diff --git a/compiler/include/zamalang/Conversion/MidLFHEGlobalParametrization/Pass.h b/compiler/include/zamalang/Conversion/MidLFHEGlobalParametrization/Pass.h
new file mode 100644
index 000000000..d2435751c
--- /dev/null
+++ b/compiler/include/zamalang/Conversion/MidLFHEGlobalParametrization/Pass.h
@@ -0,0 +1,18 @@
+
+#ifndef ZAMALANG_CONVERSION_MIDLFHEGLOBALPARAMETRIZATION_PASS_H_
+#define ZAMALANG_CONVERSION_MIDLFHEGLOBALPARAMETRIZATION_PASS_H_
+
+#include "mlir/Pass/Pass.h"
+
+#include "zamalang/Conversion/Utils/GlobalFHEContext.h"
+
+namespace mlir {
+namespace zamalang {
+/// Create a pass to inject fhe parameters to the MidLFHE types and operators.
+std::unique_ptr<OperationPass<ModuleOp>>
+createConvertMidLFHEGlobalParametrizationPass(
+    mlir::zamalang::V0FHEContext &fheContext);
+} // namespace zamalang
+} // namespace mlir
+
+#endif
\ No newline at end of file
diff --git a/compiler/include/zamalang/Conversion/Passes.h b/compiler/include/zamalang/Conversion/Passes.h
index 822ffd108..524fc8985 100644
--- a/compiler/include/zamalang/Conversion/Passes.h
+++ b/compiler/include/zamalang/Conversion/Passes.h
@@ -10,9 +10,11 @@
 #include "zamalang/Conversion/HLFHEToMidLFHE/Pass.h"
 #include "zamalang/Conversion/LowLFHEToConcreteCAPI/Pass.h"
 #include "zamalang/Conversion/MLIRLowerableDialectsToLLVM/Pass.h"
+#include "zamalang/Conversion/MidLFHEGlobalParametrization/Pass.h"
 #include "zamalang/Conversion/MidLFHEToLowLFHE/Pass.h"
 #include "zamalang/Dialect/HLFHE/IR/HLFHEDialect.h"
 #include "zamalang/Dialect/LowLFHE/IR/LowLFHEDialect.h"
+#include "zamalang/Dialect/MidLFHE/IR/MidLFHEDialect.h"
 
 #define GEN_PASS_CLASSES
 #include "zamalang/Conversion/Passes.h.inc"
diff --git a/compiler/include/zamalang/Conversion/Passes.td b/compiler/include/zamalang/Conversion/Passes.td
index 1781abcf6..f4c7f6cd5 100644
--- a/compiler/include/zamalang/Conversion/Passes.td
+++ b/compiler/include/zamalang/Conversion/Passes.td
@@ -17,6 +17,13 @@ def HLFHEToMidLFHE : Pass<"hlfhe-to-midlfhe", "mlir::ModuleOp"> {
   let dependentDialects = ["mlir::linalg::LinalgDialect"];
 }
 
+def MidLFHEGlobalParametrization : Pass<"midlfhe-global-parametrization", "mlir::ModuleOp"> {
+  let summary = "Inject global fhe parameters to the MidLFHE dialect";
+  let constructor = "mlir::zamalang::createConvertMidLFHEToLowLFHEPass()";
+  let options = [];
+  let dependentDialects = ["mlir::zamalang::MidLFHE::MidLFHEDialect"];
+}
+
 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 }];
diff --git a/compiler/lib/Conversion/CMakeLists.txt b/compiler/lib/Conversion/CMakeLists.txt
index 070482fac..c6646bdc9 100644
--- a/compiler/lib/Conversion/CMakeLists.txt
+++ b/compiler/lib/Conversion/CMakeLists.txt
@@ -1,4 +1,5 @@
 add_subdirectory(HLFHEToMidLFHE)
+add_subdirectory(MidLFHEGlobalParametrization)
 add_subdirectory(MidLFHEToLowLFHE)
 add_subdirectory(HLFHETensorOpsToLinalg)
 add_subdirectory(LowLFHEToConcreteCAPI)
diff --git a/compiler/lib/Conversion/MidLFHEGlobalParametrization/CMakeLists.txt b/compiler/lib/Conversion/MidLFHEGlobalParametrization/CMakeLists.txt
new file mode 100644
index 000000000..1094979d8
--- /dev/null
+++ b/compiler/lib/Conversion/MidLFHEGlobalParametrization/CMakeLists.txt
@@ -0,0 +1,15 @@
+add_mlir_dialect_library(MidLFHEGlobalParametrization
+MidLFHEGlobalParametrization.cpp
+
+  ADDITIONAL_HEADER_DIRS
+  ${PROJECT_SOURCE_DIR}/include/zamalang/Dialect/MidLFHE
+
+  DEPENDS
+  MidLFHEDialect
+
+  LINK_LIBS PUBLIC
+  MLIRIR
+  MLIRTransforms
+)
+
+target_link_libraries(MidLFHEGlobalParametrization PUBLIC MLIRIR)
diff --git a/compiler/lib/Conversion/MidLFHEGlobalParametrization/MidLFHEGlobalParametrization.cpp b/compiler/lib/Conversion/MidLFHEGlobalParametrization/MidLFHEGlobalParametrization.cpp
new file mode 100644
index 000000000..bb721c20a
--- /dev/null
+++ b/compiler/lib/Conversion/MidLFHEGlobalParametrization/MidLFHEGlobalParametrization.cpp
@@ -0,0 +1,198 @@
+#include <iostream>
+
+#include "mlir/Pass/Pass.h"
+#include "mlir/Transforms/DialectConversion.h"
+
+#include "zamalang/Conversion/Passes.h"
+#include "zamalang/Dialect/MidLFHE/IR/MidLFHEDialect.h"
+#include "zamalang/Dialect/MidLFHE/IR/MidLFHEOps.h"
+#include "zamalang/Dialect/MidLFHE/IR/MidLFHETypes.h"
+
+namespace {
+struct MidLFHEGlobalParametrizationPass
+    : public MidLFHEGlobalParametrizationBase<
+          MidLFHEGlobalParametrizationPass> {
+  MidLFHEGlobalParametrizationPass(mlir::zamalang::V0FHEContext &fheContext)
+      : fheContext(fheContext){};
+  void runOnOperation() final;
+  mlir::zamalang::V0FHEContext &fheContext;
+};
+} // namespace
+
+using mlir::zamalang::MidLFHE::GLWECipherTextType;
+
+/// MidLFHEGlobalParametrizationTypeConverter is a TypeConverter that transform
+/// `MidLFHE.gwle<{_,_,_}{p}>` to
+/// `MidLFHE.gwle<{glweSize,polynomialSize,bits}{p'}>`
+class MidLFHEGlobalParametrizationTypeConverter : public mlir::TypeConverter {
+
+public:
+  MidLFHEGlobalParametrizationTypeConverter(
+      mlir::zamalang::V0FHEContext &fheContext) {
+    addConversion([](mlir::Type type) { return type; });
+    addConversion([&](GLWECipherTextType type) {
+      auto glweSize = fheContext.parameter.getNBigGlweSize();
+      auto p = fheContext.constraint.p;
+      if (type.getDimension() == glweSize && type.getP() == p) {
+        return type;
+      }
+      return GLWECipherTextType::get(type.getContext(), glweSize,
+                                     1 /*for the v0, is always lwe ciphertext*/,
+                                     64 /*for the v0 we handle only q=64*/, p);
+    });
+  }
+};
+
+template <typename Op>
+struct MidLFHEOpTypeConversionPattern : public mlir::OpRewritePattern<Op> {
+  MidLFHEOpTypeConversionPattern(mlir::MLIRContext *context,
+                                 mlir::TypeConverter &typeConverter,
+                                 mlir::PatternBenefit benefit = 1)
+      : mlir::OpRewritePattern<Op>(context, benefit),
+        typeConverter(typeConverter) {}
+
+  mlir::LogicalResult
+  matchAndRewrite(Op op, mlir::PatternRewriter &rewriter) const override {
+    mlir::SmallVector<mlir::Type, 1> newResultTypes;
+    if (typeConverter.convertTypes(op->getResultTypes(), newResultTypes)
+            .failed()) {
+      return mlir::failure();
+    }
+    rewriter.replaceOpWithNewOp<Op>(op, newResultTypes, op->getOperands());
+    return mlir::success();
+  };
+
+private:
+  mlir::TypeConverter &typeConverter;
+};
+
+struct MidLFHEApplyLookupTableParametrizationPattern
+    : public mlir::OpRewritePattern<mlir::zamalang::MidLFHE::ApplyLookupTable> {
+  MidLFHEApplyLookupTableParametrizationPattern(
+      mlir::MLIRContext *context, mlir::TypeConverter &typeConverter,
+      mlir::zamalang::V0Parameter &v0Parameter,
+      mlir::PatternBenefit benefit = 1)
+      : mlir::OpRewritePattern<mlir::zamalang::MidLFHE::ApplyLookupTable>(
+            context, benefit),
+        typeConverter(typeConverter), v0Parameter(v0Parameter) {}
+
+  mlir::LogicalResult
+  matchAndRewrite(mlir::zamalang::MidLFHE::ApplyLookupTable op,
+                  mlir::PatternRewriter &rewriter) const override {
+    mlir::SmallVector<mlir::Type, 1> newResultTypes;
+    if (typeConverter.convertTypes(op->getResultTypes(), newResultTypes)
+            .failed()) {
+      return mlir::failure();
+    }
+
+    mlir::SmallVector<mlir::NamedAttribute, 6> newAttributes{
+        mlir::NamedAttribute(rewriter.getIdentifier("k"),
+                             rewriter.getI32IntegerAttr(v0Parameter.k)),
+        mlir::NamedAttribute(
+            rewriter.getIdentifier("polynomialSize"),
+            rewriter.getI32IntegerAttr(v0Parameter.polynomialSize)),
+        mlir::NamedAttribute(rewriter.getIdentifier("levelKS"),
+                             rewriter.getI32IntegerAttr(v0Parameter.ksLevel)),
+        mlir::NamedAttribute(rewriter.getIdentifier("baseLogKS"),
+                             rewriter.getI32IntegerAttr(v0Parameter.ksLogBase)),
+        mlir::NamedAttribute(rewriter.getIdentifier("levelBS"),
+                             rewriter.getI32IntegerAttr(v0Parameter.brLevel)),
+        mlir::NamedAttribute(rewriter.getIdentifier("baseLogBS"),
+                             rewriter.getI32IntegerAttr(v0Parameter.brLogBase)),
+    };
+
+    rewriter.replaceOpWithNewOp<mlir::zamalang::MidLFHE::ApplyLookupTable>(
+        op, newResultTypes, op->getOperands(), newAttributes);
+
+    return mlir::success();
+  };
+
+private:
+  mlir::TypeConverter &typeConverter;
+  mlir::zamalang::V0Parameter &v0Parameter;
+};
+
+template <typename Op>
+void populateWithMidLFHEOpTypeConversionPattern(
+    mlir::RewritePatternSet &patterns, mlir::ConversionTarget &target,
+    mlir::TypeConverter &typeConverter) {
+  patterns.add<MidLFHEOpTypeConversionPattern<Op>>(patterns.getContext(),
+                                                   typeConverter);
+  target.addDynamicallyLegalOp<Op>(
+      [&](Op op) { return typeConverter.isLegal(op->getResultTypes()); });
+}
+
+void populateWithMidLFHEApplyLookupTableParametrizationPattern(
+    mlir::RewritePatternSet &patterns, mlir::ConversionTarget &target,
+    mlir::TypeConverter &typeConverter,
+    mlir::zamalang::V0Parameter &v0Parameter) {
+  patterns.add<MidLFHEApplyLookupTableParametrizationPattern>(
+      patterns.getContext(), typeConverter, v0Parameter);
+  target.addDynamicallyLegalOp<mlir::zamalang::MidLFHE::ApplyLookupTable>(
+      [&](mlir::zamalang::MidLFHE::ApplyLookupTable op) {
+        if (op.k() != v0Parameter.k ||
+            op.polynomialSize() != v0Parameter.polynomialSize ||
+            op.levelKS() != v0Parameter.ksLevel ||
+            op.baseLogKS() != v0Parameter.ksLogBase ||
+            op.levelBS() != v0Parameter.brLevel ||
+            op.baseLogBS() != v0Parameter.brLogBase) {
+          return false;
+        }
+        return typeConverter.isLegal(op->getResultTypes());
+      });
+}
+
+/// Populate the RewritePatternSet with all patterns that rewrite LowLFHE
+/// operators to the corresponding function call to the `Concrete C API`.
+void populateWithMidLFHEOpTypeConversionPatterns(
+    mlir::RewritePatternSet &patterns, mlir::ConversionTarget &target,
+    mlir::TypeConverter &typeConverter,
+    mlir::zamalang::V0Parameter &v0Parameter) {
+  populateWithMidLFHEOpTypeConversionPattern<
+      mlir::zamalang::MidLFHE::AddGLWEIntOp>(patterns, target, typeConverter);
+  populateWithMidLFHEOpTypeConversionPattern<
+      mlir::zamalang::MidLFHE::AddGLWEOp>(patterns, target, typeConverter);
+  populateWithMidLFHEOpTypeConversionPattern<
+      mlir::zamalang::MidLFHE::SubIntGLWEOp>(patterns, target, typeConverter);
+  populateWithMidLFHEOpTypeConversionPattern<
+      mlir::zamalang::MidLFHE::MulGLWEIntOp>(patterns, target, typeConverter);
+  populateWithMidLFHEApplyLookupTableParametrizationPattern(
+      patterns, target, typeConverter, v0Parameter);
+}
+
+void MidLFHEGlobalParametrizationPass::runOnOperation() {
+  auto op = this->getOperation();
+
+  mlir::ConversionTarget target(getContext());
+  MidLFHEGlobalParametrizationTypeConverter converter(fheContext);
+
+  // Make sure that no ops from `MidLFHE` remain after the lowering
+  target.addIllegalDialect<mlir::zamalang::MidLFHE::MidLFHEDialect>();
+
+  // Make sure func has legal signature
+  target.addDynamicallyLegalOp<mlir::FuncOp>([&](mlir::FuncOp funcOp) {
+    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());
+  populateWithMidLFHEOpTypeConversionPatterns(patterns, target, converter,
+                                              fheContext.parameter);
+  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>>
+createConvertMidLFHEGlobalParametrizationPass(
+    mlir::zamalang::V0FHEContext &fheContext) {
+  return std::make_unique<MidLFHEGlobalParametrizationPass>(fheContext);
+}
+} // namespace zamalang
+} // namespace mlir
diff --git a/compiler/lib/Support/CompilerTools.cpp b/compiler/lib/Support/CompilerTools.cpp
index 9334b1186..f7d5853b8 100644
--- a/compiler/lib/Support/CompilerTools.cpp
+++ b/compiler/lib/Support/CompilerTools.cpp
@@ -44,7 +44,9 @@ mlir::LogicalResult CompilerTools::lowerHLFHEToMlirStdsDialect(
   addFilteredPassToPassManager(
       pm, mlir::zamalang::createConvertHLFHEToMidLFHEPass(), enablePass);
   addFilteredPassToPassManager(
-      pm, mlir::zamalang::createConvertHLFHEToMidLFHEPass(), enablePass);
+      pm,
+      mlir::zamalang::createConvertMidLFHEGlobalParametrizationPass(fheContext),
+      enablePass);
   addFilteredPassToPassManager(
       pm, mlir::zamalang::createConvertMidLFHEToLowLFHEPass(), enablePass);
   addFilteredPassToPassManager(
diff --git a/compiler/tests/RunJit/hlfhe_add_eint_int_6.mlir b/compiler/tests/RunJit/hlfhe_add_eint_int_6.mlir
new file mode 100644
index 000000000..88f86fc7c
--- /dev/null
+++ b/compiler/tests/RunJit/hlfhe_add_eint_int_6.mlir
@@ -0,0 +1,7 @@
+// RUN: zamacompiler %s --run-jit --jit-args 10 --jit-args 54 2>&1| FileCheck %s
+
+// CHECK-LABEL: 64
+func @main(%arg0: !HLFHE.eint<6>, %arg1: i7) -> !HLFHE.eint<6> {
+  %1 = "HLFHE.add_eint_int"(%arg0, %arg1): (!HLFHE.eint<6>, i7) -> (!HLFHE.eint<6>)
+  return %1: !HLFHE.eint<6>
+}
\ No newline at end of file
diff --git a/compiler/tests/RunJit/hlfhe_add_eint_int.mlir b/compiler/tests/RunJit/hlfhe_add_eint_int_7.mlir
similarity index 63%
rename from compiler/tests/RunJit/hlfhe_add_eint_int.mlir
rename to compiler/tests/RunJit/hlfhe_add_eint_int_7.mlir
index 0898b77bd..719302f5b 100644
--- a/compiler/tests/RunJit/hlfhe_add_eint_int.mlir
+++ b/compiler/tests/RunJit/hlfhe_add_eint_int_7.mlir
@@ -1,6 +1,6 @@
-// RUN: zamacompiler %s --run-jit --jit-args 12 --jit-args 30 2>&1| FileCheck %s
+// RUN: zamacompiler %s --run-jit --jit-args 100 --jit-args 27 2>&1| FileCheck %s
 
-// CHECK-LABEL: 42
+// CHECK-LABEL: 127
 func @main(%arg0: !HLFHE.eint<7>, %arg1: i8) -> !HLFHE.eint<7> {
   %1 = "HLFHE.add_eint_int"(%arg0, %arg1): (!HLFHE.eint<7>, i8) -> (!HLFHE.eint<7>)
   return %1: !HLFHE.eint<7>