diff --git a/compiler/include/zamalang/Dialect/MidLFHE/IR/MidLFHEOps.td b/compiler/include/zamalang/Dialect/MidLFHE/IR/MidLFHEOps.td
index fb60dfeba..be0ac6b25 100644
--- a/compiler/include/zamalang/Dialect/MidLFHE/IR/MidLFHEOps.td
+++ b/compiler/include/zamalang/Dialect/MidLFHE/IR/MidLFHEOps.td
@@ -42,6 +42,10 @@ def MulPlainOp : MidLFHE_Op<"mul_plain"> {
             build($_builder, $_state, a.getType(), a, b);
         }]>
     ];
+
+    let verifier = [{
+        return ::mlir::zamalang::verifyMulPlainOp(*this);
+    }];
 }
 
 def HAddOp : MidLFHE_Op<"h_add"> {
@@ -53,6 +57,10 @@ def HAddOp : MidLFHE_Op<"h_add"> {
             build($_builder, $_state, a.getType(), a, b);
         }]>
     ];
+
+    let verifier = [{
+        return ::mlir::zamalang::verifyHAddOp(*this);
+    }];
 }
 
 
diff --git a/compiler/include/zamalang/Dialect/MidLFHE/IR/MidLFHETypes.h b/compiler/include/zamalang/Dialect/MidLFHE/IR/MidLFHETypes.h
index 9c119fed4..8dff854ca 100644
--- a/compiler/include/zamalang/Dialect/MidLFHE/IR/MidLFHETypes.h
+++ b/compiler/include/zamalang/Dialect/MidLFHE/IR/MidLFHETypes.h
@@ -2,6 +2,7 @@
 #define ZAMALANG_DIALECT_MIDLFHE_IR_MIDLFHETYPES_H
 
 #include "llvm/ADT/TypeSwitch.h"
+#include <mlir/Dialect/StandardOps/IR/Ops.h>
 #include <mlir/IR/BuiltinOps.h>
 #include <mlir/IR/BuiltinTypes.h>
 #include <mlir/IR/DialectImplementation.h>
diff --git a/compiler/include/zamalang/Dialect/MidLFHE/IR/MidLFHETypes.td b/compiler/include/zamalang/Dialect/MidLFHE/IR/MidLFHETypes.td
index 24d77d8cb..756d00a40 100644
--- a/compiler/include/zamalang/Dialect/MidLFHE/IR/MidLFHETypes.td
+++ b/compiler/include/zamalang/Dialect/MidLFHE/IR/MidLFHETypes.td
@@ -121,9 +121,11 @@ def GLWECipherTextType : MidLFHE_Type<"GLWECipherText"> {
 
         if ($_parser.parseGreater())
             return Type();
-
-        return get($_ctxt, dimension, polynomialSize, bits, paddingBits, p, phantomBits, scalingFactor, log2StdDev);
+        Location loc = $_parser.getEncodedSourceLoc($_parser.getNameLoc());
+        return getChecked(loc, loc.getContext(), dimension, polynomialSize, bits, paddingBits, p, phantomBits, scalingFactor, log2StdDev);
     }];
+
+    let genVerifyDecl = true;
 }
 
 #endif
diff --git a/compiler/lib/Dialect/MidLFHE/IR/MidLFHEDialect.cpp b/compiler/lib/Dialect/MidLFHE/IR/MidLFHEDialect.cpp
index 3e7f5f5fd..e81d9415d 100644
--- a/compiler/lib/Dialect/MidLFHE/IR/MidLFHEDialect.cpp
+++ b/compiler/lib/Dialect/MidLFHE/IR/MidLFHEDialect.cpp
@@ -37,3 +37,75 @@ void MidLFHEDialect::printType(::mlir::Type type,
   // TODO - What should be done here?
   printer << "unknwontype";
 }
+
+/*
+ * Returns the nubmer of bits from the log2StdDev parameter of a GLWE.
+ * This is widely inspired by the rust version on concrete:
+ *
+ * pub fn nb_bit_from_variance_99(var: f64, torus_bit: usize) -> usize {
+ *     // compute sigma
+ *     let sigma: f64 = f64::sqrt(var);
+ *
+ *     // the constant to get 99% of the normal distribution
+ *     let z: f64 = 3.;
+ *     let tmp = torus_bit as f64 + f64::log2(sigma * z);
+ *     if tmp < 0. {
+ *         // means no bits are affected by the noise in the integer
+ * representation (discrete space) 0usize } else { tmp.ceil() as usize
+ *     }
+ * }
+ */
+unsigned nbBitsFromLog2StdDev(signed log2StdDev, signed bits) {
+  long double sigma = std::pow(2, log2StdDev);
+  long double z = 3;
+  long double tmp = bits + std::log2(sigma * z);
+  if (tmp < 0.) {
+    return 0;
+  }
+  return std::ceil(tmp);
+}
+
+/**
+ * Verify that GLWE parameter are consistant, the layout of the ciphertext is
+ * organized like that.
+ *
+ * [0 0 0 0 0 0 0 0 X X X X X X X M M M M M M M X X X X X X X X 0 0 0 0 0 0 0 E
+ * E E E E E E E E E E E E] ^ paddingBits ^               ^      p    ^ ^
+ * phantomBits ^               ^ nb_bits of log2StdDev ^ ^ scalingFactor We
+ * verify :
+ * - The bits parameter is 32 or 64 (we support only this value for now)
+ * - The message is not overlaped by the error
+ * - The message is still in the ciphertext
+ */
+::mlir::LogicalResult GLWECipherTextType::verify(
+    ::llvm::function_ref<::mlir::InFlightDiagnostic()> emitError,
+    signed dimension, signed polynomialSize, signed bits, signed paddingBits,
+    signed p, signed phantomBits, signed scalingFactor, signed log2StdDev) {
+  if (bits != -1 && bits != 32 && bits != 64) {
+    emitError() << "GLWE bits parameter can only be 32 or 64";
+    return ::mlir::failure();
+  }
+  if (bits != -1 && log2StdDev != -1 && scalingFactor != -1 &&
+      phantomBits != -1) {
+    unsigned errBits = nbBitsFromLog2StdDev(log2StdDev, bits);
+    if (errBits > scalingFactor + phantomBits) {
+      emitError() << "GLWE error overlap message, errBits(" << errBits
+                  << ") > scalingFactor(" << scalingFactor << ") + phantomBits("
+                  << phantomBits << ")";
+      return ::mlir::failure();
+    }
+  }
+  if (bits != -1 && paddingBits != -1 && p != -1 && phantomBits != -1 &&
+      scalingFactor != -1) {
+    signed int phantomLeft =
+        (bits - scalingFactor) - phantomBits - p - paddingBits;
+    if (phantomLeft < 0) {
+      // TODO: better message ...
+      emitError() << "GLWE message cannot be represented "
+                  << (bits - scalingFactor) << "vs"
+                  << (phantomBits - p - paddingBits);
+      return ::mlir::failure();
+    }
+  }
+  return ::mlir::success();
+}
diff --git a/compiler/lib/Dialect/MidLFHE/IR/MidLFHEOps.cpp b/compiler/lib/Dialect/MidLFHE/IR/MidLFHEOps.cpp
index b0842acd3..7d126e910 100644
--- a/compiler/lib/Dialect/MidLFHE/IR/MidLFHEOps.cpp
+++ b/compiler/lib/Dialect/MidLFHE/IR/MidLFHEOps.cpp
@@ -7,6 +7,8 @@ namespace mlir {
 namespace zamalang {
 using ::mlir::zamalang::MidLFHE::AddPlainOp;
 using ::mlir::zamalang::MidLFHE::GLWECipherTextType;
+using ::mlir::zamalang::MidLFHE::HAddOp;
+using ::mlir::zamalang::MidLFHE::MulPlainOp;
 
 bool predPBSRegion(::mlir::Region &region) {
   if (region.getBlocks().size() != 1) {
@@ -93,6 +95,169 @@ bool verifyAddResultHasSameParameters(::mlir::OpState &op,
   return ::mlir::success();
 }
 
+bool verifyHAddResultPadding(::mlir::OpState &op, GLWECipherTextType &inA,
+                             GLWECipherTextType &inB, GLWECipherTextType &out) {
+  // If the inputs has no value of paddingBits that doesn't constraint output.
+  if (inA.getPaddingBits() == -1 && inB.getPaddingBits() == -1) {
+    return true;
+  }
+  return verifyAddResultPadding(op, inA, out);
+}
+
+int hAddLog2StdDevOfResult(int a, int b) {
+  long double va = std::pow(std::pow(2, a), 2);
+  long double vb = std::pow(std::pow(2, b), 2);
+  long double vr = va + vb;
+  return std::log2(::sqrt(vr));
+}
+
+bool verifyHAddResultLog2StdDev(::mlir::OpState &op, GLWECipherTextType &inA,
+                                GLWECipherTextType &inB,
+                                GLWECipherTextType &out) {
+  // If the inputs has no value of log2StdDev that doesn't constraint output.
+  if (inA.getLog2StdDev() == -1 && inB.getLog2StdDev() == -1) {
+    return true;
+  }
+  int expectedLog2StdDev =
+      hAddLog2StdDevOfResult(inA.getLog2StdDev(), inB.getLog2StdDev());
+  if (out.getLog2StdDev() != expectedLog2StdDev) {
+    ::llvm::Twine msg(
+        "has unexpected log2StdDev parameter of its GLWE result, expected:");
+    op.emitOpError(msg.concat(::llvm::Twine(expectedLog2StdDev)));
+    return false;
+  }
+  return true;
+}
+
+bool verifyHAddSameGLWEParameter(::mlir::OpState &op, GLWECipherTextType &inA,
+                                 GLWECipherTextType &inB,
+                                 GLWECipherTextType &out) {
+  if (inA.getDimension() != inB.getDimension() ||
+      inA.getDimension() != out.getDimension()) {
+    emitOpErrorForIncompatibleGLWEParameter(op, "dimension");
+    return false;
+  }
+  if (inA.getPolynomialSize() != inB.getPolynomialSize() &&
+      inA.getPolynomialSize() != out.getPolynomialSize()) {
+    emitOpErrorForIncompatibleGLWEParameter(op, "polynomialSize");
+    return false;
+  }
+  if (inA.getBits() != inB.getBits() && inA.getBits() != out.getBits()) {
+    emitOpErrorForIncompatibleGLWEParameter(op, "bits");
+    return false;
+  }
+  if (inA.getP() != inB.getP() && inA.getP() != out.getP()) {
+    emitOpErrorForIncompatibleGLWEParameter(op, "p");
+    return false;
+  }
+  if (inA.getPhantomBits() != inB.getPhantomBits() &&
+      inA.getPhantomBits() != out.getPhantomBits()) {
+    emitOpErrorForIncompatibleGLWEParameter(op, "phantomBits");
+    return false;
+  }
+  if (inA.getScalingFactor() && inB.getScalingFactor() &&
+      inA.getScalingFactor() != out.getScalingFactor()) {
+    emitOpErrorForIncompatibleGLWEParameter(op, "scalingFactor");
+    return false;
+  }
+  return true;
+}
+
+::mlir::LogicalResult verifyHAddOp(HAddOp &op) {
+  GLWECipherTextType inA = op.a().getType().cast<GLWECipherTextType>();
+  GLWECipherTextType inB = op.b().getType().cast<GLWECipherTextType>();
+  GLWECipherTextType out = op.getResult().getType().cast<GLWECipherTextType>();
+  if (!verifyHAddResultPadding(op, inA, inB, out)) {
+    return ::mlir::failure();
+  }
+  if (!verifyHAddResultLog2StdDev(op, inA, inB, out)) {
+    return ::mlir::failure();
+  }
+  if (!verifyHAddSameGLWEParameter(op, inA, inB, out)) {
+    return ::mlir::failure();
+  }
+  return ::mlir::success();
+}
+
+bool verifyMulPlainOpPadding(::mlir::OpState &op, GLWECipherTextType &inA,
+                             ::mlir::Value &inB, GLWECipherTextType &out) {
+  if (inA.getPaddingBits() == -1) {
+    return true;
+  }
+  if (inA.getPaddingBits() == 0) {
+    if (out.getPaddingBits() != 0) {
+      op.emitError(
+          "the result shoud have 0 paddingBits has input has 0 paddingBits");
+      return false;
+    }
+    return true;
+  }
+  unsigned int additionalBit = 0;
+  ::mlir::ConstantIntOp constantOp = inB.getDefiningOp<::mlir::ConstantIntOp>();
+  if (constantOp != nullptr) {
+    int64_t value = constantOp.getValue();
+    additionalBit = std::ceil(std::log2(value)) + 1;
+  } else {
+    ::mlir::IntegerType tyB = inB.getType().cast<::mlir::IntegerType>();
+    additionalBit = tyB.getIntOrFloatBitWidth();
+  }
+  unsigned int expectedPadding = inA.getPaddingBits() - additionalBit;
+  if (out.getPaddingBits() != expectedPadding) {
+    ::llvm::Twine msg(
+        "has unexpected padding parameter of its GLWE result, expected:");
+    op.emitOpError(msg.concat(::llvm::Twine(expectedPadding)));
+    return false;
+  }
+  return true;
+}
+
+bool verifyMulPlainResultHasSameParameters(::mlir::OpState &op,
+                                           GLWECipherTextType &in,
+                                           GLWECipherTextType &out) {
+  if (in.getDimension() != out.getDimension()) {
+    emitOpErrorForIncompatibleGLWEParameter(op, "dimension");
+    return false;
+  }
+  if (in.getPolynomialSize() != out.getPolynomialSize()) {
+    emitOpErrorForIncompatibleGLWEParameter(op, "polynomialSize");
+    return false;
+  }
+  if (in.getBits() != out.getBits()) {
+    emitOpErrorForIncompatibleGLWEParameter(op, "bits");
+    return false;
+  }
+  if (in.getP() != out.getP()) {
+    emitOpErrorForIncompatibleGLWEParameter(op, "p");
+    return false;
+  }
+  if (in.getPhantomBits() != out.getPhantomBits()) {
+    emitOpErrorForIncompatibleGLWEParameter(op, "phantomBits");
+    return false;
+  }
+  if (in.getScalingFactor() != out.getScalingFactor()) {
+    emitOpErrorForIncompatibleGLWEParameter(op, "scalingFactor");
+    return false;
+  }
+  if (in.getLog2StdDev() != out.getLog2StdDev()) {
+    emitOpErrorForIncompatibleGLWEParameter(op, "log2StdDev");
+    return false;
+  }
+  return true;
+}
+
+::mlir::LogicalResult verifyMulPlainOp(MulPlainOp &op) {
+  GLWECipherTextType inA = op.a().getType().cast<GLWECipherTextType>();
+  ::mlir::Value inB = op.b();
+  GLWECipherTextType out = op.getResult().getType().cast<GLWECipherTextType>();
+  if (!verifyMulPlainOpPadding(op, inA, inB, out)) {
+    return ::mlir::failure();
+  }
+  if (!verifyMulPlainResultHasSameParameters(op, inA, out)) {
+    return ::mlir::failure();
+  }
+  return ::mlir::success();
+}
+
 } // namespace zamalang
 } // namespace mlir
 
diff --git a/compiler/tests/Dialect/MidLFHE/op_add_plain.mlir b/compiler/tests/Dialect/MidLFHE/op_add_plain.mlir
index dc0cc8d22..2501b1478 100644
--- a/compiler/tests/Dialect/MidLFHE/op_add_plain.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_add_plain.mlir
@@ -1,23 +1,23 @@
 // RUN: zamacompiler %s  2>&1| FileCheck %s
 
-// CHECK-LABEL: func @add_plain_no_padding(%arg0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
-func @add_plain_no_padding(%arg0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}> {
+// CHECK-LABEL: func @add_plain_no_padding(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}>
+func @add_plain_no_padding(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}> {
   // CHECK-NEXT: %[[V1:.*]] = constant 1 : i32
-  // CHECK-NEXT: %[[V2:.*]] = "MidLFHE.add_plain"(%arg0, %[[V1]]) : (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, i32) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
-  // CHECK-NEXT: return %[[V2]] : !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
+  // CHECK-NEXT: %[[V2:.*]] = "MidLFHE.add_plain"(%arg0, %[[V1]]) : (!MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}>, i32) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}>
+  // CHECK-NEXT: return %[[V2]] : !MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}>
 
   %0 = constant 1 : i32
-  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>)
-  return %1: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
+  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}>
 }
 
-// CHECK-LABEL: func @add_plain_padding(%arg0: !MidLFHE.glwe<{1024,12,-64}{2,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{1,7,0,32,-25}>
-func @add_plain_padding(%arg0: !MidLFHE.glwe<{1024,12,-64}{2,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{1,7,0,32,-25}> {
+// CHECK-LABEL: func @add_plain_padding(%arg0: !MidLFHE.glwe<{1024,12,64}{2,7,0,41,-25}>) -> !MidLFHE.glwe<{1024,12,64}{1,7,0,41,-25}>
+func @add_plain_padding(%arg0: !MidLFHE.glwe<{1024,12,64}{2,7,0,41,-25}>) -> !MidLFHE.glwe<{1024,12,64}{1,7,0,41,-25}> {
   // CHECK-NEXT: %[[V1:.*]] = constant 1 : i32
-  // CHECK-NEXT: %[[V2:.*]] = "MidLFHE.add_plain"(%arg0, %[[V1]]) : (!MidLFHE.glwe<{1024,12,-64}{2,7,0,32,-25}>, i32) -> !MidLFHE.glwe<{1024,12,-64}{1,7,0,32,-25}>
-  // CHECK-NEXT: return %[[V2]] : !MidLFHE.glwe<{1024,12,-64}{1,7,0,32,-25}>
+  // CHECK-NEXT: %[[V2:.*]] = "MidLFHE.add_plain"(%arg0, %[[V1]]) : (!MidLFHE.glwe<{1024,12,64}{2,7,0,41,-25}>, i32) -> !MidLFHE.glwe<{1024,12,64}{1,7,0,41,-25}>
+  // CHECK-NEXT: return %[[V2]] : !MidLFHE.glwe<{1024,12,64}{1,7,0,41,-25}>
 
   %0 = constant 1 : i32
-  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,-64}{2,7,0,32,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,-64}{1,7,0,32,-25}>)
-  return %1: !MidLFHE.glwe<{1024,12,-64}{1,7,0,32,-25}>
+  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{2,7,0,41,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{1,7,0,41,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{1,7,0,41,-25}>
 }
diff --git a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_bits.mlir b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_bits.mlir
index 6501e51ae..a8a9a5269 100644
--- a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_bits.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_bits.mlir
@@ -1,8 +1,8 @@
 // RUN: not zamacompiler %s 2>&1| FileCheck %s
 
 // CHECK-LABEL: should have the same GLWE bits parameter
-func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,32}{0,7,0,32,-25}> {
+func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}> {
   %0 = constant 1 : i32
-  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,32}{0,7,0,32,-25}>)
-  return %1: !MidLFHE.glwe<{1024,12,32}{0,7,0,32,-25}>
+  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,32}{0,7,0,25,-82}>)
+  return %1: !MidLFHE.glwe<{1024,12,32}{0,7,0,25,-82}>
 }
diff --git a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_dimension.mlir b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_dimension.mlir
index 8d0a5af9e..9fe56cecf 100644
--- a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_dimension.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_dimension.mlir
@@ -1,8 +1,8 @@
 // RUN: not zamacompiler %s 2>&1| FileCheck %s
 
 // CHECK-LABEL: error: should have the same GLWE dimension parameter
-func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1023,12,64}{0,7,0,32,-25}> {
+func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>) -> !MidLFHE.glwe<{1023,12,64}{0,7,0,57,-25}> {
   %0 = constant 1 : i32
-  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>, i32) -> (!MidLFHE.glwe<{1023,12,64}{0,7,0,32,-25}>)
-  return %1: !MidLFHE.glwe<{1023,12,64}{0,7,0,32,-25}>
+  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>, i32) -> (!MidLFHE.glwe<{1023,12,64}{0,7,0,57,-25}>)
+  return %1: !MidLFHE.glwe<{1023,12,64}{0,7,0,57,-25}>
 }
diff --git a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_log2StdDev.mlir b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_log2StdDev.mlir
index 531c42001..01fbe252f 100644
--- a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_log2StdDev.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_log2StdDev.mlir
@@ -1,8 +1,8 @@
 // RUN: not zamacompiler %s 2>&1| FileCheck %s
 
 // CHECK-LABEL: should have the same GLWE log2StdDev parameter
-func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,32,-29}> {
+func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-29}> {
   %0 = constant 1 : i32
-  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,7,0,32,-29}>)
-  return %1: !MidLFHE.glwe<{1024,12,64}{0,7,0,32,-29}>
+  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,7,0,57,-29}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-29}>
 }
\ No newline at end of file
diff --git a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_p.mlir b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_p.mlir
index 2f4ea64cf..a991338bf 100644
--- a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_p.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_p.mlir
@@ -1,8 +1,8 @@
 // RUN: not zamacompiler %s 2>&1| FileCheck %s
 
 // CHECK-LABEL: should have the same GLWE p parameter
-func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,6,0,32,-25}> {
+func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,6,0,57,-25}> {
   %0 = constant 1 : i32
-  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,6,0,32,-25}>)
-  return %1: !MidLFHE.glwe<{1024,12,64}{0,6,0,32,-25}>
+  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,6,0,57,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{0,6,0,57,-25}>
 }
diff --git a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_padding1.mlir b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_padding1.mlir
index d2af370a3..a354677c4 100644
--- a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_padding1.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_padding1.mlir
@@ -1,8 +1,8 @@
 // RUN: not zamacompiler %s 2>&1| FileCheck %s
 
 // CHECK-LABEL: error: the result shoud have 0 paddingBits has input has 0 paddingBits
-func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,64}{1,7,0,32,-25}> {
+func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> !MidLFHE.glwe<{1024,12,64}{1,7,0,50,-25}> {
   %0 = constant 1 : i32
-  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{1,7,0,32,-25}>)
-  return %1: !MidLFHE.glwe<{1024,12,64}{1,7,0,32,-25}>
+  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{1,7,0,50,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{1,7,0,50,-25}>
 }
\ No newline at end of file
diff --git a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_padding2.mlir b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_padding2.mlir
index e8308da48..9d78e1feb 100644
--- a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_padding2.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_padding2.mlir
@@ -1,8 +1,8 @@
 // RUN: not zamacompiler %s 2>&1| FileCheck %s
 
 // CHECK-LABEL: error: the result should have one less padding bit than the input
-func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{2,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,64}{2,7,0,32,-25}> {
+func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{2,7,0,51,-25}>) -> !MidLFHE.glwe<{1024,12,64}{2,7,0,51,-25}> {
   %0 = constant 1 : i32
-  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{2,7,0,32,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{2,7,0,32,-25}>)
-  return %1: !MidLFHE.glwe<{1024,12,64}{2,7,0,32,-25}>
+  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{2,7,0,51,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{2,7,0,51,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{2,7,0,51,-25}>
 }
\ No newline at end of file
diff --git a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_phantomBits.mlir b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_phantomBits.mlir
index c9e629443..441107e06 100644
--- a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_phantomBits.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_phantomBits.mlir
@@ -1,8 +1,8 @@
 // RUN: not zamacompiler %s 2>&1| FileCheck %s
 
 // CHECK-LABEL: should have the same GLWE phantomBits parameter
-func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,1,32,-25}> {
+func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,51,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,1,51,-25}> {
   %0 = constant 1 : i32
-  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,7,1,32,-25}>)
-  return %1: !MidLFHE.glwe<{1024,12,64}{0,7,1,32,-25}>
+  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,51,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,7,1,51,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{0,7,1,51,-25}>
 }
\ No newline at end of file
diff --git a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_polynomialSize.mlir b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_polynomialSize.mlir
index 8b9d43246..c279f4ae7 100644
--- a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_polynomialSize.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_polynomialSize.mlir
@@ -1,8 +1,8 @@
 // RUN: not zamacompiler %s 2>&1| FileCheck %s
 
 // CHECK-LABEL: should have the same GLWE polynomialSize parameter
-func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,10,64}{0,7,0,32,-25}> {
+func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> !MidLFHE.glwe<{1024,10,64}{0,7,0,50,-25}> {
   %0 = constant 1 : i32
-  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>, i32) -> (!MidLFHE.glwe<{1024,10,64}{0,7,0,32,-25}>)
-  return %1: !MidLFHE.glwe<{1024,10,64}{0,7,0,32,-25}>
+  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, i32) -> (!MidLFHE.glwe<{1024,10,64}{0,7,0,50,-25}>)
+  return %1: !MidLFHE.glwe<{1024,10,64}{0,7,0,50,-25}>
 }
diff --git a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_scalingFactor.mlir b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_scalingFactor.mlir
index 09589a3d2..a21a5d960 100644
--- a/compiler/tests/Dialect/MidLFHE/op_add_plain_err_scalingFactor.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_add_plain_err_scalingFactor.mlir
@@ -1,8 +1,8 @@
 // RUN: not zamacompiler %s 2>&1| FileCheck %s
 
 // CHECK-LABEL: should have the same GLWE scalingFactor parameter
-func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,30,-25}> {
+func @add_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,49,-25}> {
   %0 = constant 1 : i32
-  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,32,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,7,0,30,-25}>)
-  return %1: !MidLFHE.glwe<{1024,12,64}{0,7,0,30,-25}>
+  %1 = "MidLFHE.add_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,7,0,49,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{0,7,0,49,-25}>
 }
\ No newline at end of file
diff --git a/compiler/tests/Dialect/MidLFHE/op_h_add.mlir b/compiler/tests/Dialect/MidLFHE/op_h_add.mlir
index 93e60f1f2..de224b32a 100644
--- a/compiler/tests/Dialect/MidLFHE/op_h_add.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_h_add.mlir
@@ -1,11 +1,10 @@
 // RUN: zamacompiler %s  2>&1| FileCheck %s
 
+// CHECK-LABEL: func @add_plain_glwe(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, %arg1: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-24}>
+func @add_plain_glwe(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, %arg1: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-24}> {
+  // CHECK-NEXT: %[[V1:.*]] = "MidLFHE.h_add"(%arg0, %arg1) : (!MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-24}>
+  // CHECK-NEXT: return %[[V1]] : !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-24}>
 
-// CHECK-LABEL: func @add_plain_glwe(%arg0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, %arg1: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
-func @add_plain_glwe(%arg0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, %arg1: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}> {
-  // CHECK-NEXT: %[[V1:.*]] = "MidLFHE.h_add"(%arg0, %arg1) : (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
-  // CHECK-NEXT: return %[[V1]] : !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
-
-  %0 = "MidLFHE.h_add"(%arg0, %arg1): (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>)
-  return %0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
+  %0 = "MidLFHE.h_add"(%arg0, %arg1): (!MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> (!MidLFHE.glwe<{1024,12,64}{0,7,0,50,-24}>)
+  return %0: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-24}>
 }
diff --git a/compiler/tests/Dialect/MidLFHE/op_h_mul.mlir b/compiler/tests/Dialect/MidLFHE/op_h_mul.mlir
index 9c39659bf..27d647b1e 100644
--- a/compiler/tests/Dialect/MidLFHE/op_h_mul.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_h_mul.mlir
@@ -1,11 +1,11 @@
 // RUN: zamacompiler %s  2>&1| FileCheck %s
 
 
-// CHECK-LABEL: func @mul_plain_glwe(%arg0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, %arg1: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
-func @mul_plain_glwe(%arg0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, %arg1: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}> {
-  // CHECK-NEXT: %[[V1:.*]] = "MidLFHE.h_mul"(%arg0, %arg1) : (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
-  // CHECK-NEXT: return %[[V1]] : !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
+// CHECK-LABEL: func @mul_plain_glwe(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, %arg1: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>
+func @mul_plain_glwe(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, %arg1: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}> {
+  // CHECK-NEXT: %[[V1:.*]] = "MidLFHE.h_mul"(%arg0, %arg1) : (!MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>
+  // CHECK-NEXT: return %[[V1]] : !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>
 
-  %0 = "MidLFHE.h_mul"(%arg0, %arg1): (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>)
-  return %0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
+  %0 = "MidLFHE.h_mul"(%arg0, %arg1): (!MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> (!MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>)
+  return %0: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>
 }
diff --git a/compiler/tests/Dialect/MidLFHE/op_mul_plain.mlir b/compiler/tests/Dialect/MidLFHE/op_mul_plain.mlir
index 95dfee848..f37771b39 100644
--- a/compiler/tests/Dialect/MidLFHE/op_mul_plain.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_mul_plain.mlir
@@ -1,11 +1,23 @@
 // RUN: zamacompiler %s  2>&1| FileCheck %s
-// CHECK-LABEL: func @mul_plain_glwe(%arg0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
-func @mul_plain_glwe(%arg0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}> {
+
+// CHECK-LABEL: func @mul_plain_no_padding(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>
+func @mul_plain_no_padding(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}> {
   // CHECK-NEXT: %[[V1:.*]] = constant 1 : i32
-  // CHECK-NEXT: %[[V2:.*]] = "MidLFHE.mul_plain"(%arg0, %[[V1]]) : (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, i32) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
-  // CHECK-NEXT: return %[[V2]] : !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
+  // CHECK-NEXT: %[[V2:.*]] = "MidLFHE.mul_plain"(%arg0, %[[V1]]) : (!MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>, i32) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>
+  // CHECK-NEXT: return %[[V2]] : !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>
 
   %0 = constant 1 : i32
-  %1 = "MidLFHE.mul_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>)
-  return %1: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
+  %1 = "MidLFHE.mul_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>
+}
+
+// CHECK-LABEL: func @mul_plain_padding(%arg0: !MidLFHE.glwe<{1024,12,64}{2,7,0,55,-25}>) -> !MidLFHE.glwe<{1024,12,64}{1,7,0,55,-25}>
+func @mul_plain_padding(%arg0: !MidLFHE.glwe<{1024,12,64}{2,7,0,55,-25}>) -> !MidLFHE.glwe<{1024,12,64}{1,7,0,55,-25}> {
+  // CHECK-NEXT: %[[V1:.*]] = constant 1 : i32
+  // CHECK-NEXT: %[[V2:.*]] = "MidLFHE.mul_plain"(%arg0, %[[V1]]) : (!MidLFHE.glwe<{1024,12,64}{2,7,0,55,-25}>, i32) -> !MidLFHE.glwe<{1024,12,64}{1,7,0,55,-25}>
+  // CHECK-NEXT: return %[[V2]] : !MidLFHE.glwe<{1024,12,64}{1,7,0,55,-25}>
+
+  %0 = constant 1 : i32
+  %1 = "MidLFHE.mul_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{2,7,0,55,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{1,7,0,55,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{1,7,0,55,-25}>
 }
\ No newline at end of file
diff --git a/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_bits.mlir b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_bits.mlir
new file mode 100644
index 000000000..33d5f4d8d
--- /dev/null
+++ b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_bits.mlir
@@ -0,0 +1,8 @@
+// RUN: not zamacompiler %s 2>&1| FileCheck %s
+
+// CHECK-LABEL: should have the same GLWE bits parameter
+func @mul_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}> {
+  %0 = constant 1 : i32
+  %1 = "MidLFHE.mul_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,41,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,32}{0,7,0,25,-82}>)
+  return %1: !MidLFHE.glwe<{1024,12,32}{0,7,0,25,-82}>
+}
diff --git a/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_dimension.mlir b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_dimension.mlir
new file mode 100644
index 000000000..e72e66d5a
--- /dev/null
+++ b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_dimension.mlir
@@ -0,0 +1,8 @@
+// RUN: not zamacompiler %s 2>&1| FileCheck %s
+
+// CHECK-LABEL: error: should have the same GLWE dimension parameter
+func @mul_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>) -> !MidLFHE.glwe<{1023,12,64}{0,7,0,57,-25}> {
+  %0 = constant 1 : i32
+  %1 = "MidLFHE.mul_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>, i32) -> (!MidLFHE.glwe<{1023,12,64}{0,7,0,57,-25}>)
+  return %1: !MidLFHE.glwe<{1023,12,64}{0,7,0,57,-25}>
+}
diff --git a/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_log2StdDev.mlir b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_log2StdDev.mlir
new file mode 100644
index 000000000..6c2465ee5
--- /dev/null
+++ b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_log2StdDev.mlir
@@ -0,0 +1,8 @@
+// RUN: not zamacompiler %s 2>&1| FileCheck %s
+
+// CHECK-LABEL: should have the same GLWE log2StdDev parameter
+func @mul_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-29}> {
+  %0 = constant 1 : i32
+  %1 = "MidLFHE.mul_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,7,0,57,-29}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-29}>
+}
\ No newline at end of file
diff --git a/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_p.mlir b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_p.mlir
new file mode 100644
index 000000000..691da4354
--- /dev/null
+++ b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_p.mlir
@@ -0,0 +1,8 @@
+// RUN: not zamacompiler %s 2>&1| FileCheck %s
+
+// CHECK-LABEL: should have the same GLWE p parameter
+func @mul_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,6,0,57,-25}> {
+  %0 = constant 1 : i32
+  %1 = "MidLFHE.mul_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,6,0,57,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{0,6,0,57,-25}>
+}
diff --git a/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_padding1.mlir b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_padding1.mlir
new file mode 100644
index 000000000..f4175c295
--- /dev/null
+++ b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_padding1.mlir
@@ -0,0 +1,8 @@
+// RUN: not zamacompiler %s 2>&1| FileCheck %s
+
+// CHECK-LABEL: error: the result shoud have 0 paddingBits has input has 0 paddingBits
+func @mul_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> !MidLFHE.glwe<{1024,12,64}{1,7,0,50,-25}> {
+  %0 = constant 1 : i32
+  %1 = "MidLFHE.mul_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{1,7,0,50,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{1,7,0,50,-25}>
+}
\ No newline at end of file
diff --git a/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_padding2.mlir b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_padding2.mlir
new file mode 100644
index 000000000..1fcc4e5cb
--- /dev/null
+++ b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_padding2.mlir
@@ -0,0 +1,8 @@
+// RUN: not zamacompiler %s 2>&1| FileCheck %s
+
+// CHECK-LABEL: error: the result should have one less padding bit than the input
+func @mul_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{2,7,0,51,-25}>) -> !MidLFHE.glwe<{1024,12,64}{2,7,0,51,-25}> {
+  %0 = constant 1 : i32
+  %1 = "MidLFHE.mul_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{2,7,0,51,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{2,7,0,51,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{2,7,0,51,-25}>
+}
\ No newline at end of file
diff --git a/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_phantomBits.mlir b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_phantomBits.mlir
new file mode 100644
index 000000000..829677ad8
--- /dev/null
+++ b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_phantomBits.mlir
@@ -0,0 +1,8 @@
+// RUN: not zamacompiler %s 2>&1| FileCheck %s
+
+// CHECK-LABEL: should have the same GLWE phantomBits parameter
+func @mul_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,51,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,1,51,-25}> {
+  %0 = constant 1 : i32
+  %1 = "MidLFHE.mul_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,51,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,7,1,51,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{0,7,1,51,-25}>
+}
\ No newline at end of file
diff --git a/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_polynomialSize.mlir b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_polynomialSize.mlir
new file mode 100644
index 000000000..3e9673789
--- /dev/null
+++ b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_polynomialSize.mlir
@@ -0,0 +1,8 @@
+// RUN: not zamacompiler %s 2>&1| FileCheck %s
+
+// CHECK-LABEL: should have the same GLWE polynomialSize parameter
+func @mul_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> !MidLFHE.glwe<{1024,10,64}{0,7,0,50,-25}> {
+  %0 = constant 1 : i32
+  %1 = "MidLFHE.mul_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, i32) -> (!MidLFHE.glwe<{1024,10,64}{0,7,0,50,-25}>)
+  return %1: !MidLFHE.glwe<{1024,10,64}{0,7,0,50,-25}>
+}
diff --git a/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_scalingFactor.mlir b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_scalingFactor.mlir
new file mode 100644
index 000000000..a6edb0aa5
--- /dev/null
+++ b/compiler/tests/Dialect/MidLFHE/op_mul_plain_err_scalingFactor.mlir
@@ -0,0 +1,8 @@
+// RUN: not zamacompiler %s 2>&1| FileCheck %s
+
+// CHECK-LABEL: should have the same GLWE scalingFactor parameter
+func @mul_plain(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,49,-25}> {
+  %0 = constant 1 : i32
+  %1 = "MidLFHE.mul_plain"(%arg0, %0): (!MidLFHE.glwe<{1024,12,64}{0,7,0,50,-25}>, i32) -> (!MidLFHE.glwe<{1024,12,64}{0,7,0,49,-25}>)
+  return %1: !MidLFHE.glwe<{1024,12,64}{0,7,0,49,-25}>
+}
\ No newline at end of file
diff --git a/compiler/tests/Dialect/MidLFHE/op_pbs.mlir b/compiler/tests/Dialect/MidLFHE/op_pbs.mlir
index c7850e029..64b0f962b 100644
--- a/compiler/tests/Dialect/MidLFHE/op_pbs.mlir
+++ b/compiler/tests/Dialect/MidLFHE/op_pbs.mlir
@@ -1,18 +1,18 @@
 // RUN: zamacompiler %s  2>&1| FileCheck %s
 
-// CHECK-LABEL: func @pbs_ciphertext(%arg0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, %arg1: i32) -> !MidLFHE.glwe<{2048,10,64}{0,7,0,32,-20}> {
-func @pbs_ciphertext(%arg0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>, %arg1: i32) -> !MidLFHE.glwe<{2048,10,64}{0,7,0,32,-20}> {
+// CHECK-LABEL: func @pbs_ciphertext(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>, %arg1: i32) -> !MidLFHE.glwe<{2048,10,64}{0,7,0,2,-82}> {
+func @pbs_ciphertext(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>, %arg1: i32) -> !MidLFHE.glwe<{2048,10,64}{0,7,0,2,-82}> {
   // CHECK-NEXT: %[[V1:.*]] = "MidLFHE.pbs"(%arg0) ( {
   // CHECK-NEXT: ^bb0(%[[V2:.*]]: i32):  // no predecessors
   // CHECK-NEXT:   %[[V4:.*]] = divi_unsigned %[[V2]], %arg1 : i32
   // CHECK-NEXT:   "MidLFHE.pbs_return"(%[[V4]]) : (i32) -> ()
-  // CHECK-NEXT: }) {base_log = 8 : i32, big_n = 1024 : i32, level = 2 : i32, log_noise = -20 : i32} : (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{2048,10,64}{0,7,0,32,-20}>
-  // CHECK-NEXT: return %[[V1]] : !MidLFHE.glwe<{2048,10,64}{0,7,0,32,-20}>
+  // CHECK-NEXT: }) {base_log = 8 : i32, big_n = 1024 : i32, level = 2 : i32, log_noise = -82 : i32} : (!MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>) -> !MidLFHE.glwe<{2048,10,64}{0,7,0,2,-82}>
+  // CHECK-NEXT: return %[[V1]] : !MidLFHE.glwe<{2048,10,64}{0,7,0,2,-82}>
   %0 = "MidLFHE.pbs"(%arg0)({
     ^bb0(%a:i32):
       %1 = std.divi_unsigned %a, %arg1 : i32
       "MidLFHE.pbs_return"(%1) : (i32) -> ()
-  }){big_n=1024: i32, log_noise=-20: i32, base_log=8 : i32, level=2 : i32} : (!MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{2048,10,64}{0,7,0,32,-20}>
+  }){big_n=1024: i32, log_noise=-82: i32, base_log=8 : i32, level=2 : i32} : (!MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>) -> !MidLFHE.glwe<{2048,10,64}{0,7,0,2,-82}>
 
-  return %0 : !MidLFHE.glwe<{2048,10,64}{0,7,0,32,-20}>
+  return %0 : !MidLFHE.glwe<{2048,10,64}{0,7,0,2,-82}>
 }
\ No newline at end of file
diff --git a/compiler/tests/Dialect/MidLFHE/types_glwe.mlir b/compiler/tests/Dialect/MidLFHE/types_glwe.mlir
index 7ddef3581..19afca182 100644
--- a/compiler/tests/Dialect/MidLFHE/types_glwe.mlir
+++ b/compiler/tests/Dialect/MidLFHE/types_glwe.mlir
@@ -1,13 +1,7 @@
 // RUN: zamacompiler %s  2>&1| FileCheck %s
 
-// CHECK-LABEL: func @glwe_unknwon_parameter(%arg0: !MidLFHE.glwe<{_,_,_}{_,7,_,_,_}>) -> !MidLFHE.glwe<{_,_,_}{_,7,_,_,_}>
-func @glwe_unknwon_parameter(%arg0: !MidLFHE.glwe<{_,_,_}{_,7,_,_,_}>) -> !MidLFHE.glwe<{_,_,_}{_,7,_,_,_}> {
-  // CHECK-LABEL: return %arg0 : !MidLFHE.glwe<{_,_,_}{_,7,_,_,_}>
-  return %arg0: !MidLFHE.glwe<{_,_,_}{_,7,_,_,_}>
-}
-
-// CHECK-LABEL: func @glwe(%arg0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
-func @glwe(%arg0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>) -> !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}> {
-  // CHECK-LABEL: return %arg0 : !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
-  return %arg0: !MidLFHE.glwe<{1024,12,-64}{0,7,0,32,-25}>
+// CHECK-LABEL: func @glwe(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>
+func @glwe(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}> {
+  // CHECK-LABEL: return %arg0 : !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>
+  return %arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,57,-25}>
 }
\ No newline at end of file
diff --git a/compiler/tests/Dialect/MidLFHE/types_glwe_err_error_overlap_message1.mlir b/compiler/tests/Dialect/MidLFHE/types_glwe_err_error_overlap_message1.mlir
new file mode 100644
index 000000000..a6fc1499e
--- /dev/null
+++ b/compiler/tests/Dialect/MidLFHE/types_glwe_err_error_overlap_message1.mlir
@@ -0,0 +1,6 @@
+// RUN: not zamacompiler %s 2>&1| FileCheck %s
+
+// CHECK-LABEL: error: GLWE error overlap message, errBits(41) > scalingFactor(40) + phantomBits(0)
+func @glwe(%arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,40,-25}>) -> !MidLFHE.glwe<{1024,12,64}{0,7,0,40,-25}> {
+  return %arg0: !MidLFHE.glwe<{1024,12,64}{0,7,0,40,-25}>
+}
\ No newline at end of file