diff --git a/compiler/include/zamalang/Conversion/CMakeLists.txt b/compiler/include/zamalang/Conversion/CMakeLists.txt
index 35343356a..578527e23 100644
--- a/compiler/include/zamalang/Conversion/CMakeLists.txt
+++ b/compiler/include/zamalang/Conversion/CMakeLists.txt
@@ -3,4 +3,5 @@ mlir_tablegen(Passes.h.inc -gen-pass-decls -name Conversion)
 add_public_tablegen_target(MLIRConversionPassIncGen)
 
 
-add_subdirectory(HLFHEToMidLFHE)
\ No newline at end of file
+add_subdirectory(HLFHEToMidLFHE)
+add_subdirectory(MidLFHEToLowLFHE)
\ No newline at end of file
diff --git a/compiler/include/zamalang/Conversion/MidLFHEToLowLFHE/CMakeLists.txt b/compiler/include/zamalang/Conversion/MidLFHEToLowLFHE/CMakeLists.txt
new file mode 100644
index 000000000..cef0de880
--- /dev/null
+++ b/compiler/include/zamalang/Conversion/MidLFHEToLowLFHE/CMakeLists.txt
@@ -0,0 +1,3 @@
+set(LLVM_TARGET_DEFINITIONS Patterns.td)
+mlir_tablegen(Patterns.h.inc -gen-rewriters -name MidLFHE)
+add_public_tablegen_target(MidLFHEToLowLFHEPatternsIncGen)
diff --git a/compiler/include/zamalang/Conversion/MidLFHEToLowLFHE/Pass.h b/compiler/include/zamalang/Conversion/MidLFHEToLowLFHE/Pass.h
new file mode 100644
index 000000000..b73d8c572
--- /dev/null
+++ b/compiler/include/zamalang/Conversion/MidLFHEToLowLFHE/Pass.h
@@ -0,0 +1,14 @@
+
+#ifndef ZAMALANG_CONVERSION_MIDLFHETOLOWLFHE_PASS_H_
+#define ZAMALANG_CONVERSION_MIDLFHETOLOWLFHE_PASS_H_
+
+#include "mlir/Pass/Pass.h"
+
+namespace mlir {
+namespace zamalang {
+/// Create a pass to convert `MidLFHE` dialect to `LowLFHE` dialect.
+std::unique_ptr<OperationPass<ModuleOp>> createConvertMidLFHEToLowLFHEPass();
+} // namespace zamalang
+} // namespace mlir
+
+#endif
\ No newline at end of file
diff --git a/compiler/include/zamalang/Conversion/MidLFHEToLowLFHE/Patterns.h b/compiler/include/zamalang/Conversion/MidLFHEToLowLFHE/Patterns.h
new file mode 100644
index 000000000..1efbbead8
--- /dev/null
+++ b/compiler/include/zamalang/Conversion/MidLFHEToLowLFHE/Patterns.h
@@ -0,0 +1,116 @@
+#ifndef ZAMALANG_CONVERSION_MIDLFHETOLOWLFHE_PATTERNS_H_
+#define ZAMALANG_CONVERSION_MIDLFHETOLOWLFHE_PATTERNS_H_
+
+#include "mlir/Dialect/StandardOps/IR/Ops.h"
+#include "mlir/IR/Builders.h"
+#include "mlir/IR/PatternMatch.h"
+#include "zamalang/Dialect/LowLFHE/IR/LowLFHEOps.h"
+#include "zamalang/Dialect/MidLFHE/IR/MidLFHEOps.h"
+
+namespace mlir {
+namespace zamalang {
+
+using LowLFHE::CleartextType;
+using LowLFHE::LweCiphertextType;
+using LowLFHE::PlaintextType;
+using MidLFHE::GLWECipherTextType;
+
+LweCiphertextType convertTypeGLWEToLWE(mlir::MLIRContext *context,
+                                       GLWECipherTextType &glwe) {
+  return LweCiphertextType::get(context);
+}
+
+PlaintextType convertIntToPlaintextType(mlir::MLIRContext *context,
+                                        IntegerType &type) {
+  return PlaintextType::get(context, type.getWidth());
+}
+
+CleartextType convertIntToCleartextType(mlir::MLIRContext *context,
+                                        IntegerType &type) {
+  return CleartextType::get(context, type.getWidth());
+}
+
+template <class Operator>
+mlir::Value createLowLFHEOpFromMidLFHE(mlir::PatternRewriter rewriter,
+                                       mlir::Location loc, mlir::Value arg0,
+                                       mlir::Value arg1,
+                                       mlir::OpResult result) {
+  mlir::SmallVector<mlir::Value, 2> args{arg0, arg1};
+  mlir::SmallVector<mlir::NamedAttribute, 0> attrs;
+  auto glwe = result.getType().cast<GLWECipherTextType>();
+  mlir::SmallVector<mlir::Type, 1> resTypes{
+      convertTypeGLWEToLWE(rewriter.getContext(), glwe)};
+  Operator op = rewriter.create<Operator>(loc, resTypes, args, attrs);
+  return op.getODSResults(0).front();
+}
+
+mlir::Value createAddPlainLweCiphertext(mlir::PatternRewriter rewriter,
+                                        mlir::Location loc, mlir::Value arg0,
+                                        mlir::Value arg1,
+                                        mlir::OpResult result) {
+  auto integer_type = arg1.getType().cast<IntegerType>();
+  PlaintextType encoded_type =
+      convertIntToPlaintextType(rewriter.getContext(), integer_type);
+  // encode int into plaintext
+  mlir::Value encoded =
+      rewriter
+          .create<mlir::zamalang::LowLFHE::EncodeIntOp>(loc, encoded_type, arg1)
+          .plaintext();
+  // convert result type
+  GLWECipherTextType glwe_type = result.getType().cast<GLWECipherTextType>();
+  LweCiphertextType lwe_type =
+      convertTypeGLWEToLWE(rewriter.getContext(), glwe_type);
+  // replace op using the encoded plaintext instead of int
+  auto op =
+      rewriter.create<mlir::zamalang::LowLFHE::AddPlaintextLweCiphertextOp>(
+          loc, lwe_type, arg0, encoded);
+  return op.getODSResults(0).front();
+}
+
+mlir::Value createSubIntLweCiphertext(mlir::PatternRewriter rewriter,
+                                      mlir::Location loc, mlir::Value arg0,
+                                      mlir::Value arg1, mlir::OpResult result) {
+  auto arg1_type = arg1.getType().cast<GLWECipherTextType>();
+  auto negated_arg1 =
+      rewriter
+          .create<mlir::zamalang::LowLFHE::NegateLweCiphertextOp>(
+              loc, convertTypeGLWEToLWE(rewriter.getContext(), arg1_type), arg1)
+          .result();
+  return createAddPlainLweCiphertext(rewriter, loc, negated_arg1, arg0, result);
+}
+
+mlir::Value createMulClearLweCiphertext(mlir::PatternRewriter rewriter,
+                                        mlir::Location loc, mlir::Value arg0,
+                                        mlir::Value arg1,
+                                        mlir::OpResult result) {
+  auto integer_type = arg1.getType().cast<IntegerType>();
+  CleartextType encoded_type =
+      convertIntToCleartextType(rewriter.getContext(), integer_type);
+  // encode int into plaintext
+  mlir::Value encoded = rewriter
+                            .create<mlir::zamalang::LowLFHE::IntToCleartextOp>(
+                                loc, encoded_type, arg1)
+                            .cleartext();
+  // convert result type
+  GLWECipherTextType glwe_type = result.getType().cast<GLWECipherTextType>();
+  LweCiphertextType lwe_type =
+      convertTypeGLWEToLWE(rewriter.getContext(), glwe_type);
+  // replace op using the encoded plaintext instead of int
+  auto op =
+      rewriter.create<mlir::zamalang::LowLFHE::MulCleartextLweCiphertextOp>(
+          loc, lwe_type, arg0, encoded);
+  return op.getODSResults(0).front();
+}
+
+} // namespace zamalang
+} // namespace mlir
+
+namespace {
+#include "zamalang/Conversion/MidLFHEToLowLFHE/Patterns.h.inc"
+}
+
+void populateWithGeneratedMidLFHEToLowLFHE(mlir::RewritePatternSet &patterns) {
+  populateWithGenerated(patterns);
+}
+
+#endif
diff --git a/compiler/include/zamalang/Conversion/MidLFHEToLowLFHE/Patterns.td b/compiler/include/zamalang/Conversion/MidLFHEToLowLFHE/Patterns.td
new file mode 100644
index 000000000..6157dbce1
--- /dev/null
+++ b/compiler/include/zamalang/Conversion/MidLFHEToLowLFHE/Patterns.td
@@ -0,0 +1,32 @@
+#ifndef ZAMALANG_CONVERSION_MIDLFHETOLOWLFHE_PATTERNS
+#define ZAMALANG_CONVERSION_MIDLFHETOLOWLFHE_PATTERNS
+
+include "mlir/Dialect/StandardOps/IR/Ops.td"
+include "zamalang/Dialect/LowLFHE/IR/LowLFHEOps.td"
+include "zamalang/Dialect/MidLFHE/IR/MidLFHEOps.td"
+
+def createAddLWEOp : NativeCodeCall<"mlir::zamalang::createLowLFHEOpFromMidLFHE<mlir::zamalang::LowLFHE::AddLweCiphertextsOp>($_builder, $_loc, $0, $1, $2)">;
+
+def AddGLWEPattern : Pat<
+    (AddGLWEOp:$result $arg0, $arg1),
+    (createAddLWEOp $arg0, $arg1, $result)>;
+
+def createAddPlainLweOp : NativeCodeCall<"mlir::zamalang::createAddPlainLweCiphertext($_builder, $_loc, $0, $1, $2)">;
+
+def AddGLWEIntPattern : Pat<
+    (AddGLWEIntOp:$result $arg0, $arg1),
+    (createAddPlainLweOp $arg0, $arg1, $result)>;
+
+def createMulClearLweOp : NativeCodeCall<"mlir::zamalang::createMulClearLweCiphertext($_builder, $_loc, $0, $1, $2)">;
+
+def MulGLWEIntPattern : Pat<
+    (MulGLWEIntOp:$result $arg0, $arg1),
+    (createMulClearLweOp $arg0, $arg1, $result)>;
+
+def createSubIntLweOp : NativeCodeCall<"mlir::zamalang::createSubIntLweCiphertext($_builder, $_loc, $0, $1, $2)">;
+
+def SubIntGLWEPattern : Pat<
+    (SubIntGLWEOp:$result $arg0, $arg1),
+    (createSubIntLweOp $arg0, $arg1, $result)>;
+
+#endif
diff --git a/compiler/include/zamalang/Conversion/Passes.h b/compiler/include/zamalang/Conversion/Passes.h
index 991e4e8fa..e90ed5758 100644
--- a/compiler/include/zamalang/Conversion/Passes.h
+++ b/compiler/include/zamalang/Conversion/Passes.h
@@ -9,6 +9,7 @@
 #include "zamalang/Conversion/HLFHETensorOpsToLinalg/Pass.h"
 #include "zamalang/Conversion/HLFHEToMidLFHE/Pass.h"
 #include "zamalang/Conversion/MLIRLowerableDialectsToLLVM/Pass.h"
+#include "zamalang/Conversion/MidLFHEToLowLFHE/Pass.h"
 #include "zamalang/Dialect/HLFHE/IR/HLFHEDialect.h"
 
 #define GEN_PASS_CLASSES
diff --git a/compiler/include/zamalang/Conversion/Passes.td b/compiler/include/zamalang/Conversion/Passes.td
index d0e68e15f..f1f39f203 100644
--- a/compiler/include/zamalang/Conversion/Passes.td
+++ b/compiler/include/zamalang/Conversion/Passes.td
@@ -17,6 +17,14 @@ def HLFHEToMidLFHE : Pass<"hlfhe-to-midlfhe", "mlir::ModuleOp"> {
   let dependentDialects = ["mlir::linalg::LinalgDialect"];
 }
 
+def MidLFHEToLowLFHE : Pass<"midlfhe-to-lowlfhe", "mlir::ModuleOp"> {
+  let summary = "Lowers operations from the MidLFHE dialect to LowLFHE";
+  let description = [{ Lowers operations from the MidLFHE dialect to LowLFHE }];
+  let constructor = "mlir::zamalang::createConvertMidLFHEToLowLFHEPass()";
+  let options = [];
+  let dependentDialects = ["mlir::linalg::LinalgDialect"];
+}
+
 def MLIRLowerableDialectsToLLVM : Pass<"mlir-lowerable-dialects-to-llvm", "mlir::ModuleOp"> {
   let summary = "Lowers operations from MLIR lowerable dialects to LLVM";
   let constructor = "mlir::zamalang::createConvertMLIRLowerableDialectsToLLVMPass()";
diff --git a/compiler/lib/Conversion/CMakeLists.txt b/compiler/lib/Conversion/CMakeLists.txt
index 75629b843..9de41dd79 100644
--- a/compiler/lib/Conversion/CMakeLists.txt
+++ b/compiler/lib/Conversion/CMakeLists.txt
@@ -1,3 +1,4 @@
 add_subdirectory(HLFHEToMidLFHE)
+add_subdirectory(MidLFHEToLowLFHE)
 add_subdirectory(HLFHETensorOpsToLinalg)
 add_subdirectory(MLIRLowerableDialectsToLLVM)
diff --git a/compiler/lib/Conversion/MidLFHEToLowLFHE/CMakeLists.txt b/compiler/lib/Conversion/MidLFHEToLowLFHE/CMakeLists.txt
new file mode 100644
index 000000000..bed556503
--- /dev/null
+++ b/compiler/lib/Conversion/MidLFHEToLowLFHE/CMakeLists.txt
@@ -0,0 +1,17 @@
+add_mlir_dialect_library(MidLFHEToLowLFHE
+  MidLFHEToLowLFHE.cpp
+
+  ADDITIONAL_HEADER_DIRS
+  ${PROJECT_SOURCE_DIR}/include/zamalang/Dialect/MidLFHE
+
+  DEPENDS
+  MidLFHEDialect
+  LowLFHEDialect
+  MidLFHEToLowLFHEPatternsIncGen
+
+  LINK_LIBS PUBLIC
+  MLIRIR
+  MLIRTransforms
+  MLIRMath)
+
+target_link_libraries(MidLFHEToLowLFHE PUBLIC MLIRIR)
diff --git a/compiler/lib/Conversion/MidLFHEToLowLFHE/MidLFHEToLowLFHE.cpp b/compiler/lib/Conversion/MidLFHEToLowLFHE/MidLFHEToLowLFHE.cpp
new file mode 100644
index 000000000..127d85825
--- /dev/null
+++ b/compiler/lib/Conversion/MidLFHEToLowLFHE/MidLFHEToLowLFHE.cpp
@@ -0,0 +1,99 @@
+#include <iostream>
+
+#include "mlir/Pass/Pass.h"
+#include "mlir/Transforms/DialectConversion.h"
+
+#include "zamalang/Conversion/MidLFHEToLowLFHE/Patterns.h"
+#include "zamalang/Conversion/Passes.h"
+#include "zamalang/Conversion/Utils/LinalgGenericTypeConverterPattern.h"
+#include "zamalang/Dialect/LowLFHE/IR/LowLFHEDialect.h"
+#include "zamalang/Dialect/LowLFHE/IR/LowLFHETypes.h"
+#include "zamalang/Dialect/MidLFHE/IR/MidLFHEDialect.h"
+#include "zamalang/Dialect/MidLFHE/IR/MidLFHETypes.h"
+
+namespace {
+struct MidLFHEToLowLFHEPass
+    : public MidLFHEToLowLFHEBase<MidLFHEToLowLFHEPass> {
+  void runOnOperation() final;
+};
+} // namespace
+
+using mlir::zamalang::LowLFHE::LweCiphertextType;
+using mlir::zamalang::MidLFHE::GLWECipherTextType;
+
+/// MidLFHEToLowLFHETypeConverter is a TypeConverter that transform
+/// `MidLFHE.gwle<{_,_,_}{p}>` to LowLFHE.lwe_ciphertext
+class MidLFHEToLowLFHETypeConverter : public mlir::TypeConverter {
+
+public:
+  MidLFHEToLowLFHETypeConverter() {
+    addConversion([&](GLWECipherTextType type) {
+      return mlir::zamalang::convertTypeGLWEToLWE(type.getContext(), type);
+    });
+    addConversion([&](mlir::MemRefType type) {
+      auto glwe = type.getElementType().dyn_cast_or_null<GLWECipherTextType>();
+      if (glwe == nullptr) {
+        return (mlir::Type)(type);
+      }
+      mlir::Type r = mlir::MemRefType::get(
+          type.getShape(),
+          mlir::zamalang::convertTypeGLWEToLWE(glwe.getContext(), glwe),
+          type.getAffineMaps(), type.getMemorySpace());
+      return r;
+    });
+    // [workaround] need these converters to consider those types legal
+    addConversion([&](mlir::IntegerType type) { return type; });
+    addConversion(
+        [&](mlir::zamalang::LowLFHE::LweCiphertextType type) { return type; });
+  }
+};
+
+void MidLFHEToLowLFHEPass::runOnOperation() {
+  auto op = this->getOperation();
+
+  mlir::ConversionTarget target(getContext());
+  MidLFHEToLowLFHETypeConverter converter;
+
+  // Mark ops from the target dialect as legal operations
+  target.addLegalDialect<mlir::zamalang::LowLFHE::LowLFHEDialect>();
+
+  // Make sure that no ops from `MidLFHE` remain after the lowering
+  target.addIllegalDialect<mlir::zamalang::MidLFHE::MidLFHEDialect>();
+
+  // Make sure that no ops `linalg.generic` that have illegal types
+  target.addDynamicallyLegalOp<mlir::linalg::GenericOp>(
+      [&](mlir::linalg::GenericOp op) {
+        return (converter.isLegal(op.getOperandTypes()) &&
+                converter.isLegal(op.getResultTypes()) &&
+                converter.isLegal(op->getRegion(0).front().getArgumentTypes()));
+      });
+
+  // Make sure that func has legal signature
+  target.addDynamicallyLegalOp<mlir::FuncOp>([](mlir::FuncOp funcOp) {
+    MidLFHEToLowLFHETypeConverter converter;
+    return converter.isSignatureLegal(funcOp.getType()) &&
+           converter.isLegal(&funcOp.getBody());
+  });
+  // Add all patterns required to lower all ops from `MidLFHE` to
+  // `LowLFHE`
+  mlir::OwningRewritePatternList patterns(&getContext());
+
+  populateWithGeneratedMidLFHEToLowLFHE(patterns);
+  patterns
+      .add<LinalgGenericTypeConverterPattern<MidLFHEToLowLFHETypeConverter>>(
+          &getContext(), converter);
+  mlir::populateFuncOpTypeConversionPattern(patterns, converter);
+
+  // Apply conversion
+  if (mlir::applyPartialConversion(op, target, std::move(patterns)).failed()) {
+    this->signalPassFailure();
+  }
+}
+
+namespace mlir {
+namespace zamalang {
+std::unique_ptr<OperationPass<ModuleOp>> createConvertMidLFHEToLowLFHEPass() {
+  return std::make_unique<MidLFHEToLowLFHEPass>();
+}
+} // namespace zamalang
+} // namespace mlir
diff --git a/compiler/lib/Support/CompilerTools.cpp b/compiler/lib/Support/CompilerTools.cpp
index 43bdc7e30..598d9ee65 100644
--- a/compiler/lib/Support/CompilerTools.cpp
+++ b/compiler/lib/Support/CompilerTools.cpp
@@ -37,6 +37,8 @@ mlir::LogicalResult CompilerTools::lowerHLFHEToMlirLLVMDialect(
       pm, mlir::zamalang::createConvertHLFHETensorOpsToLinalg(), enablePass);
   addFilteredPassToPassManager(
       pm, mlir::zamalang::createConvertHLFHEToMidLFHEPass(), enablePass);
+  addFilteredPassToPassManager(
+      pm, mlir::zamalang::createConvertMidLFHEToLowLFHEPass(), enablePass);
   addFilteredPassToPassManager(
       pm, mlir::zamalang::createConvertMLIRLowerableDialectsToLLVMPass(),
       enablePass);
diff --git a/compiler/tests/Conversion/MidLFHEToLowLFHE/add_glwe.mlir b/compiler/tests/Conversion/MidLFHEToLowLFHE/add_glwe.mlir
new file mode 100644
index 000000000..45f1c8d3e
--- /dev/null
+++ b/compiler/tests/Conversion/MidLFHEToLowLFHE/add_glwe.mlir
@@ -0,0 +1,10 @@
+// RUN: zamacompiler --passes midlfhe-to-lowlfhe %s  2>&1| FileCheck %s
+
+// CHECK-LABEL: func @add_glwe(%arg0: !LowLFHE.lwe_ciphertext, %arg1: !LowLFHE.lwe_ciphertext) -> !LowLFHE.lwe_ciphertext
+func @add_glwe(%arg0: !MidLFHE.glwe<{1024,12,64}{7}>, %arg1: !MidLFHE.glwe<{1024,12,64}{7}>) -> !MidLFHE.glwe<{1024,12,64}{7}> {
+  // CHECK-NEXT: %[[V1:.*]] = "LowLFHE.add_lwe_ciphertexts"(%arg0, %arg1) : (!LowLFHE.lwe_ciphertext, !LowLFHE.lwe_ciphertext) -> !LowLFHE.lwe_ciphertext
+  // CHECK-NEXT: return %[[V1]] : !LowLFHE.lwe_ciphertext
+
+  %0 = "MidLFHE.add_glwe"(%arg0, %arg1): (!MidLFHE.glwe<{1024,12,64}{7}>, !MidLFHE.glwe<{1024,12,64}{7}>) -> (!MidLFHE.glwe<{1024,12,64}{7}>)
+  return %0: !MidLFHE.glwe<{1024,12,64}{7}>
+}
diff --git a/compiler/tests/Conversion/MidLFHEToLowLFHE/add_glwe_int.mlir b/compiler/tests/Conversion/MidLFHEToLowLFHE/add_glwe_int.mlir
new file mode 100644
index 000000000..bbb921749
--- /dev/null
+++ b/compiler/tests/Conversion/MidLFHEToLowLFHE/add_glwe_int.mlir
@@ -0,0 +1,22 @@
+// RUN: zamacompiler --passes midlfhe-to-lowlfhe %s  2>&1| FileCheck %s
+
+// CHECK-LABEL: func @add_glwe_const_int(%arg0: !LowLFHE.lwe_ciphertext) -> !LowLFHE.lwe_ciphertext
+func @add_glwe_const_int(%arg0: !MidLFHE.glwe<{1024,1,64}{7}>) -> !MidLFHE.glwe<{1024,1,64}{7}> {
+  // CHECK-NEXT: %[[V1:.*]] = constant 1 : i8
+  // CHECK-NEXT: %[[V2:.*]] = "LowLFHE.encode_int"(%[[V1]]) : (i8) -> !LowLFHE.plaintext<8>
+  // CHECK-NEXT: %[[V3:.*]] = "LowLFHE.add_plaintext_lwe_ciphertext"(%arg0, %[[V2]]) : (!LowLFHE.lwe_ciphertext, !LowLFHE.plaintext<8>) -> !LowLFHE.lwe_ciphertext
+  // CHECK-NEXT: return %[[V3]] : !LowLFHE.lwe_ciphertext
+  %0 = constant 1 : i8
+  %1 = "MidLFHE.add_glwe_int"(%arg0, %0): (!MidLFHE.glwe<{1024,1,64}{7}>, i8) -> (!MidLFHE.glwe<{1024,1,64}{7}>)
+  return %1: !MidLFHE.glwe<{1024,1,64}{7}>
+}
+
+
+// CHECK-LABEL: func @add_glwe_int(%arg0: !LowLFHE.lwe_ciphertext, %arg1: i5) -> !LowLFHE.lwe_ciphertext
+func @add_glwe_int(%arg0: !MidLFHE.glwe<{1024,1,64}{4}>, %arg1: i5) -> !MidLFHE.glwe<{1024,1,64}{4}> {
+  // CHECK-NEXT: %[[V1:.*]] = "LowLFHE.encode_int"(%arg1) : (i5) -> !LowLFHE.plaintext<5>
+  // CHECK-NEXT: %[[V2:.*]] = "LowLFHE.add_plaintext_lwe_ciphertext"(%arg0, %[[V1]]) : (!LowLFHE.lwe_ciphertext, !LowLFHE.plaintext<5>) -> !LowLFHE.lwe_ciphertext
+  // CHECK-NEXT: return %[[V2]] : !LowLFHE.lwe_ciphertext
+  %1 = "MidLFHE.add_glwe_int"(%arg0, %arg1): (!MidLFHE.glwe<{1024,1,64}{4}>, i5) -> (!MidLFHE.glwe<{1024,1,64}{4}>)
+  return %1: !MidLFHE.glwe<{1024,1,64}{4}>
+}
\ No newline at end of file
diff --git a/compiler/tests/Conversion/MidLFHEToLowLFHE/mul_glwe_int.mlir b/compiler/tests/Conversion/MidLFHEToLowLFHE/mul_glwe_int.mlir
new file mode 100644
index 000000000..090316780
--- /dev/null
+++ b/compiler/tests/Conversion/MidLFHEToLowLFHE/mul_glwe_int.mlir
@@ -0,0 +1,22 @@
+// RUN: zamacompiler --passes midlfhe-to-lowlfhe %s  2>&1| FileCheck %s
+
+// CHECK-LABEL: func @mul_glwe_const_int(%arg0: !LowLFHE.lwe_ciphertext) -> !LowLFHE.lwe_ciphertext
+func @mul_glwe_const_int(%arg0: !MidLFHE.glwe<{1024,1,64}{7}>) -> !MidLFHE.glwe<{1024,1,64}{7}> {
+  // CHECK-NEXT: %[[V1:.*]] = constant 1 : i8
+  // CHECK-NEXT: %[[V2:.*]] = "LowLFHE.int_to_cleartext"(%[[V1]]) : (i8) -> !LowLFHE.cleartext<8>
+  // CHECK-NEXT: %[[V3:.*]] = "LowLFHE.mul_cleartext_lwe_ciphertext"(%arg0, %[[V2]]) : (!LowLFHE.lwe_ciphertext, !LowLFHE.cleartext<8>) -> !LowLFHE.lwe_ciphertext
+  // CHECK-NEXT: return %[[V3]] : !LowLFHE.lwe_ciphertext
+  %0 = constant 1 : i8
+  %1 = "MidLFHE.mul_glwe_int"(%arg0, %0): (!MidLFHE.glwe<{1024,1,64}{7}>, i8) -> (!MidLFHE.glwe<{1024,1,64}{7}>)
+  return %1: !MidLFHE.glwe<{1024,1,64}{7}>
+}
+
+
+// CHECK-LABEL: func @mul_glwe_int(%arg0: !LowLFHE.lwe_ciphertext, %arg1: i5) -> !LowLFHE.lwe_ciphertext
+func @mul_glwe_int(%arg0: !MidLFHE.glwe<{1024,1,64}{4}>, %arg1: i5) -> !MidLFHE.glwe<{1024,1,64}{4}> {
+  // CHECK-NEXT: %[[V1:.*]] = "LowLFHE.int_to_cleartext"(%arg1) : (i5) -> !LowLFHE.cleartext<5>
+  // CHECK-NEXT: %[[V2:.*]] = "LowLFHE.mul_cleartext_lwe_ciphertext"(%arg0, %[[V1]]) : (!LowLFHE.lwe_ciphertext, !LowLFHE.cleartext<5>) -> !LowLFHE.lwe_ciphertext
+  // CHECK-NEXT: return %[[V3]] : !LowLFHE.lwe_ciphertext
+  %1 = "MidLFHE.mul_glwe_int"(%arg0, %arg1): (!MidLFHE.glwe<{1024,1,64}{4}>, i5) -> (!MidLFHE.glwe<{1024,1,64}{4}>)
+  return %1: !MidLFHE.glwe<{1024,1,64}{4}>
+}
\ No newline at end of file
diff --git a/compiler/tests/Conversion/MidLFHEToLowLFHE/sub_int_glwe.mlir b/compiler/tests/Conversion/MidLFHEToLowLFHE/sub_int_glwe.mlir
new file mode 100644
index 000000000..c5936cfe9
--- /dev/null
+++ b/compiler/tests/Conversion/MidLFHEToLowLFHE/sub_int_glwe.mlir
@@ -0,0 +1,23 @@
+// RUN: zamacompiler --passes midlfhe-to-lowlfhe %s  2>&1| FileCheck %s
+
+// CHECK-LABEL: func @sub_const_int_glwe(%arg0: !LowLFHE.lwe_ciphertext) -> !LowLFHE.lwe_ciphertext
+func @sub_const_int_glwe(%arg0: !MidLFHE.glwe<{1024,1,64}{7}>) -> !MidLFHE.glwe<{1024,1,64}{7}> {
+  // CHECK-NEXT: %[[V1:.*]] = constant 1 : i8
+  // CHECK-NEXT: %[[NEG:.*]] = "LowLFHE.negate_lwe_ciphertext"(%arg0) : (!LowLFHE.lwe_ciphertext) -> !LowLFHE.lwe_ciphertext
+  // CHECK-NEXT: %[[V2:.*]] = "LowLFHE.encode_int"(%[[V1]]) : (i8) -> !LowLFHE.plaintext<8>
+  // CHECK-NEXT: %[[V3:.*]] = "LowLFHE.add_plaintext_lwe_ciphertext"(%[[NEG]], %[[V2]]) : (!LowLFHE.lwe_ciphertext, !LowLFHE.plaintext<8>) -> !LowLFHE.lwe_ciphertext
+  // CHECK-NEXT: return %[[V3]] : !LowLFHE.lwe_ciphertext
+  %0 = constant 1 : i8
+  %1 = "MidLFHE.sub_int_glwe"(%0, %arg0): (i8, !MidLFHE.glwe<{1024,1,64}{7}>) -> (!MidLFHE.glwe<{1024,1,64}{7}>)
+  return %1: !MidLFHE.glwe<{1024,1,64}{7}>
+}
+
+// CHECK-LABEL: func @sub_int_glwe(%arg0: !LowLFHE.lwe_ciphertext, %arg1: i5) -> !LowLFHE.lwe_ciphertext
+func @sub_int_glwe(%arg0: !MidLFHE.glwe<{1024,1,64}{4}>, %arg1: i5) -> !MidLFHE.glwe<{1024,1,64}{4}> {
+  // CHECK-NEXT: %[[NEG:.*]] = "LowLFHE.negate_lwe_ciphertext"(%arg0) : (!LowLFHE.lwe_ciphertext) -> !LowLFHE.lwe_ciphertext
+  // CHECK-NEXT: %[[V1:.*]] = "LowLFHE.encode_int"(%arg1) : (i5) -> !LowLFHE.plaintext<5>
+  // CHECK-NEXT: %[[V2:.*]] = "LowLFHE.add_plaintext_lwe_ciphertext"(%[[NEG]], %[[V1]]) : (!LowLFHE.lwe_ciphertext, !LowLFHE.plaintext<5>) -> !LowLFHE.lwe_ciphertext
+  // CHECK-NEXT: return %[[V2]] : !LowLFHE.lwe_ciphertext
+  %1 = "MidLFHE.sub_int_glwe"(%arg1, %arg0): (i5, !MidLFHE.glwe<{1024,1,64}{4}>) -> (!MidLFHE.glwe<{1024,1,64}{4}>)
+  return %1: !MidLFHE.glwe<{1024,1,64}{4}>
+}
\ No newline at end of file