.td",
+    deps = [
+        "@heir//lib/DRR",
+        "@heir//lib/Dialect/ArithExt/IR:ops_inc_gen",
+        "@heir//lib/Dialect/ArithExt/IR:td_files",
+        "@heir//lib/Dialect/Polynomial/IR:td_files",
+        "@llvm-project//mlir:ArithOpsTdFiles",
+    ],
+)
diff --git a/lib/Dialect/ArithExt/Transforms/Passes.h b/lib/Dialect/ArithExt/Transforms/Passes.h
new file mode 100644
index 000000000..725513ba0
--- /dev/null
+++ b/lib/Dialect/ArithExt/Transforms/Passes.h
@@ -0,0 +1,18 @@
+#ifndef LIB_DIALECT_ARITHEXT_TRANSFORMS_PASSES_H_
+#define LIB_DIALECT_ARITHEXT_TRANSFORMS_PASSES_H_
+
+#include "lib/Dialect/ArithExt/IR/ArithExtDialect.h"
+#include "lib/Dialect/ArithExt/Transforms/RewriteModulo.h"
+
+namespace mlir {
+namespace heir {
+namespace arith_ext {
+
+#define GEN_PASS_REGISTRATION
+#include "lib/Dialect/ArithExt/Transforms/Passes.h.inc"
+
+}  // namespace arith_ext
+}  // namespace heir
+}  // namespace mlir
+
+#endif  // LIB_DIALECT_ARITHEXT_TRANSFORMS_PASSES_H_
diff --git a/lib/Dialect/ArithExt/Transforms/Passes.td b/lib/Dialect/ArithExt/Transforms/Passes.td
new file mode 100644
index 000000000..ec0b6e544
--- /dev/null
+++ b/lib/Dialect/ArithExt/Transforms/Passes.td
@@ -0,0 +1,15 @@
+#ifndef LIB_DIALECT_ARITHEXT_TRANSFORMS_PASSES_TD_
+#define LIB_DIALECT_ARITHEXT_TRANSFORMS_PASSES_TD_
+
+include "mlir/Pass/PassBase.td"
+
+def RewriteModulo : Pass<"convert-remui-to-arith-ext"> {
+  let summary = "Rewrites arith remui patterns to their arith_ext equivalents";
+  let description = [{
+    Applies a rewrite pattern to convert the following arith patterns to their
+    equivalent using the arith_ext operations.
+  }];
+  let dependentDialects = ["mlir::heir::arith_ext::ArithExtDialect"];
+}
+
+#endif  // LIB_DIALECT_ARITHEXT_TRANSFORMS_PASSES_TD_
diff --git a/lib/Dialect/ArithExt/Transforms/RewriteModulo.cpp b/lib/Dialect/ArithExt/Transforms/RewriteModulo.cpp
new file mode 100644
index 000000000..425bed658
--- /dev/null
+++ b/lib/Dialect/ArithExt/Transforms/RewriteModulo.cpp
@@ -0,0 +1,32 @@
+#include "lib/Dialect/ArithExt/Transforms/RewriteModulo.h"
+
+#include "lib/Dialect/ArithExt/IR/ArithExtOps.h"
+#include "lib/Dialect/Polynomial/IR/PolynomialAttributes.h"
+#include "mlir/include/mlir/IR/MLIRContext.h"   // from @llvm-project
+#include "mlir/include/mlir/IR/PatternMatch.h"  // from @llvm-project
+#include "mlir/include/mlir/Transforms/GreedyPatternRewriteDriver.h"  // from @llvm-project
+
+namespace mlir {
+namespace heir {
+namespace arith_ext {
+
+#define GEN_PASS_DEF_REWRITEMODULO
+#include "lib/Dialect/ArithExt/Transforms/Passes.h.inc"
+
+namespace rewrites {
+// In an inner namespace to avoid conflicts with canonicalization patterns
+#include "lib/Dialect/ArithExt/Transforms/RewriteModulo.cpp.inc"
+}  // namespace rewrites
+
+struct RewriteModulo : impl::RewriteModuloBase<RewriteModulo> {
+  void runOnOperation() override {
+    MLIRContext *context = &getContext();
+    RewritePatternSet patterns(context);
+    rewrites::populateWithGenerated(patterns);
+    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+  }
+};
+
+}  // namespace arith_ext
+}  // namespace heir
+}  // namespace mlir
diff --git a/lib/Dialect/ArithExt/Transforms/RewriteModulo.h b/lib/Dialect/ArithExt/Transforms/RewriteModulo.h
new file mode 100644
index 000000000..482924854
--- /dev/null
+++ b/lib/Dialect/ArithExt/Transforms/RewriteModulo.h
@@ -0,0 +1,18 @@
+#ifndef LIB_DIALECT_ARITHEXT_TRANSFORMS_REWRITEMODULO_H_
+#define LIB_DIALECT_ARITHEXT_TRANSFORMS_REWRITEMODULO_H_
+
+#include "mlir/include/mlir/Dialect/Arith/IR/Arith.h"  // from @llvm-project
+#include "mlir/include/mlir/Pass/Pass.h"               // from @llvm-project
+
+namespace mlir {
+namespace heir {
+namespace arith_ext {
+
+#define GEN_PASS_DECL_REWRITEMODULO
+#include "lib/Dialect/ArithExt/Transforms/Passes.h.inc"
+
+}  // namespace arith_ext
+}  // namespace heir
+}  // namespace mlir
+
+#endif  // LIB_DIALECT_ARITHEXT_TRANSFORMS_REWRITEMODULO_H_
diff --git a/lib/Dialect/ArithExt/Transforms/RewriteModulo.td b/lib/Dialect/ArithExt/Transforms/RewriteModulo.td
new file mode 100644
index 000000000..855689ef6
--- /dev/null
+++ b/lib/Dialect/ArithExt/Transforms/RewriteModulo.td
@@ -0,0 +1,64 @@
+#ifndef LIB_DIALECT_ARITHEXT_TRANSFORMS_REWRITEMODULO_TD_
+#define LIB_DIALECT_ARITHEXT_TRANSFORMS_REWRITEMODULO_TD_
+
+include "lib/DRR/Utils.td"
+include "lib/Dialect/Polynomial/IR/PolynomialAttributes.td"
+include "lib/Dialect/ArithExt/IR/ArithExtOps.td"
+include "mlir/Dialect/Arith/IR/ArithOps.td"
+include "mlir/IR/PatternBase.td"
+
+def DefaultBitWidth : NativeCodeCall<
+    "IntegerAttr::get("
+    " IntegerType::get($_builder.getContext(), 64), "
+    " (dyn_cast<RankedTensorType>($0.getType())).getElementTypeBitWidth() / 2)">;
+
+def Normalised : Constraint<
+    CPred<"true">,
+    "ensure the values will be within the range [0, cmod).">;
+
+def EncodedRankedTensorType : Constraint<
+    CPred<"(dyn_cast<RankedTensorType>($0.getType())).getEncoding()">,
+    "ensure the operation type is a ranked tensor type with a will be within the range [0, cmod).">;
+
+def GetEncodedRingModulo : NativeCodeCall<
+    "IntegerAttr::get("
+    " IntegerType::get($_builder.getContext(), 64), "
+    " (dyn_cast<::mlir::heir::polynomial::RingAttr>((dyn_cast<RankedTensorType>($0.getType())).getEncoding())).coefficientModulus())">;
+
+def RewriteAddRem : Pattern<
+  (Arith_RemUIOp:$remOp (Arith_AddIOp:$addOp $lhs, $rhs, $overflow), $cmod),
+  [
+    (ArithExt_SubIfGEOp $addOp, $cmod)
+  ],
+  [
+    (Normalised $lhs),
+    (Normalised $rhs)
+  ]
+>;
+
+def RewriteSubRem : Pattern<
+  (Arith_RemUIOp:$remOp (Arith_SubIOp:$subOp $lhs, $rhs, $overflow), $cmod),
+  [
+    (ArithExt_SubIfGEOp
+      (Arith_AddIOp $subOp, $cmod, $overflow), $cmod)
+  ],
+  [
+    (Normalised $lhs),
+    (Normalised $rhs)
+  ]
+>;
+
+def RewriteMulRem : Pattern<
+  (Arith_RemUIOp:$remOp (Arith_MulIOp:$mulOp $lhs, $rhs, $overflow), $cmod),
+  [
+    (ArithExt_SubIfGEOp
+      (ArithExt_BarrettReduceOp $mulOp, (DefaultBitWidth $mulOp), (GetEncodedRingModulo $mulOp)), $cmod)
+  ],
+  [
+    (Normalised $lhs),
+    (Normalised $rhs),
+    (EncodedRankedTensorType $mulOp)
+  ]
+>;
+
+#endif  // LIB_DIALECT_ARITHEXT_TRANSFORMS_REWRITEMODULO_TD_
diff --git a/tests/arith/rewrite-modulo.mlir b/tests/arith/rewrite-modulo.mlir
new file mode 100644
index 000000000..43fcb20d6
--- /dev/null
+++ b/tests/arith/rewrite-modulo.mlir
@@ -0,0 +1,42 @@
+// RUN: heir-opt -convert-remui-to-arith-ext %s | FileCheck %s
+
+// CHECK-LABEL: @test_add_rewrite
+func.func @test_add_rewrite(%lhs : tensor<4xi8>, %rhs : tensor<4xi8>) -> tensor<4xi8> {
+  %cmod_vec = arith.constant dense<17> : tensor<4xi8>
+
+  // CHECK: arith.addi
+  // CHECK: arith_ext.subifge
+  %add = arith.addi %lhs, %rhs : tensor<4xi8>
+  %res = arith.remui %add, %cmod_vec: tensor<4xi8>
+
+  return %res : tensor<4xi8>
+}
+
+// CHECK-LABEL: @test_sub_rewrite
+func.func @test_sub_rewrite(%lhs : tensor<4xi8>, %rhs : tensor<4xi8>) -> tensor<4xi8> {
+  %cmod_vec = arith.constant dense<17> : tensor<4xi8>
+
+  // CHECK: arith.subi
+  // CHECK: arith.addi
+  // CHECK: arith_ext.subifge
+  %sub = arith.subi %lhs, %rhs : tensor<4xi8>
+  %res = arith.remui %sub, %cmod_vec : tensor<4xi8>
+
+  return %res : tensor<4xi8>
+}
+
+#ideal = #_polynomial.polynomial<1 + x**4>
+#ring = #_polynomial.ring<cmod=17, ideal=#ideal, root=2>
+
+// CHECK-LABEL: @test_mul_rewrite
+func.func @test_mul_rewrite(%lhs : tensor<4xi8, #ring>, %rhs : tensor<4xi8, #ring>) -> tensor<4xi8, #ring> {
+  %cmod_vec = arith.constant dense<17> : tensor<4xi8, #ring>
+
+  // CHECK: arith.muli
+  // CHECK: arith_ext.barrett_reduce
+  // CHECK: arith_ext.subifge
+  %sub = arith.muli %lhs, %rhs : tensor<4xi8, #ring>
+  %res = arith.remui %sub, %cmod_vec : tensor<4xi8, #ring>
+
+  return %res : tensor<4xi8, #ring>
+}
diff --git a/tools/BUILD b/tools/BUILD
index 9b4d113f0..3b06eeccf 100644
--- a/tools/BUILD
+++ b/tools/BUILD
@@ -42,6 +42,8 @@ cc_binary(
         "@heir//lib/Conversion/PolynomialToStandard",
         "@heir//lib/Conversion/SecretToBGV",
         "@heir//lib/Dialect/ArithExt/IR:Dialect",
+        "@heir//lib/Dialect/ArithExt/Transforms",
+        "@heir//lib/Dialect/ArithExt/Transforms:RewriteModulo",
         "@heir//lib/Dialect/BGV/IR:Dialect",
         "@heir//lib/Dialect/BGV/Transforms",
         "@heir//lib/Dialect/BGV/Transforms:AddClientInterface",
diff --git a/tools/heir-opt.cpp b/tools/heir-opt.cpp
index c6a335d64..e68fe5107 100644
--- a/tools/heir-opt.cpp
+++ b/tools/heir-opt.cpp
@@ -11,6 +11,8 @@
 #include "lib/Conversion/PolynomialToStandard/PolynomialToStandard.h"
 #include "lib/Conversion/SecretToBGV/SecretToBGV.h"
 #include "lib/Dialect/ArithExt/IR/ArithExtDialect.h"
+#include "lib/Dialect/ArithExt/Transforms/Passes.h"
+#include "lib/Dialect/ArithExt/Transforms/RewriteModulo.h"
 #include "lib/Dialect/BGV/IR/BGVDialect.h"
 #include "lib/Dialect/BGV/Transforms/AddClientInterface.h"
 #include "lib/Dialect/BGV/Transforms/Passes.h"
@@ -498,6 +500,7 @@ int main(int argc, char **argv) {
   registerAllPasses();
 
   // Custom passes in HEIR
+  arith_ext::registerArithExtPasses();
   bgv::registerBGVPasses();
   cggi::registerCGGIPasses();
   lwe::registerLWEPasses();