feat(concrete-compiler): add support for key type parameters and attributes

2026-04-17 03:00:54 -04:00 · 2023-02-17 10:41:45 +01:00
parent 5c1a15c514
commit a2b143f409
62 changed files with 881 additions and 634 deletions
--- a/compilers/concrete-compiler/compiler/include/concretelang/Dialect/Concrete/IR/ConcreteOps.td
+++ b/compilers/concrete-compiler/compiler/include/concretelang/Dialect/Concrete/IR/ConcreteOps.td
@@ -357,7 +357,8 @@ def Concrete_WopPBSCRTLweTensorOp : Concrete_Op<"wop_pbs_crt_lwe_tensor", [Pure]
        I32Attr : $packingKeySwitchBaseLog,
        // Circuit bootstrap parameters
        I32Attr : $circuitBootstrapLevel,
-        I32Attr : $circuitBootstrapBaseLog
+        I32Attr : $circuitBootstrapBaseLog,
+        I64ArrayAttr:$crtDecomposition
    );
    let results = (outs Concrete_LweCRTTensor:$result);
 }
--- a/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/CMakeLists.txt
+++ b/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/CMakeLists.txt
@@ -1,3 +1,7 @@
+set(LLVM_TARGET_DEFINITIONS TFHEAttrs.td)
+mlir_tablegen(TFHEAttrs.h.inc -gen-attrdef-decls -attrdefs-dialect=TFHE)
+mlir_tablegen(TFHEAttrs.cpp.inc -gen-attrdef-defs -attrdefs-dialect=TFHE)
+
 set(LLVM_TARGET_DEFINITIONS TFHEOps.td)
 mlir_tablegen(TFHEOps.h.inc -gen-op-decls)
 mlir_tablegen(TFHEOps.cpp.inc -gen-op-defs)
@@ -10,4 +14,5 @@ add_dependencies(mlir-headers MLIRTFHEOpsIncGen)

 add_concretelang_doc(TFHEOps TFHEDialect concretelang/ -gen-dialect-doc -dialect=TFHE)
 add_concretelang_doc(TFHEOps TFHEOps concretelang/ -gen-op-doc)
+add_concretelang_doc(TFHEOps TFHEAttrs concretelang/ -gen-attrdef-doc)
 add_concretelang_doc(TFHETypes TFHETypes concretelang/ -gen-typedef-doc)
--- a/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHEAttrs.h
+++ b/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHEAttrs.h
@@ -0,0 +1,19 @@
+// Part of the Concrete Compiler Project, under the BSD3 License with Zama
+// Exceptions. See
+// https://github.com/zama-ai/concrete-compiler-internal/blob/main/LICENSE.txt
+// for license information.
+
+#ifndef CONCRETELANG_DIALECT_TFHE_IR_TFHEATTRS_H
+#define CONCRETELANG_DIALECT_TFHE_IR_TFHEATTRS_H
+
+#include "concretelang/Dialect/TFHE/IR/TFHEParameters.h"
+#include "llvm/ADT/TypeSwitch.h"
+#include <mlir/Dialect/Func/IR/FuncOps.h>
+#include <mlir/IR/BuiltinOps.h>
+#include <mlir/IR/BuiltinTypes.h>
+#include <mlir/IR/DialectImplementation.h>
+
+#define GET_ATTRDEF_CLASSES
+#include "concretelang/Dialect/TFHE/IR/TFHEAttrs.h.inc"
+
+#endif
--- a/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHEAttrs.td
+++ b/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHEAttrs.td
@@ -0,0 +1,69 @@
+//===- TFHEOps.td - High level FHE dialect ops ----------------*- tablegen
+//-*-===//
+//
+// This file is licensed under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef CONCRETELANG_DIALECT_TFHE_IR_TFHE_ATTRS
+#define CONCRETELANG_DIALECT_TFHE_IR_TFHE_ATTRS
+
+include "concretelang/Dialect/TFHE/IR/TFHEDialect.td"
+include "concretelang/Dialect/TFHE/IR/TFHETypes.td"
+include "mlir/IR/AttrTypeBase.td"
+include "mlir/IR/OpBase.td"
+
+class TFHE_Attr<string name, string attrMnemonic, list<Trait> traits = []>: AttrDef<TFHE_Dialect, name, traits> {
+    let mnemonic = attrMnemonic;
+}
+
+def TFHE_KeyswitchKeyAttr: TFHE_Attr<"GLWEKeyswitchKey", "ksk"> {
+
+    let summary = "An attribute representing keyswitch key.";
+
+    let parameters = (ins
+        "mlir::concretelang::TFHE::GLWESecretKey":$inputKey,
+        "mlir::concretelang::TFHE::GLWESecretKey":$outputKey,
+        "int":$levels,
+        "int":$baseLog
+    );
+
+    let assemblyFormat = "`<` $inputKey `,` $outputKey `,` $levels `,` $baseLog `>`";
+}
+
+def TFHE_BootstrapKeyAttr: TFHE_Attr<"GLWEBootstrapKey", "bsk"> {
+
+    let summary = "An attribute representing bootstrap key.";
+
+    let parameters = (ins
+        "mlir::concretelang::TFHE::GLWESecretKey":$inputKey,
+        "mlir::concretelang::TFHE::GLWESecretKey":$outputKey,
+        "int":$polySize,
+        "int":$glweDim,
+        "int":$levels,
+        "int":$baseLog
+    );
+
+    let assemblyFormat = "`<` $inputKey `,` $outputKey `,` $polySize `,` $glweDim `,` $levels `,` $baseLog `>`";
+}
+
+def TFHE_PackingKeyswitchKeyAttr: TFHE_Attr<"GLWEPackingKeyswitchKey", "pksk"> {
+
+    let summary = "An attribute representing Wop Pbs key.";
+
+    let parameters = (ins
+        "mlir::concretelang::TFHE::GLWESecretKey":$inputKey,
+        "mlir::concretelang::TFHE::GLWESecretKey":$outputKey,
+        "int" : $outputPolySize,
+        "int" : $inputLweDim,
+        "int" : $levels,
+        "int" : $baseLog
+);
+
+let assemblyFormat = "`<` $inputKey `,` $outputKey`,` $outputPolySize`,` $inputLweDim `,` $levels `,` $baseLog `>`";
+
+}
+
+#endif
--- a/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHEDialect.td
+++ b/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHEDialect.td
@@ -18,6 +18,7 @@ def TFHE_Dialect : Dialect {
    A dialect for representation of high level operation on fully homomorphic ciphertext.
  }];
  let useDefaultTypePrinterParser = 1;
+  let useDefaultAttributePrinterParser = 1;
  let cppNamespace = "::mlir::concretelang::TFHE";
 }

--- a/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHEOps.h
+++ b/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHEOps.h
@@ -12,6 +12,7 @@
 #include <mlir/Interfaces/ControlFlowInterfaces.h>
 #include <mlir/Interfaces/SideEffectInterfaces.h>

+#include "concretelang/Dialect/TFHE/IR/TFHEAttrs.h"
 #include "concretelang/Dialect/TFHE/IR/TFHETypes.h"

 #define GET_OP_CLASSES
--- a/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHEOps.td
+++ b/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHEOps.td
@@ -12,9 +12,9 @@

 include "mlir/Interfaces/SideEffectInterfaces.td"
 include "mlir/Interfaces/ControlFlowInterfaces.td"
-
 include "concretelang/Dialect/TFHE/IR/TFHEDialect.td"
 include "concretelang/Dialect/TFHE/IR/TFHETypes.td"
+include "concretelang/Dialect/TFHE/IR/TFHEAttrs.td"

 class TFHE_Op<string mnemonic, list<Trait> traits = []>
    : Op<TFHE_Dialect, mnemonic, traits>;
@@ -125,12 +125,11 @@ def TFHE_KeySwitchGLWEOp : TFHE_Op<"keyswitch_glwe"> {
  let summary = "Change the encryption parameters of a glwe ciphertext by "
                "applying a keyswitch";

-  let arguments = (ins 
+  let arguments = (ins
    TFHE_GLWECipherTextType : $ciphertext,
-    I32Attr : $level,
-    I32Attr : $baseLog
+    TFHE_KeyswitchKeyAttr : $key
  );
-  
+

  let results = (outs TFHE_GLWECipherTextType : $result);
 }
@@ -143,10 +142,7 @@ def TFHE_BootstrapGLWEOp : TFHE_Op<"bootstrap_glwe"> {
  let arguments = (ins
    TFHE_GLWECipherTextType : $ciphertext,
    1DTensorOf<[I64]> : $lookup_table,
-    I32Attr : $level,
-    I32Attr : $baseLog,
-    I32Attr : $polySize,
-    I32Attr : $glweDimension
+    TFHE_BootstrapKeyAttr: $key
  );

  let results = (outs TFHE_GLWECipherTextType : $result);
@@ -158,23 +154,14 @@ def TFHE_WopPBSGLWEOp : TFHE_Op<"wop_pbs_glwe"> {
    let arguments = (ins
        Type<And<[TensorOf<[TFHE_GLWECipherTextType]>.predicate, HasStaticShapePred]>>: $ciphertexts,
        2DTensorOf<[I64]> : $lookupTable,
-        // Bootstrap parameters
-        I32Attr : $bootstrapLevel,
-        I32Attr : $bootstrapBaseLog,
-        // Keyswitch parameters
-        I32Attr : $keyswitchLevel,
-        I32Attr : $keyswitchBaseLog,
-        // Packing keyswitch key parameters
-        I32Attr : $packingKeySwitchInputLweDimension,
-        I32Attr : $packingKeySwitchoutputPolynomialSize,
-        I32Attr : $packingKeySwitchLevel,
-        I32Attr : $packingKeySwitchBaseLog,
-        // Circuit bootstrap parameters
-        I32Attr : $circuitBootstrapLevel,
-        I32Attr : $circuitBootstrapBaseLog,
-        // Crt decomposition
-        I64ArrayAttr: $crtDecomposition
+        TFHE_KeyswitchKeyAttr: $ksk,
+        TFHE_BootstrapKeyAttr: $bsk,
+        TFHE_PackingKeyswitchKeyAttr: $pksk,
+        I64ArrayAttr: $crtDecomposition,
+        I32Attr: $cbsLevels,
+        I32Attr: $cbsBaseLog
    );
+
    let results = (outs Type<And<[TensorOf<[TFHE_GLWECipherTextType]>.predicate, HasStaticShapePred]>>:$result);
 }

--- a/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHEParameters.h
+++ b/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHEParameters.h
@@ -0,0 +1,71 @@
+// Part of the Concrete Compiler Project, under the BSD3 License with Zama
+// Exceptions. See
+// https://github.com/zama-ai/concrete-compiler-internal/blob/main/LICENSE.txt
+// for license information.
+
+#ifndef CONCRETELANG_DIALECT_TFHE_IR_TFHEPARAMETERS_H
+#define CONCRETELANG_DIALECT_TFHE_IR_TFHEPARAMETERS_H
+
+#include "llvm/ADT/TypeSwitch.h"
+#include <mlir/Dialect/Func/IR/FuncOps.h>
+#include <mlir/IR/BuiltinOps.h>
+#include <mlir/IR/BuiltinTypes.h>
+#include <mlir/IR/DialectImplementation.h>
+
+namespace mlir {
+namespace concretelang {
+namespace TFHE {
+
+/// A type parameter representing GLWE secret key.
+///
+/// A glwe secret key is basically a glwe dimension, a polynomial size, and an
+/// id that makes it possible to disambiguate potential keys with with same
+/// parameters.
+///
+/// Note that a key can be instantiated to a `none` key, to serve as a
+/// placeholder in the IR. In this case, none of its data are actually usable
+/// for lowering to the `Concrete` dialect. Once the
+/// `TFHEGlobalParameterization` was performed, there should remain no such
+/// `none` keys in the IR.
+class GLWESecretKey {
+public:
+  /// Creates a new none key.
+  GLWESecretKey();
+  /// Create a new key from parameters.
+  GLWESecretKey(int64_t dimension, int64_t polySize, int64_t id);
+  bool operator==(GLWESecretKey other);
+  bool operator==(const GLWESecretKey other) const;
+  bool operator!=(GLWESecretKey other);
+  /// Returns the dimension associated with this key, if the key is not none.
+  mlir::Optional<int64_t> getDimension() const;
+  /// Returns the polynomial size associated with this key, if the key is not
+  /// none.
+  mlir::Optional<int64_t> getPolySize() const;
+  /// Returns the id associated with this key, if the key is not none.
+  mlir::Optional<int64_t> getId() const;
+  /// Returns true if the key was not filled with valid parameters.
+  bool isNotParameterized() const;
+
+private:
+  int64_t dimension;
+  int64_t polySize;
+  int64_t id;
+};
+
+llvm::hash_code hash_value(const GLWESecretKey &key);
+} // namespace TFHE
+} // namespace concretelang
+} // namespace mlir
+
+namespace mlir {
+
+AsmPrinter &operator<<(AsmPrinter &p,
+                       mlir::concretelang::TFHE::GLWESecretKey key);
+
+template <> struct FieldParser<mlir::concretelang::TFHE::GLWESecretKey> {
+  static FailureOr<mlir::concretelang::TFHE::GLWESecretKey>
+  parse(AsmParser &parser);
+};
+} // namespace mlir
+
+#endif
--- a/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHETypes.h
+++ b/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHETypes.h
@@ -6,6 +6,7 @@
 #ifndef CONCRETELANG_DIALECT_TFHE_IR_TFHETYPES_H
 #define CONCRETELANG_DIALECT_TFHE_IR_TFHETYPES_H

+#include "concretelang/Dialect/TFHE/IR/TFHEParameters.h"
 #include "llvm/ADT/TypeSwitch.h"
 #include <mlir/Dialect/Func/IR/FuncOps.h>
 #include <mlir/IR/BuiltinOps.h>
--- a/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHETypes.td
+++ b/compilers/concrete-compiler/compiler/include/concretelang/Dialect/TFHE/IR/TFHETypes.td
@@ -10,7 +10,7 @@ class TFHE_Type<string name, list<Trait> traits = []>
    : TypeDef<TFHE_Dialect, name, traits> {}

 def TFHE_GLWECipherTextType
-    : TFHE_Type<"GLWECipherText", [MemRefElementTypeInterface]> {
+    : TFHE_Type<"GLWECipherText", [ MemRefElementTypeInterface ]> {
  let mnemonic = "glwe";

  let summary = "A GLWE ciphertext";
@@ -18,15 +18,9 @@ def TFHE_GLWECipherTextType
  let description = [{An GLWE cipher text}];

  let parameters = (ins
-        // The size of the mask
-        "signed":$dimension,
-        // Size of the polynome
-        "signed":$polynomialSize,
-        // Number of bits of the ciphertext
-        "signed":$bits,
-        // Number of bits of the plain text representation
-        "signed":$p
-    );
+                    // The size of the mask
+                    "mlir::concretelang::TFHE::GLWESecretKey"
+                    : $key);

  let hasCustomAssemblyFormat = 1;

@@ -35,8 +29,7 @@ def TFHE_GLWECipherTextType
  let extraClassDeclaration = [{
    // Returns true if has an unparametrized parameters
    bool hasUnparametrizedParameters() {
-      return getDimension() == -1 || getPolynomialSize() == -1 ||
-             getBits() == -1 || getP() == -1;
+      return getKey().isNotParameterized();
    };
  }];
 }
--- a/compilers/concrete-compiler/compiler/lib/Conversion/FHETensorOpsToLinalg/TensorOpsToLinalg.cpp
+++ b/compilers/concrete-compiler/compiler/lib/Conversion/FHETensorOpsToLinalg/TensorOpsToLinalg.cpp
@@ -309,13 +309,13 @@ llvm::SmallVector<mlir::utils::IteratorType> parallelIteratorType(int n) {
 /// becomes:
 ///
 /// #map = affine_map<(d0, d1) -> (d0, d1)>
-/// %init = linalg.init_tensor [2, 3] : tensor<2x3x!TFHE.glwe<{_,_,_}{2}>>
+/// %init = linalg.init_tensor [2, 3] : tensor<2x3x!TFHE.glwe<sk?>>
 /// %output = linalg.generic {indexing_maps = [#map, #map, #map], iterator_types
 /// = ["parallel", "parallel"]} ins(%arg0, %arg2 :
-/// tensor<2x3x!TFHE.glwe<{_,_,_}{2}>>, tensor<2x3xindex>) outs(%0 :
-/// tensor<2x3x!TFHE.glwe<{_,_,_}{2}>>) {
-///          ^bb0(%arg3: !TFHE.glwe<{_,_,_}{2}>, %lut_idx: index, %arg5:
-///          !TFHE.glwe<{_,_,_}{2}>):  // no predecessors
+/// tensor<2x3x!TFHE.glwe<sk?>>, tensor<2x3xindex>) outs(%0 :
+/// tensor<2x3x!TFHE.glwe<sk?>>) {
+///          ^bb0(%arg3: !TFHE.glwe<sk?>, %lut_idx: index, %arg5:
+///          !TFHE.glwe<sk?>):  // no predecessors
 ///          %lut = tensor.extract_slice %arg1[%[[LUTIDX]], 0] [1,4] [1, 1]
 ///                 : tensor<5x4xi64> to tensor<4xi64>
 ///          %res  = "TFHE.apply_lookup_table"(%arg3, %[[LUT]])
@@ -323,10 +323,10 @@ llvm::SmallVector<mlir::utils::IteratorType> parallelIteratorType(int n) {
 ///                    glweDimension = -1 : i32,
 ///                      levelBS = -1 : i32, levelKS = -1 : i32, outputSizeKS =
 ///                      -1 : i32, polynomialSize = -1 : i32}
-///                 : (!TFHE.glwe<{_,_,_}{2}>, tensor<4xi64>) ->
-///          !TFHE.glwe<{_,_,_}{2}> linalg.yield %res :
-///          !TFHE.glwe<{_,_,_}{2}>
-/// } -> tensor<2x3x!TFHE.glwe<{_,_,_}{2}>>
+///                 : (!TFHE.glwe<sk?>, tensor<4xi64>) ->
+///          !TFHE.glwe<sk?> linalg.yield %res :
+///          !TFHE.glwe<sk?>
+/// } -> tensor<2x3x!TFHE.glwe<sk?>>

 namespace FHELinalg = mlir::concretelang::FHELinalg;

@@ -450,8 +450,8 @@ struct FHELinalgApplyMappedLookupTableToLinalgGeneric
 ///             %lut) {baseLogBS = -1 : i32, baseLogKS = -1 : i32, glweDimension
 ///             = -1 : i32, levelBS = -1 : i32, levelKS = -1 : i32, outputSizeKS
 ///             = -1 : i32, polynomialSize = -1 : i32} :
-///             (!TFHE.glwe<{_,_,_}{2}>, tensor<4xi64>) ->
-///             !TFHE.glwe<{_,_,_}{2}>
+///             (!TFHE.glwe<sk?>, tensor<4xi64>) ->
+///             !TFHE.glwe<sk?>
 ///         linalg.yield %0 : !FHE.eint<2>
 ///     }
 /// }
--- a/compilers/concrete-compiler/compiler/lib/Conversion/FHEToTFHECrt/FHEToTFHECrt.cpp
+++ b/compilers/concrete-compiler/compiler/lib/Conversion/FHEToTFHECrt/FHEToTFHECrt.cpp
@@ -46,7 +46,7 @@ mlir::RankedTensorType convertEncrypted(mlir::MLIRContext *context,
                                        uint64_t crtLength) {
  return mlir::RankedTensorType::get(
      mlir::ArrayRef<int64_t>((int64_t)crtLength),
-      TFHE::GLWECipherTextType::get(context, -1, -1, -1, enc.getWidth()));
+      TFHE::GLWECipherTextType::get(context, TFHE::GLWESecretKey()));
 }

 /// Converts `Tensor<FHE::AnyEncryptedInteger>` into a
@@ -59,15 +59,13 @@ maybeConvertEncryptedTensor(mlir::MLIRContext *context,
  if (!maybeEncryptedTensor.getElementType().isa<FHE::FheIntegerInterface>()) {
    return (mlir::Type)(maybeEncryptedTensor);
  }
-  auto encType =
-      maybeEncryptedTensor.getElementType().cast<FHE::FheIntegerInterface>();
  auto currentShape = maybeEncryptedTensor.getShape();
  mlir::SmallVector<int64_t> newShape =
      mlir::SmallVector<int64_t>(currentShape.begin(), currentShape.end());
  newShape.push_back((int64_t)crtLength);
  return mlir::RankedTensorType::get(
      llvm::ArrayRef<int64_t>(newShape),
-      TFHE::GLWECipherTextType::get(context, -1, -1, -1, encType.getWidth()));
+      TFHE::GLWECipherTextType::get(context, TFHE::GLWESecretKey()));
 }

 /// Converts any encrypted type to `TFHE::GlweCiphetext` if the
@@ -580,8 +578,16 @@ struct ApplyLookupTableEintOpPattern
    // Replace the lut with an encoded / expanded one.
    auto wopPBS = rewriter.create<TFHE::WopPBSGLWEOp>(
        op.getLoc(), converter->convertType(op.getType()), adaptor.getA(),
-        newLut, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-        rewriter.getI64ArrayAttr({}));
+        newLut,
+        TFHE::GLWEKeyswitchKeyAttr::get(op.getContext(), TFHE::GLWESecretKey(),
+                                        TFHE::GLWESecretKey(), -1, -1),
+        TFHE::GLWEBootstrapKeyAttr::get(op.getContext(), TFHE::GLWESecretKey(),
+                                        TFHE::GLWESecretKey(), -1, -1, -1, -1),
+        TFHE::GLWEPackingKeyswitchKeyAttr::get(
+            op.getContext(), TFHE::GLWESecretKey(), TFHE::GLWESecretKey(), -1,
+            -1, -1, -1),
+        rewriter.getI64ArrayAttr({}), rewriter.getI32IntegerAttr(-1),
+        rewriter.getI32IntegerAttr(-1));

    rewriter.replaceOp(op, {wopPBS.getResult()});
    return ::mlir::success();
--- a/compilers/concrete-compiler/compiler/lib/Conversion/FHEToTFHEScalar/FHEToTFHEScalar.cpp
+++ b/compilers/concrete-compiler/compiler/lib/Conversion/FHEToTFHEScalar/FHEToTFHEScalar.cpp
@@ -27,6 +27,7 @@
 #include "concretelang/Dialect/RT/IR/RTTypes.h"
 #include "concretelang/Dialect/TFHE/IR/TFHEDialect.h"
 #include "concretelang/Dialect/TFHE/IR/TFHEOps.h"
+#include "concretelang/Dialect/TFHE/IR/TFHEParameters.h"
 #include "concretelang/Dialect/TFHE/IR/TFHETypes.h"
 #include "concretelang/Dialect/Tracing/IR/TracingOps.h"

@@ -42,7 +43,7 @@ namespace typing {
 /// Converts an encrypted integer into `TFHE::GlweCiphetext`.
 TFHE::GLWECipherTextType convertEncrypted(mlir::MLIRContext *context,
                                          FHE::FheIntegerInterface enc) {
-  return TFHE::GLWECipherTextType::get(context, -1, -1, -1, enc.getWidth());
+  return TFHE::GLWECipherTextType::get(context, TFHE::GLWESecretKey());
 }

 /// Converts `Tensor<FHE::AnyEncryptedInteger>` into a
@@ -54,12 +55,10 @@ maybeConvertEncryptedTensor(mlir::MLIRContext *context,
  if (!maybeEncryptedTensor.getElementType().isa<FHE::FheIntegerInterface>()) {
    return (mlir::Type)(maybeEncryptedTensor);
  }
-  auto enc =
-      maybeEncryptedTensor.getElementType().cast<FHE::FheIntegerInterface>();
  auto currentShape = maybeEncryptedTensor.getShape();
  return mlir::RankedTensorType::get(
      currentShape,
-      TFHE::GLWECipherTextType::get(context, -1, -1, -1, enc.getWidth()));
+      TFHE::GLWECipherTextType::get(context, TFHE::GLWESecretKey()));
 }

 /// Converts any encrypted type to `TFHE::GlweCiphetext` if the
@@ -81,9 +80,8 @@ public:
      return convertEncrypted(type.getContext(), type);
    });
    addConversion([](FHE::EncryptedBooleanType type) {
-      return TFHE::GLWECipherTextType::get(
-          type.getContext(), -1, -1, -1,
-          mlir::concretelang::FHE::EncryptedBooleanType::getWidth());
+      return TFHE::GLWECipherTextType::get(type.getContext(),
+                                           TFHE::GLWESecretKey());
    });
    addConversion([](mlir::RankedTensorType type) {
      return maybeConvertEncryptedTensor(type.getContext(), type);
@@ -369,12 +367,15 @@ struct ApplyLookupTableEintOpPattern
    // Insert keyswitch
    auto ksOp = rewriter.create<TFHE::KeySwitchGLWEOp>(
        op.getLoc(), getTypeConverter()->convertType(adaptor.getA().getType()),
-        input, -1, -1);
+        input,
+        TFHE::GLWEKeyswitchKeyAttr::get(op.getContext(), TFHE::GLWESecretKey(),
+                                        TFHE::GLWESecretKey(), -1, -1));

    // Insert bootstrap
    rewriter.replaceOpWithNewOp<TFHE::BootstrapGLWEOp>(
-        op, getTypeConverter()->convertType(op.getType()), ksOp, newLut, -1, -1,
-        -1, -1);
+        op, getTypeConverter()->convertType(op.getType()), ksOp, newLut,
+        TFHE::GLWEBootstrapKeyAttr::get(op.getContext(), TFHE::GLWESecretKey(),
+                                        TFHE::GLWESecretKey(), -1, -1, -1, -1));

    return mlir::success();
  };
@@ -553,9 +554,15 @@ struct RoundEintOpPattern : public ScalarOpPattern<FHE::RoundEintOp> {
      // The lookup is performed ...

      mlir::Value keyswitched = rewriter.create<TFHE::KeySwitchGLWEOp>(
-          op.getLoc(), truncationInputTy, shiftedRotatedInput, -1, -1);
+          op.getLoc(), truncationInputTy, shiftedRotatedInput,
+          TFHE::GLWEKeyswitchKeyAttr::get(op->getContext(),
+                                          TFHE::GLWESecretKey(),
+                                          TFHE::GLWESecretKey(), -1, -1));
      mlir::Value bootstrapped = rewriter.create<TFHE::BootstrapGLWEOp>(
-          op.getLoc(), truncationInputTy, keyswitched, lut, -1, -1, -1, -1);
+          op.getLoc(), truncationInputTy, keyswitched, lut,
+          TFHE::GLWEBootstrapKeyAttr::get(
+              op->getContext(), TFHE::GLWESecretKey(), TFHE::GLWESecretKey(),
+              -1, -1, -1, -1));

      //------------------------------------------------------------- CORRECTION
      // The correction is performed to achieve our right shift semantic.
@@ -571,8 +578,8 @@ struct RoundEintOpPattern : public ScalarOpPattern<FHE::RoundEintOp> {

      mlir::Value minusIsolatedBit = rewriter.create<TFHE::NegGLWEOp>(
          op.getLoc(), truncationInputTy, extractedBit);
-      truncationInputTy = TFHE::GLWECipherTextType::get(
-          rewriter.getContext(), -1, -1, -1, truncationInputTy.getP() - 1);
+      truncationInputTy = TFHE::GLWECipherTextType::get(rewriter.getContext(),
+                                                        TFHE::GLWESecretKey());
      mlir::Value truncationOutput = rewriter.create<TFHE::AddGLWEOp>(
          op.getLoc(), truncationInputTy, previousOutput, minusIsolatedBit);
      previousOutput = truncationOutput;
--- a/compilers/concrete-compiler/compiler/lib/Conversion/TFHEGlobalParametrization/TFHEGlobalParametrization.cpp
+++ b/compilers/concrete-compiler/compiler/lib/Conversion/TFHEGlobalParametrization/TFHEGlobalParametrization.cpp
@@ -35,8 +35,8 @@ struct TFHEGlobalParametrizationPass
 using mlir::concretelang::TFHE::GLWECipherTextType;

 /// TFHEGlobalParametrizationTypeConverter is a TypeConverter that transform
-/// `TFHE.glwe<{_,_,_}{p}>` to
-/// `TFHE.glwe<{glweDimension,polynomialSize,bits}{p'}>`
+/// `TFHE.glwe<sk[?]>` to
+/// `TFHE.glwe<sk[id]<glweDimension,polynomialSize>>`
 class TFHEGlobalParametrizationTypeConverter : public mlir::TypeConverter {

 public:
@@ -67,35 +67,32 @@ public:
    });
  }

-  TFHE::GLWECipherTextType glweInterPBSType(GLWECipherTextType &type) {
-    auto bits = 64;
+  TFHE::GLWESecretKey getInterPBSKey() {
    auto dimension = cryptoParameters.getNBigLweDimension();
    auto polynomialSize = 1;
-    auto precision = (signed)type.getP();
-    if ((int)dimension == type.getDimension() &&
-        (int)polynomialSize == type.getPolynomialSize()) {
-      return type;
-    }
-    return TFHE::GLWECipherTextType::get(type.getContext(), dimension,
-                                         polynomialSize, bits, precision);
+    // Warning, for now we use hardcoded ids. Later on, we expect the optimizer
+    // to give the id.
+    auto id = 1;
+    return mlir::concretelang::TFHE::GLWESecretKey(dimension, polynomialSize,
+                                                   id);
  }

-  TFHE::GLWECipherTextType glweLookupTableType(GLWECipherTextType &type) {
-    auto bits = 64;
-    auto dimension = cryptoParameters.glweDimension;
-    auto polynomialSize = cryptoParameters.getPolynomialSize();
-    auto precision = (signed)type.getP();
-    return TFHE::GLWECipherTextType::get(type.getContext(), dimension,
-                                         polynomialSize, bits, precision);
+  TFHE::GLWECipherTextType glweInterPBSType(GLWECipherTextType &type) {
+    return TFHE::GLWECipherTextType::get(type.getContext(), getInterPBSKey());
+  }
+
+  TFHE::GLWESecretKey getIntraPBSKey() {
+    auto dimension = cryptoParameters.nSmall;
+    auto polynomialSize = 1;
+    // Warning, for now we use hardcoded ids. Later on, we expect the optimizer
+    // to give the id.
+    auto id = 3;
+    return mlir::concretelang::TFHE::GLWESecretKey(dimension, polynomialSize,
+                                                   id);
  }

  TFHE::GLWECipherTextType glweIntraPBSType(GLWECipherTextType &type) {
-    auto bits = 64;
-    auto dimension = cryptoParameters.nSmall;
-    auto polynomialSize = 1;
-    auto precision = (signed)type.getP();
-    return TFHE::GLWECipherTextType::get(type.getContext(), dimension,
-                                         polynomialSize, bits, precision);
+    return TFHE::GLWECipherTextType::get(type.getContext(), getIntraPBSKey());
  }

  mlir::concretelang::V0Parameter cryptoParameters;
@@ -120,9 +117,13 @@ struct KeySwitchGLWEOpPattern
                          .cast<mlir::concretelang::TFHE::GLWECipherTextType>();
    auto outputTy = ksOp.getResult().getType().cast<TFHE::GLWECipherTextType>();
    auto newOutputTy = converter.glweIntraPBSType(outputTy);
-    auto newOp = rewriter.replaceOpWithNewOp<TFHE::KeySwitchGLWEOp>(
-        ksOp, newOutputTy, ksOp.getCiphertext(), cryptoParameters.ksLevel,
+    auto newInputKey = converter.getInterPBSKey();
+    auto newOutputKey = converter.getIntraPBSKey();
+    auto keyswitchKey = TFHE::GLWEKeyswitchKeyAttr::get(
+        ksOp->getContext(), newInputKey, newOutputKey, cryptoParameters.ksLevel,
        cryptoParameters.ksLogBase);
+    auto newOp = rewriter.replaceOpWithNewOp<TFHE::KeySwitchGLWEOp>(
+        ksOp, newOutputTy, ksOp.getCiphertext(), keyswitchKey);
    rewriter.startRootUpdate(newOp);
    newOp.getCiphertext().setType(newInputTy);
    rewriter.finalizeRootUpdate(newOp);
@@ -151,11 +152,17 @@ struct BootstrapGLWEOpPattern
        bsOp.getCiphertext().getType().cast<TFHE::GLWECipherTextType>();
    auto newInputTy = converter.glweIntraPBSType(inputTy);
    auto outputTy = bsOp.getResult().getType().cast<TFHE::GLWECipherTextType>();
-    auto newOutputTy = converter.convertType(outputTy);
+    auto newOutputTy =
+        converter.convertType(outputTy).cast<TFHE::GLWECipherTextType>();
+    auto newInputKey = converter.getIntraPBSKey();
+    auto newOutputKey = converter.getInterPBSKey();
+    auto bootstrapKey = TFHE::GLWEBootstrapKeyAttr::get(
+        bsOp->getContext(), newInputKey, newOutputKey,
+        cryptoParameters.getPolynomialSize(), cryptoParameters.glweDimension,
+        cryptoParameters.brLevel, cryptoParameters.brLogBase);
    auto newOp = rewriter.replaceOpWithNewOp<TFHE::BootstrapGLWEOp>(
        bsOp, newOutputTy, bsOp.getCiphertext(), bsOp.getLookupTable(),
-        cryptoParameters.brLevel, cryptoParameters.brLogBase,
-        cryptoParameters.getPolynomialSize(), cryptoParameters.glweDimension);
+        bootstrapKey);
    rewriter.startRootUpdate(newOp);
    newOp.getCiphertext().setType(newInputTy);
    rewriter.finalizeRootUpdate(newOp);
@@ -179,34 +186,41 @@ struct WopPBSGLWEOpPattern : public mlir::OpRewritePattern<TFHE::WopPBSGLWEOp> {
  mlir::LogicalResult
  matchAndRewrite(TFHE::WopPBSGLWEOp wopPBSOp,
                  mlir::PatternRewriter &rewriter) const override {
-    auto newOp = rewriter.replaceOpWithNewOp<TFHE::WopPBSGLWEOp>(
-        wopPBSOp, converter.convertType(wopPBSOp.getResult().getType()),
-        wopPBSOp.getCiphertexts(), wopPBSOp.getLookupTable(),
-        // Bootstrap parameters
-        cryptoParameters.brLevel, cryptoParameters.brLogBase,
-        // Keyswitch parameters
-        cryptoParameters.ksLevel, cryptoParameters.ksLogBase,
-        // Packing keyswitch key parameters
-        cryptoParameters.largeInteger->wopPBS.packingKeySwitch
-            .inputLweDimension,
+    auto inputTy =
+        wopPBSOp.getCiphertexts().getType().cast<mlir::RankedTensorType>();
+    auto newInputTy =
+        converter.convertType(inputTy).cast<mlir::RankedTensorType>();
+    auto outputTy = wopPBSOp.getType().cast<mlir::RankedTensorType>();
+    auto newOutputType = converter.convertType(outputTy);
+    auto interKey = converter.getInterPBSKey();
+    auto intraKey = converter.getIntraPBSKey();
+    auto keyswitchKey = TFHE::GLWEKeyswitchKeyAttr::get(
+        wopPBSOp->getContext(), interKey, intraKey, cryptoParameters.ksLevel,
+        cryptoParameters.ksLogBase);
+    auto bootstrapKey = TFHE::GLWEBootstrapKeyAttr::get(
+        wopPBSOp->getContext(), intraKey, interKey,
+        cryptoParameters.getPolynomialSize(), cryptoParameters.glweDimension,
+        cryptoParameters.brLevel, cryptoParameters.brLogBase);
+    auto packingKeyswitchKey = TFHE::GLWEPackingKeyswitchKeyAttr::get(
+        wopPBSOp->getContext(), interKey, interKey,
        cryptoParameters.largeInteger->wopPBS.packingKeySwitch
            .outputPolynomialSize,
+        cryptoParameters.largeInteger->wopPBS.packingKeySwitch
+            .inputLweDimension,
        cryptoParameters.largeInteger->wopPBS.packingKeySwitch.level,
-        cryptoParameters.largeInteger->wopPBS.packingKeySwitch.baseLog,
-        // Circuit bootstrap parameters
-        cryptoParameters.largeInteger->wopPBS.circuitBootstrap.level,
-        cryptoParameters.largeInteger->wopPBS.circuitBootstrap.baseLog,
-        // Crt decomposition
+        cryptoParameters.largeInteger->wopPBS.packingKeySwitch.baseLog);
+    auto newOp = rewriter.replaceOpWithNewOp<TFHE::WopPBSGLWEOp>(
+        wopPBSOp, newOutputType, wopPBSOp.getCiphertexts(),
+        wopPBSOp.getLookupTable(), keyswitchKey, bootstrapKey,
+        packingKeyswitchKey,
        rewriter.getI64ArrayAttr(
-            cryptoParameters.largeInteger->crtDecomposition));
+            cryptoParameters.largeInteger->crtDecomposition),
+        rewriter.getI32IntegerAttr(
+            cryptoParameters.largeInteger->wopPBS.circuitBootstrap.level),
+        rewriter.getI32IntegerAttr(
+            cryptoParameters.largeInteger->wopPBS.circuitBootstrap.baseLog));
    rewriter.startRootUpdate(newOp);
-    auto ctType =
-        wopPBSOp.getCiphertexts().getType().cast<mlir::RankedTensorType>();
-    auto ciphertextType =
-        ctType.getElementType().cast<TFHE::GLWECipherTextType>();
-    auto newType = mlir::RankedTensorType::get(
-        ctType.getShape(), converter.glweInterPBSType(ciphertextType));
-    newOp.getCiphertexts().setType(newType);
+    newOp.getCiphertexts().setType(newInputTy);
    rewriter.finalizeRootUpdate(newOp);
    return mlir::success();
  };
@@ -282,8 +296,9 @@ void TFHEGlobalParametrizationPass::runOnOperation() {
                                         cryptoParameters);
    target.addDynamicallyLegalOp<TFHE::KeySwitchGLWEOp>(
        [&](TFHE::KeySwitchGLWEOp op) {
-          return op.getLevel() != (uint32_t)-1 &&
-                 op.getBaseLog() != (uint32_t)-1;
+          return !op.getKey().getInputKey().isNotParameterized() &&
+                 !op.getKey().getOutputKey().isNotParameterized() &&
+                 op.getKey().getBaseLog() != 0 && op.getKey().getLevels() != 0;
        });
    patterns.add<BootstrapGLWEOpPattern>(&getContext(), converter,
                                         cryptoParameters);
--- a/compilers/concrete-compiler/compiler/lib/Conversion/TFHEToConcrete/TFHEToConcrete.cpp
+++ b/compilers/concrete-compiler/compiler/lib/Conversion/TFHEToConcrete/TFHEToConcrete.cpp
@@ -37,8 +37,8 @@ struct TFHEToConcretePass : public TFHEToConcreteBase<TFHEToConcretePass> {
 using mlir::concretelang::TFHE::GLWECipherTextType;

 /// TFHEToConcreteTypeConverter is a TypeConverter that transform
-/// `TFHE.glwe<{dimension,1,bits}{p}>` to `tensor<dimension+1, i64>>`
-/// `tensor<...xTFHE.glwe<{dimension,1,bits}{p}>>` to
+/// `TFHE.glwe<sk(id){dimension,1}>` to `tensor<dimension+1, i64>>`
+/// `tensor<...xTFHE.glwe<sk(id){dimension,1}>>` to
 /// `tensor<...xdimension+1, i64>>`
 class TFHEToConcreteTypeConverter : public mlir::TypeConverter {

@@ -46,11 +46,11 @@ public:
  TFHEToConcreteTypeConverter() {
    addConversion([](mlir::Type type) { return type; });
    addConversion([&](GLWECipherTextType type) {
-      assert(type.getPolynomialSize() <= 1 &&
+      assert(!type.getKey().isNotParameterized());
+      assert(type.getKey().getPolySize().value() == 1 &&
             "converter doesn't support polynomialSize > 1");
-      assert(type.getDimension() != -1);
      llvm::SmallVector<int64_t, 2> shape;
-      shape.push_back(type.getDimension() + 1);
+      shape.push_back(type.getKey().getDimension().value() + 1);
      return mlir::RankedTensorType::get(
          shape, mlir::IntegerType::get(type.getContext(), 64));
    });
@@ -62,8 +62,8 @@ public:
      mlir::SmallVector<int64_t> newShape;
      newShape.reserve(type.getShape().size() + 1);
      newShape.append(type.getShape().begin(), type.getShape().end());
-      assert(glwe.getDimension() != -1);
-      newShape.push_back(glwe.getDimension() + 1);
+      assert(!glwe.getKey().isNotParameterized());
+      newShape.push_back(glwe.getKey().getDimension().value() + 1);
      mlir::Type r = mlir::RankedTensorType::get(
          newShape, mlir::IntegerType::get(type.getContext(), 64));
      return r;
@@ -124,11 +124,52 @@ struct BootstrapGLWEOpPattern
    TFHE::GLWECipherTextType inputType =
        bsOp.getCiphertext().getType().cast<TFHE::GLWECipherTextType>();

+    auto polySize = adaptor.getKey().getPolySize();
+    auto glweDimension = adaptor.getKey().getGlweDim();
+    auto levels = adaptor.getKey().getLevels();
+    auto baseLog = adaptor.getKey().getBaseLog();
+    auto inputLweDimension = inputType.getKey().getDimension().value();
+
    rewriter.replaceOpWithNewOp<Concrete::BootstrapLweTensorOp>(
        bsOp, this->getTypeConverter()->convertType(resultType),
-        adaptor.getCiphertext(), adaptor.getLookupTable(),
-        inputType.getDimension(), adaptor.getPolySize(), adaptor.getLevel(),
-        adaptor.getBaseLog(), adaptor.getGlweDimension());
+        adaptor.getCiphertext(), adaptor.getLookupTable(), inputLweDimension,
+        polySize, levels, baseLog, glweDimension);
+
+    return mlir::success();
+  }
+};
+
+struct WopPBSGLWEOpPattern
+    : public mlir::OpConversionPattern<TFHE::WopPBSGLWEOp> {
+
+  WopPBSGLWEOpPattern(mlir::MLIRContext *context,
+                      mlir::TypeConverter &typeConverter)
+      : mlir::OpConversionPattern<TFHE::WopPBSGLWEOp>(
+            typeConverter, context,
+            mlir::concretelang::DEFAULT_PATTERN_BENEFIT) {}
+
+  ::mlir::LogicalResult
+  matchAndRewrite(TFHE::WopPBSGLWEOp op, TFHE::WopPBSGLWEOp::Adaptor adaptor,
+                  mlir::ConversionPatternRewriter &rewriter) const override {
+
+    auto bsBaseLog = adaptor.getBsk().getBaseLog();
+    auto bsLevels = adaptor.getBsk().getLevels();
+    auto cbsBaseLog = adaptor.getCbsBaseLog();
+    auto cbsLevels = adaptor.getCbsLevels();
+    auto ksBaseLog = adaptor.getKsk().getBaseLog();
+    auto ksLevels = adaptor.getKsk().getLevels();
+    auto pksBaseLog = adaptor.getPksk().getBaseLog();
+    auto pksLevels = adaptor.getPksk().getLevels();
+    auto pksInputLweDim = adaptor.getPksk().getInputLweDim();
+    auto pksOutputPolySize = adaptor.getPksk().getOutputPolySize();
+    auto crtDecomposition = adaptor.getCrtDecompositionAttr();
+    auto resultType = op.getType();
+
+    rewriter.replaceOpWithNewOp<Concrete::WopPBSCRTLweTensorOp>(
+        op, this->getTypeConverter()->convertType(resultType),
+        adaptor.getCiphertexts(), adaptor.getLookupTable(), bsLevels, bsBaseLog,
+        ksLevels, ksBaseLog, pksInputLweDim, pksOutputPolySize, pksLevels,
+        pksBaseLog, cbsLevels, cbsBaseLog, crtDecomposition);

    return mlir::success();
  }
@@ -153,10 +194,14 @@ struct KeySwitchGLWEOpPattern
    TFHE::GLWECipherTextType inputType =
        ksOp.getCiphertext().getType().cast<TFHE::GLWECipherTextType>();

+    auto levels = adaptor.getKey().getLevels();
+    auto baseLog = adaptor.getKey().getBaseLog();
+    auto inputDim = inputType.getKey().getDimension().value();
+    auto outputDim = resultType.getKey().getDimension().value();
+
    rewriter.replaceOpWithNewOp<Concrete::KeySwitchLweTensorOp>(
        ksOp, this->getTypeConverter()->convertType(resultType),
-        adaptor.getCiphertext(), adaptor.getLevel(), adaptor.getBaseLog(),
-        inputType.getDimension(), resultType.getDimension());
+        adaptor.getCiphertext(), levels, baseLog, inputDim, outputDim);

    return mlir::success();
  }
@@ -521,8 +566,8 @@ struct FromElementsOpPattern
 //
 // ```mlir
 // %0 = "ShapeOp" %arg0 [reassocations...]
-//        : tensor<...x!TFHE.glwe<{dimension,1,bits}{p}>> into
-//          tensor<...x!TFHE.glwe<{dimension,1,bits}{p}>>
+//        : tensor<...x!TFHE.glwe<sk(id){dimension,1}>> into
+//          tensor<...x!TFHE.glwe<sk(id){dimension,1}>>
 // ```
 //
 // becomes:
@@ -663,17 +708,15 @@ void TFHEToConcretePass::runOnOperation() {
          mlir::concretelang::Concrete::EncodeLutForCrtWopPBSTensorOp, true>,
      mlir::concretelang::GenericOneToOneOpConversionPattern<
          mlir::concretelang::TFHE::EncodePlaintextWithCrtOp,
-          mlir::concretelang::Concrete::EncodePlaintextWithCrtTensorOp, true>,
-      mlir::concretelang::GenericOneToOneOpConversionPattern<
-          mlir::concretelang::TFHE::WopPBSGLWEOp,
-          mlir::concretelang::Concrete::WopPBSCRTLweTensorOp, true>>(
+          mlir::concretelang::Concrete::EncodePlaintextWithCrtTensorOp, true>>(
      &getContext(), converter);
  // pattern of remaining TFHE ops
  patterns.insert<ZeroOpPattern<mlir::concretelang::TFHE::ZeroGLWEOp>,
                  ZeroOpPattern<mlir::concretelang::TFHE::ZeroTensorGLWEOp>>(
      &getContext());
  patterns.insert<SubIntGLWEOpPattern, BootstrapGLWEOpPattern,
-                  KeySwitchGLWEOpPattern>(&getContext(), converter);
+                  KeySwitchGLWEOpPattern, WopPBSGLWEOpPattern>(&getContext(),
+                                                               converter);

  // Add patterns to rewrite tensor operators that works on tensors of TFHE GLWE
  // types
--- a/compilers/concrete-compiler/compiler/lib/Dialect/TFHE/IR/CMakeLists.txt
+++ b/compilers/concrete-compiler/compiler/lib/Dialect/TFHE/IR/CMakeLists.txt
@@ -3,6 +3,7 @@ add_mlir_dialect_library(
  TFHEDialect.cpp
  TFHEOps.cpp
  TFHETypes.cpp
+  TFHEParameters.cpp
  ADDITIONAL_HEADER_DIRS
  ${PROJECT_SOURCE_DIR}/include/concretelang/Dialect/TFHE
  DEPENDS
--- a/compilers/concrete-compiler/compiler/lib/Dialect/TFHE/IR/TFHEDialect.cpp
+++ b/compilers/concrete-compiler/compiler/lib/Dialect/TFHE/IR/TFHEDialect.cpp
@@ -5,7 +5,9 @@

 #include "concretelang/Dialect/TFHE/IR/TFHEDialect.h"
 #include "concretelang/Dialect/TFHE/IR/TFHEOps.h"
-#include "concretelang/Dialect/TFHE/IR/TFHETypes.h"
+
+#define GET_ATTRDEF_CLASSES
+#include "concretelang/Dialect/TFHE/IR/TFHEAttrs.cpp.inc"

 #define GET_TYPEDEF_CLASSES
 #include "concretelang/Dialect/TFHE/IR/TFHEOpsTypes.cpp.inc"
@@ -26,20 +28,25 @@ void TFHEDialect::initialize() {
 #define GET_TYPEDEF_LIST
 #include "concretelang/Dialect/TFHE/IR/TFHEOpsTypes.cpp.inc"
      >();
+
+  addAttributes<
+#define GET_ATTRDEF_LIST
+#include "concretelang/Dialect/TFHE/IR/TFHEAttrs.cpp.inc"
+      >();
 }

 /// Verify that GLWE parameter are consistant
 /// - The bits parameter is 64 (we support only this for v0)
 ::mlir::LogicalResult GLWECipherTextType::verify(
    ::llvm::function_ref<::mlir::InFlightDiagnostic()> emitError,
-    signed dimension, signed polynomialSize, signed bits, signed p) {
-  if (bits != -1 && bits != 64) {
-    emitError() << "GLWE bits parameter can only be 64";
+    GLWESecretKey key) {
+  if (!key.isNotParameterized() && key.getPolySize().value() == 0) {
+    emitError() << "GLWE key has zero poly size.";
    return ::mlir::failure();
  }
-  if (p == 0) {
-    emitError() << "GLWE p parameter must be positive";
-    return mlir::failure();
+  if (!key.isNotParameterized() && key.getDimension().value() == 0) {
+    emitError() << "GLWE key has zero dimension.";
+    return ::mlir::failure();
  }
  return ::mlir::success();
 }
--- a/compilers/concrete-compiler/compiler/lib/Dialect/TFHE/IR/TFHEOps.cpp
+++ b/compilers/concrete-compiler/compiler/lib/Dialect/TFHE/IR/TFHEOps.cpp
@@ -5,7 +5,8 @@

 #include "mlir/IR/Region.h"

-#include "concretelang/Dialect/FHE/IR/FHEOps.h"
+#include "concretelang/Dialect/TFHE/IR/TFHEAttrs.h"
+#include "concretelang/Dialect/TFHE/IR/TFHEDialect.h"
 #include "concretelang/Dialect/TFHE/IR/TFHEOps.h"
 #include "concretelang/Dialect/TFHE/IR/TFHETypes.h"

@@ -13,37 +14,20 @@ namespace mlir {
 namespace concretelang {
 namespace TFHE {

-void emitOpErrorForIncompatibleGLWEParameter(mlir::OpState &op,
-                                             llvm::Twine parameter) {
-  op.emitOpError() << "should have the same GLWE '" << parameter
-                   << "' parameter";
+void emitOpErrorForKeyMismatch(mlir::OpState &op) {
+  op.emitOpError() << "should have the same GLWE Secret Key";
 }

 mlir::LogicalResult _verifyGLWEIntegerOperator(mlir::OpState &op,
                                               GLWECipherTextType &a,
                                               IntegerType &b,
                                               GLWECipherTextType &result) {
-  // verify consistency of a and result GLWE parameter
-  if (a.getDimension() != result.getDimension()) {
-    emitOpErrorForIncompatibleGLWEParameter(op, "dimension");
-    return mlir::failure();
-  }
-  if (a.getPolynomialSize() != result.getPolynomialSize()) {
-    emitOpErrorForIncompatibleGLWEParameter(op, "polynomialSize");
-    return mlir::failure();
-  }
-  if (a.getBits() != result.getBits()) {
-    emitOpErrorForIncompatibleGLWEParameter(op, "bits");
-    return mlir::failure();
-  }
-  if (a.getP() != result.getP()) {
-    emitOpErrorForIncompatibleGLWEParameter(op, "p");
+  // verify consistency of a and result GLWE secret key
+  if (a.getKey() != result.getKey()) {
+    emitOpErrorForKeyMismatch(op);
    return mlir::failure();
  }

-  if ((int)b.getWidth() != 64) {
-    op.emitOpError() << "should have the width of `b` equals to 64.";
-  }
  // verify consistency of width of inputs
  if ((int)b.getWidth() != 64) {
    op.emitOpError() << "should have the width of `b` equals 64 : "
@@ -53,9 +37,6 @@ mlir::LogicalResult _verifyGLWEIntegerOperator(mlir::OpState &op,
  return mlir::success();
 }

-/// verifyGLWEIntegerOperator verify parameters of operators that has the
-/// following signature (!TFHE.glwe<{dim,poly,bits}{p}>, ip+1) ->
-/// (!TFHE.glwe<{dim,poly,bits}{p}>))
 template <class Operator>
 mlir::LogicalResult verifyGLWEIntegerOperator(Operator &op) {
  auto a = ((mlir::Type)(op.getA().getType())).cast<GLWECipherTextType>();
@@ -66,9 +47,6 @@ mlir::LogicalResult verifyGLWEIntegerOperator(Operator &op) {
  return _verifyGLWEIntegerOperator(op, a, b, result);
 }

-/// verifyIntegerGLWEOperator verify parameters of operators that has the
-/// following signature (ip+1, !TFHE.glwe<{dim,poly,bits}{p}>) ->
-/// (!TFHE.glwe<{dim,poly,bits}{p}>))
 template <class Operator>
 mlir::LogicalResult verifyIntegerGLWEOperator(Operator &op) {
  auto a = ((mlir::Type)(op.getA().getType())).cast<IntegerType>();
@@ -79,10 +57,8 @@ mlir::LogicalResult verifyIntegerGLWEOperator(Operator &op) {
  return _verifyGLWEIntegerOperator(op, b, a, result);
 }

-/// verifyBinaryGLWEOperator verify parameters of operators that has the
-/// following signature (!TFHE.glwe<{dim,poly,bits}{p}>,
-/// !TFHE.glwe<{dim,poly,bits}{p}>) ->
-/// (!TFHE.glwe<{dim,poly,bits}{p}>))
+/// verifyBinaryGLWEOperator verify parameters of operators that have the same
+/// secret key.
 template <class Operator>
 mlir::LogicalResult verifyBinaryGLWEOperator(Operator &op) {
  auto a = ((mlir::Type)(op.getA().getType())).cast<GLWECipherTextType>();
@@ -90,49 +66,26 @@ mlir::LogicalResult verifyBinaryGLWEOperator(Operator &op) {
  auto result =
      ((mlir::Type)(op.getResult().getType())).cast<GLWECipherTextType>();

-  // verify consistency of a and result GLWE parameter
-  if (a.getDimension() != b.getDimension() ||
-      a.getDimension() != result.getDimension()) {
-    emitOpErrorForIncompatibleGLWEParameter(op, "dimension");
-    return mlir::failure();
-  }
-  if (a.getPolynomialSize() != b.getPolynomialSize() ||
-      a.getPolynomialSize() != result.getPolynomialSize()) {
-    emitOpErrorForIncompatibleGLWEParameter(op, "polynomialSize");
-    return mlir::failure();
-  }
-  if (a.getBits() != b.getBits() || a.getBits() != result.getBits()) {
-    emitOpErrorForIncompatibleGLWEParameter(op, "bits");
+  // verify consistency of a and result GLWE secret key.
+  if (a.getKey() != b.getKey() || a.getKey() != result.getKey()) {
+    emitOpErrorForKeyMismatch(op);
    return mlir::failure();
  }

  return mlir::success();
 }

-/// verifyUnaryGLWEOperator verify parameters of operators that has the
-/// following signature (!TFHE.glwe<{dim,poly,bits}{p}>) ->
-/// (!TFHE.glwe<{dim,poly,bits}{p}>))
+/// verifyUnaryGLWEOperator verify parameters of operators that have the same
+/// secret key.
 template <class Operator>
 mlir::LogicalResult verifyUnaryGLWEOperator(Operator &op) {
  auto a = ((mlir::Type)(op.getA().getType())).cast<GLWECipherTextType>();
  auto result =
      ((mlir::Type)(op.getResult().getType())).cast<GLWECipherTextType>();

-  // verify consistency of a and result GLWE parameter
-  if (a.getDimension() != result.getDimension()) {
-    emitOpErrorForIncompatibleGLWEParameter(op, "dimension");
-    return mlir::failure();
-  }
-  if (a.getPolynomialSize() != result.getPolynomialSize()) {
-    emitOpErrorForIncompatibleGLWEParameter(op, "polynomialSize");
-    return mlir::failure();
-  }
-  if (a.getBits() != result.getBits()) {
-    emitOpErrorForIncompatibleGLWEParameter(op, "bits");
-    return mlir::failure();
-  }
-  if (a.getP() != result.getP()) {
-    emitOpErrorForIncompatibleGLWEParameter(op, "p");
+  // verify consistency of a and result GLWE secret key.
+  if (a.getKey() != result.getKey()) {
+    emitOpErrorForKeyMismatch(op);
    return mlir::failure();
  }

--- a/compilers/concrete-compiler/compiler/lib/Dialect/TFHE/IR/TFHEParameters.cpp
+++ b/compilers/concrete-compiler/compiler/lib/Dialect/TFHE/IR/TFHEParameters.cpp
@@ -0,0 +1,113 @@
+// Part of the Concrete Compiler Project, under the BSD3 License with Zama
+// Exceptions. See
+// https://github.com/zama-ai/concrete-compiler-internal/blob/main/LICENSE.txt
+// for license information.
+
+#include "concretelang/Dialect/TFHE/IR/TFHEParameters.h"
+
+namespace mlir {
+namespace concretelang {
+namespace TFHE {
+
+GLWESecretKey::GLWESecretKey() {
+  dimension = -1;
+  polySize = -1;
+  id = -1;
+}
+
+GLWESecretKey::GLWESecretKey(int64_t dimension, int64_t polySize, int64_t id) {
+  assert(dimension > 0);
+  assert(polySize > 0);
+  assert(id > 0);
+  this->dimension = dimension;
+  this->polySize = polySize;
+  this->id = id;
+}
+
+bool GLWESecretKey::operator==(GLWESecretKey other) {
+  return this->id == other.id && this->dimension == other.dimension &&
+         this->polySize == other.polySize;
+}
+
+bool GLWESecretKey::operator==(const GLWESecretKey other) const {
+  return this->id == other.id && this->dimension == other.dimension &&
+         this->polySize == other.polySize;
+}
+
+bool GLWESecretKey::operator!=(GLWESecretKey other) {
+  return this->id != other.id || this->dimension != other.dimension ||
+         this->polySize != other.polySize;
+}
+
+std::optional<int64_t> GLWESecretKey::getDimension() const {
+  if (this->isNotParameterized()) {
+    return std::nullopt;
+  } else {
+    return this->dimension;
+  }
+}
+
+std::optional<int64_t> GLWESecretKey::getPolySize() const {
+  if (this->isNotParameterized()) {
+    return std::nullopt;
+  } else {
+    return this->polySize;
+  }
+}
+
+mlir::Optional<int64_t> GLWESecretKey::getId() const {
+  if (this->isNotParameterized()) {
+    return std::nullopt;
+  } else {
+    return this->id;
+  }
+}
+
+bool GLWESecretKey::isNotParameterized() const { return id <= 0; }
+
+llvm::hash_code hash_value(const GLWESecretKey &key) {
+  return llvm::hash_combine("GlweSecretKey", key.getDimension(),
+                            key.getPolySize(), key.getId());
+}
+
+} // namespace TFHE
+} // namespace concretelang
+} // namespace mlir
+
+namespace mlir {
+AsmPrinter &operator<<(AsmPrinter &p,
+                       mlir::concretelang::TFHE::GLWESecretKey key) {
+  if (key.isNotParameterized()) {
+    p << "sk[?]";
+  } else {
+    p << "sk[" << key.getId() << "]<" << key.getPolySize().value() << ","
+      << key.getDimension().value() << ">";
+  }
+  return p;
+}
+
+FailureOr<mlir::concretelang::TFHE::GLWESecretKey>
+FieldParser<mlir::concretelang::TFHE::GLWESecretKey>::parse(AsmParser &parser) {
+  int64_t dimension = -1, polySize = -1, id = -1;
+  if (parser.parseKeyword("sk") || parser.parseLSquare()) {
+    return mlir::failure();
+  }
+  auto maybeId = parser.parseOptionalInteger(id);
+  if (maybeId.has_value()) {
+    if (maybeId.value() || parser.parseRSquare() || parser.parseLess() ||
+        parser.parseInteger(polySize) || parser.parseComma() ||
+        parser.parseInteger(dimension) || parser.parseGreater()) {
+      return mlir::failure();
+    }
+  } else {
+    if (parser.parseQuestion() || parser.parseRSquare()) {
+      return mlir::failure();
+    }
+  }
+  if (id <= 0) {
+    return mlir::concretelang::TFHE::GLWESecretKey();
+  } else {
+    return mlir::concretelang::TFHE::GLWESecretKey(dimension, polySize, id);
+  }
+}
+} // namespace mlir
--- a/compilers/concrete-compiler/compiler/lib/Dialect/TFHE/IR/TFHETypes.cpp
+++ b/compilers/concrete-compiler/compiler/lib/Dialect/TFHE/IR/TFHETypes.cpp
@@ -4,6 +4,7 @@
 // for license information.

 #include <concretelang/Dialect/TFHE/IR/TFHETypes.h>
+#include <mlir/IR/DialectImplementation.h>

 namespace mlir {
 namespace concretelang {
@@ -18,57 +19,28 @@ void printSigned(mlir::AsmPrinter &p, signed i) {

 void GLWECipherTextType::print(mlir::AsmPrinter &p) const {
  p << "<";
-  p << "{";
-  printSigned(p, getDimension());
-  p << ",";
-  printSigned(p, getPolynomialSize());
-  p << ",";
-  printSigned(p, getBits());
-  p << "}";
-
-  p << "{";
-  printSigned(p, getP());
-  p << "}>";
+  p << getKey();
+  p << ">";
 }

 mlir::Type GLWECipherTextType::parse(AsmParser &parser) {
  if (parser.parseLess())
    return mlir::Type();

-  if (parser.parseLBrace())
-    return mlir::Type();
-
  // First parameters block
-  int dimension = -1;
-  if (parser.parseOptionalKeyword("_") && parser.parseInteger(dimension))
-    return mlir::Type();
-  if (parser.parseComma())
-    return mlir::Type();
-  int polynomialSize = -1;
-  if (parser.parseOptionalKeyword("_") && parser.parseInteger(polynomialSize))
-    return mlir::Type();
-  if (parser.parseComma())
-    return mlir::Type();
-  int bits = -1;
-  if (parser.parseOptionalKeyword("_") && parser.parseInteger(bits))
-    return mlir::Type();
-  if (parser.parseRBrace())
-    return mlir::Type();
-
-  // Next parameters block
-  if (parser.parseLBrace())
-    return mlir::Type();
-  int p = -1;
-  if (parser.parseInteger(p))
-    return mlir::Type();
-  if (parser.parseRBrace())
+  FailureOr<mlir::concretelang::TFHE::GLWESecretKey> maybeKey =
+      FieldParser<GLWESecretKey>::parse(parser);
+  if (failed(maybeKey))
    return mlir::Type();

  if (parser.parseGreater())
    return mlir::Type();
+
  Location loc = parser.getEncodedSourceLoc(parser.getNameLoc());
-  return getChecked(loc, loc.getContext(), dimension, polynomialSize, bits, p);
+
+  return getChecked(loc, loc.getContext(), maybeKey.value());
 }
+
 } // namespace TFHE
 } // namespace concretelang
 } // namespace mlir
--- a/compilers/concrete-compiler/compiler/tests/check_tests/BugReport/bug_report_785.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/BugReport/bug_report_785.mlir
@@ -1,4 +1,4 @@
-// RUN: concretecompiler --action=dump-llvm-ir %s
+// RUN: concretecompiler --action=dump-llvm-ir  %s
 // Just ensure that compile
 // https://github.com/zama-ai/concrete-compiler-internal/issues/785
 func.func @main(%arg0: !FHE.eint<15>, %cst: tensor<32768xi64>) -> tensor<1x!FHE.eint<15>> {
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/add_eint.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/add_eint.mlir
@@ -1,18 +1,18 @@
 // RUN: concretecompiler --optimize-tfhe=false --action=dump-tfhe %s --large-integer-crt-decomposition=2,3,5,7,11 --large-integer-circuit-bootstrap=2,9 --large-integer-packing-keyswitch=694,1024,4,9 --v0-parameter=2,10,693,4,9,7,2 2>&1| FileCheck %s

-//CHECK:  func.func @add_eint(%[[Varg0:.*]]: tensor<5x!TFHE.glwe<{_,_,_}{7}>>, %[[Varg1:.*]]: tensor<5x!TFHE.glwe<{_,_,_}{7}>>) -> tensor<5x!TFHE.glwe<{_,_,_}{7}>> {
-//CHECK-NEXT:    %[[V0:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+//CHECK:  func.func @add_eint(%[[Varg0:.*]]: tensor<5x!TFHE.glwe<sk[?]>>, %[[Varg1:.*]]: tensor<5x!TFHE.glwe<sk[?]>>) -> tensor<5x!TFHE.glwe<sk[?]>> {
+//CHECK-NEXT:    %[[V0:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:    %[[Vc0:.*]] = arith.constant 0 : index
 //CHECK-NEXT:    %[[Vc1:.*]] = arith.constant 1 : index
 //CHECK-NEXT:    %[[Vc5:.*]] = arith.constant 5 : index
-//CHECK-NEXT:    %[[V1:.*]] = scf.for %[[Varg2:.*]] = %[[Vc0]] to %[[Vc5]] step %[[Vc1]] iter_args(%[[Varg3:.*]] = %[[V0]]) -> (tensor<5x!TFHE.glwe<{_,_,_}{7}>>) {
-//CHECK-NEXT:      %[[V2:.*]] = tensor.extract %[[Varg0]][%[[Varg2]]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
-//CHECK-NEXT:      %[[V3:.*]] = tensor.extract %[[Varg1]][%[[Varg2]]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
-//CHECK-NEXT:      %[[V4:.*]] = "TFHE.add_glwe"(%[[V2]], %[[V3]]) : (!TFHE.glwe<{_,_,_}{7}>, !TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}>
-//CHECK-NEXT:      %[[V5:.*]] = tensor.insert %[[V4]] into %[[Varg3]][%[[Varg2]]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
-//CHECK-NEXT:      scf.yield %[[V5]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+//CHECK-NEXT:    %[[V1:.*]] = scf.for %[[Varg2:.*]] = %[[Vc0]] to %[[Vc5]] step %[[Vc1]] iter_args(%[[Varg3:.*]] = %[[V0]]) -> (tensor<5x!TFHE.glwe<sk[?]>>) {
+//CHECK-NEXT:      %[[V2:.*]] = tensor.extract %[[Varg0]][%[[Varg2]]] : tensor<5x!TFHE.glwe<sk[?]>>
+//CHECK-NEXT:      %[[V3:.*]] = tensor.extract %[[Varg1]][%[[Varg2]]] : tensor<5x!TFHE.glwe<sk[?]>>
+//CHECK-NEXT:      %[[V4:.*]] = "TFHE.add_glwe"(%[[V2]], %[[V3]]) : (!TFHE.glwe<sk[?]>, !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
+//CHECK-NEXT:      %[[V5:.*]] = tensor.insert %[[V4]] into %[[Varg3]][%[[Varg2]]] : tensor<5x!TFHE.glwe<sk[?]>>
+//CHECK-NEXT:      scf.yield %[[V5]] : tensor<5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:    }
-//CHECK-NEXT:    return %[[V1]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+//CHECK-NEXT:    return %[[V1]] : tensor<5x!TFHE.glwe<sk[?]>>
 func.func @add_eint(%arg0: !FHE.eint<7>, %arg1: !FHE.eint<7>) -> !FHE.eint<7> {
  %1 = "FHE.add_eint"(%arg0, %arg1): (!FHE.eint<7>, !FHE.eint<7>) -> (!FHE.eint<7>)
  return %1: !FHE.eint<7>
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/add_eint_int.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/add_eint_int.mlir
@@ -1,21 +1,21 @@
 // RUN: concretecompiler --optimize-tfhe=false --action=dump-tfhe %s --large-integer-crt-decomposition=2,3,5,7,11 --large-integer-circuit-bootstrap=2,9 --large-integer-packing-keyswitch=694,1024,4,9 --v0-parameter=2,10,693,4,9,7,2 2>&1| FileCheck %s

-// CHECK: func.func @add_eint_int(%[[Varg0:.*]]: tensor<5x!TFHE.glwe<{_,_,_}{7}>>) -> tensor<5x!TFHE.glwe<{_,_,_}{7}>> {
+// CHECK: func.func @add_eint_int(%[[Varg0:.*]]: tensor<5x!TFHE.glwe<sk[?]>>) -> tensor<5x!TFHE.glwe<sk[?]>> {
 // CHECK-NEXT:   %[[Vc1_i8:.*]] = arith.constant 1 : i8
 // CHECK-NEXT:   %[[V0:.*]] = arith.extsi %[[Vc1_i8]] : i8 to i64
 // CHECK-NEXT:   %[[V1:.*]] = "TFHE.encode_plaintext_with_crt"(%[[V0]]) {mods = [2, 3, 5, 7, 11], modsProd = 2310 : i64} : (i64) -> tensor<5xi64>
-// CHECK-NEXT:   %[[V2:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT:   %[[V2:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:   %[[Vc0:.*]] = arith.constant 0 : index
 // CHECK-NEXT:   %[[Vc1:.*]] = arith.constant 1 : index
 // CHECK-NEXT:   %[[Vc5:.*]] = arith.constant 5 : index
-// CHECK-NEXT:   %[[V3:.*]] = scf.for %[[Varg1:.*]] = %[[Vc0]] to %[[Vc5]] step %[[Vc1]] iter_args(%[[Varg2:.*]] = %[[V2]]) -> (tensor<5x!TFHE.glwe<{_,_,_}{7}>>) {
-// CHECK-NEXT:     %[[V4:.*]] = tensor.extract %[[Varg0]][%[[Varg1]]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT:   %[[V3:.*]] = scf.for %[[Varg1:.*]] = %[[Vc0]] to %[[Vc5]] step %[[Vc1]] iter_args(%[[Varg2:.*]] = %[[V2]]) -> (tensor<5x!TFHE.glwe<sk[?]>>) {
+// CHECK-NEXT:     %[[V4:.*]] = tensor.extract %[[Varg0]][%[[Varg1]]] : tensor<5x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:     %[[V5:.*]] = tensor.extract %[[V1]][%[[Varg1]]] : tensor<5xi64>
-// CHECK-NEXT:     %[[V6:.*]] = "TFHE.add_glwe_int"(%[[V4]], %[[V5]]) : (!TFHE.glwe<{_,_,_}{7}>, i64) -> !TFHE.glwe<{_,_,_}{7}>
-// CHECK-NEXT:     %[[V7:.*]] = tensor.insert %[[V6]] into %[[Varg2]][%[[Varg1]]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
-// CHECK-NEXT:     scf.yield %[[V7]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT:     %[[V6:.*]] = "TFHE.add_glwe_int"(%[[V4]], %[[V5]]) : (!TFHE.glwe<sk[?]>, i64) -> !TFHE.glwe<sk[?]>
+// CHECK-NEXT:     %[[V7:.*]] = tensor.insert %[[V6]] into %[[Varg2]][%[[Varg1]]] : tensor<5x!TFHE.glwe<sk[?]>>
+// CHECK-NEXT:     scf.yield %[[V7]] : tensor<5x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:   }
-// CHECK-NEXT:   return %[[V3]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT:   return %[[V3]] : tensor<5x!TFHE.glwe<sk[?]>>
 func.func @add_eint_int(%arg0: !FHE.eint<7>) -> !FHE.eint<7> {
  %0 = arith.constant 1 : i8
  %1 = "FHE.add_eint_int"(%arg0, %0): (!FHE.eint<7>, i8) -> (!FHE.eint<7>)
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/apply_univariate.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/apply_univariate.mlir
@@ -1,9 +1,9 @@
 // RUN: concretecompiler --optimize-tfhe=false --action=dump-tfhe %s --large-integer-crt-decomposition=2,3,5,7,11 --large-integer-circuit-bootstrap=2,9 --large-integer-packing-keyswitch=694,1024,4,9 --v0-parameter=2,10,693,4,9,7,2 2>&1| FileCheck %s

-// CHECK: func.func @apply_lookup_table(%arg0: tensor<5x!TFHE.glwe<{_,_,_}{2}>>, %arg1: tensor<4xi64>) -> tensor<5x!TFHE.glwe<{_,_,_}{3}>>
+// CHECK: func.func @apply_lookup_table(%arg0: tensor<5x!TFHE.glwe<sk[?]>>, %arg1: tensor<4xi64>) -> tensor<5x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT: %0 = "TFHE.encode_lut_for_crt_woppbs"(%arg1) {crtBits = [1, 2, 3, 3, 4], crtDecomposition = [2, 3, 5, 7, 11], isSigned = false, modulusProduct = 2310 : i32} : (tensor<4xi64>) -> tensor<5x8192xi64>
-// CHECK-NEXT: %1 = "TFHE.wop_pbs_glwe"(%arg0, %0) {bootstrapBaseLog = -1 : i32, bootstrapLevel = -1 : i32, circuitBootstrapBaseLog = -1 : i32, circuitBootstrapLevel = -1 : i32, crtDecomposition = [], keyswitchBaseLog = -1 : i32, keyswitchLevel = -1 : i32, packingKeySwitchBaseLog = -1 : i32, packingKeySwitchInputLweDimension = -1 : i32, packingKeySwitchLevel = -1 : i32, packingKeySwitchoutputPolynomialSize = -1 : i32} : (tensor<5x!TFHE.glwe<{_,_,_}{2}>>, tensor<5x8192xi64>) -> tensor<5x!TFHE.glwe<{_,_,_}{3}>>
-// CHECK-NEXT: return %1 : tensor<5x!TFHE.glwe<{_,_,_}{3}>>
+// CHECK-NEXT: %1 = "TFHE.wop_pbs_glwe"(%arg0, %0)  {bsk = #TFHE.bsk<sk[?], sk[?], -1, -1, -1, -1>, cbsBaseLog = -1 : i32, cbsLevels = -1 : i32, crtDecomposition = [], ksk = #TFHE.ksk<sk[?], sk[?], -1, -1>, pksk = #TFHE.pksk<sk[?], sk[?], -1, -1, -1, -1>} : (tensor<5x!TFHE.glwe<sk[?]>>, tensor<5x8192xi64>) -> tensor<5x!TFHE.glwe<sk[?]>>
+// CHECK-NEXT: return %1 : tensor<5x!TFHE.glwe<sk[?]>>
 func.func @apply_lookup_table(%arg0: !FHE.eint<2>, %arg1: tensor<4xi64>) -> !FHE.eint<3> {
  %1 = "FHE.apply_lookup_table"(%arg0, %arg1): (!FHE.eint<2>, tensor<4xi64>) -> (!FHE.eint<3>)
  return %1: !FHE.eint<3>
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/apply_univariate_cst.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/apply_univariate_cst.mlir
@@ -1,10 +1,10 @@
 // RUN: concretecompiler --optimize-tfhe=false --action=dump-tfhe %s --large-integer-crt-decomposition=2,3,5,7,11 --large-integer-circuit-bootstrap=2,9 --large-integer-packing-keyswitch=694,1024,4,9 --v0-parameter=2,10,693,4,9,7,2 2>&1| FileCheck %s

-// CHECK: func.func @apply_lookup_table_cst(%arg0: tensor<5x!TFHE.glwe<{_,_,_}{7}>>) -> tensor<5x!TFHE.glwe<{_,_,_}{7}>> {
+// CHECK: func.func @apply_lookup_table_cst(%arg0: tensor<5x!TFHE.glwe<sk[?]>>) -> tensor<5x!TFHE.glwe<sk[?]>> {
 // CHECK-NEXT: %cst = arith.constant dense<"0x00000000000000000100000000000000020000000000000003000000000000000400000000000000050000000000000006000000000000000700000000000000080000000000000009000000000000000A000000000000000B000000000000000C000000000000000D000000000000000E000000000000000F0000000000000010000000000000001100000000000000120000000000000013000000000000001400000000000000150000000000000016000000000000001700000000000000180000000000000019000000000000001A000000000000001B000000000000001C000000000000001D000000000000001E000000000000001F0000000000000020000000000000002100000000000000220000000000000023000000000000002400000000000000250000000000000026000000000000002700000000000000280000000000000029000000000000002A000000000000002B000000000000002C000000000000002D000000000000002E000000000000002F0000000000000030000000000000003100000000000000320000000000000033000000000000003400000000000000350000000000000036000000000000003700000000000000380000000000000039000000000000003A000000000000003B000000000000003C000000000000003D000000000000003E000000000000003F0000000000000040000000000000004100000000000000420000000000000043000000000000004400000000000000450000000000000046000000000000004700000000000000480000000000000049000000000000004A000000000000004B000000000000004C000000000000004D000000000000004E000000000000004F0000000000000050000000000000005100000000000000520000000000000053000000000000005400000000000000550000000000000056000000000000005700000000000000580000000000000059000000000000005A000000000000005B000000000000005C000000000000005D000000000000005E000000000000005F0000000000000060000000000000006100000000000000620000000000000063000000000000006400000000000000650000000000000066000000000000006700000000000000680000000000000069000000000000006A000000000000006B000000000000006C000000000000006D000000000000006E000000000000006F0000000000000070000000000000007100000000000000720000000000000073000000000000007400000000000000750000000000000076000000000000007700000000000000780000000000000079000000000000007A000000000000007B000000000000007C000000000000007D000000000000007E000000000000007F00000000000000"> : tensor<128xi64>
 // CHECK-NEXT: %0 = "TFHE.encode_lut_for_crt_woppbs"(%cst) {crtBits = [1, 2, 3, 3, 4], crtDecomposition = [2, 3, 5, 7, 11], isSigned = false, modulusProduct = 2310 : i32} : (tensor<128xi64>) -> tensor<5x8192xi64>
-// CHECK-NEXT: %1 = "TFHE.wop_pbs_glwe"(%arg0, %0) {bootstrapBaseLog = -1 : i32, bootstrapLevel = -1 : i32, circuitBootstrapBaseLog = -1 : i32, circuitBootstrapLevel = -1 : i32, crtDecomposition = [], keyswitchBaseLog = -1 : i32, keyswitchLevel = -1 : i32, packingKeySwitchBaseLog = -1 : i32, packingKeySwitchInputLweDimension = -1 : i32, packingKeySwitchLevel = -1 : i32, packingKeySwitchoutputPolynomialSize = -1 : i32} : (tensor<5x!TFHE.glwe<{_,_,_}{7}>>, tensor<5x8192xi64>) -> tensor<5x!TFHE.glwe<{_,_,_}{7}>>
-// CHECK-NEXT: return %1 : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT: %1 = "TFHE.wop_pbs_glwe"(%arg0, %0) {bsk = #TFHE.bsk<sk[?], sk[?], -1, -1, -1, -1>, cbsBaseLog = -1 : i32, cbsLevels = -1 : i32, crtDecomposition = [], ksk = #TFHE.ksk<sk[?], sk[?], -1, -1>, pksk = #TFHE.pksk<sk[?], sk[?], -1, -1, -1, -1>} : (tensor<5x!TFHE.glwe<sk[?]>>, tensor<5x8192xi64>) -> tensor<5x!TFHE.glwe<sk[?]>>
+// CHECK-NEXT: return %1 : tensor<5x!TFHE.glwe<sk[?]>>
 func.func @apply_lookup_table_cst(%arg0: !FHE.eint<7>) -> !FHE.eint<7> {
  %tlu = arith.constant dense<[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127]> : tensor<128xi64>
  %1 = "FHE.apply_lookup_table"(%arg0, %tlu): (!FHE.eint<7>, tensor<128xi64>) -> (!FHE.eint<7>)
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/conv2d.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/conv2d.mlir
@@ -1,6 +1,6 @@
 // RUN: concretecompiler --optimize-tfhe=false --action=dump-tfhe %s --large-integer-crt-decomposition=2,3,5,7,11 --large-integer-circuit-bootstrap=2,9 --large-integer-packing-keyswitch=694,1024,4,9 --v0-parameter=2,10,693,4,9,7,2 2>&1| FileCheck %s

-//CHECK: func.func @conv2d(%[[Varg0:.*]]: tensor<100x3x28x28x5x!TFHE.glwe<{_,_,_}{2}>>, %[[Varg1:.*]]: tensor<4x3x14x14xi3>, %[[Varg2:.*]]: tensor<4xi3>) -> tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>> {
+//CHECK: func.func @conv2d(%[[Varg0:.*]]: tensor<100x3x28x28x5x!TFHE.glwe<sk[?]>>, %[[Varg1:.*]]: tensor<4x3x14x14xi3>, %[[Varg2:.*]]: tensor<4xi3>) -> tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>> {
 //CHECK-NEXT:    %[[Vc0:.*]] = arith.constant 0 : index
 //CHECK-NEXT:    %[[Vc100:.*]] = arith.constant 100 : index
 //CHECK-NEXT:    %[[Vc1:.*]] = arith.constant 1 : index
@@ -8,90 +8,90 @@
 //CHECK-NEXT:    %[[Vc15:.*]] = arith.constant 15 : index
 //CHECK-NEXT:    %[[Vc3:.*]] = arith.constant 3 : index
 //CHECK-NEXT:    %[[Vc14:.*]] = arith.constant 14 : index
-//CHECK-NEXT:    %[[V0:.*]] = "TFHE.zero_tensor"() : () -> tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
-//CHECK-NEXT:    %[[V1:.*]] = scf.for %[[Varg3:.*]] = %[[Vc0]] to %[[Vc100]] step %[[Vc1]] iter_args(%[[Varg4:.*]] = %[[V0]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>) {
-//CHECK-NEXT:      %[[V3:.*]] = scf.for %[[Varg5:.*]] = %[[Vc0]] to %[[Vc4]] step %[[Vc1]] iter_args(%[[Varg6:.*]] = %[[Varg4]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>) {
-//CHECK-NEXT:        %[[V4:.*]] = scf.for %[[Varg7:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg8:.*]] = %[[Varg6]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>) {
-//CHECK-NEXT:          %[[V5:.*]] = scf.for %[[Varg9:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg10:.*]] = %[[Varg8]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>) {
+//CHECK-NEXT:    %[[V0:.*]] = "TFHE.zero_tensor"() : () -> tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
+//CHECK-NEXT:    %[[V1:.*]] = scf.for %[[Varg3:.*]] = %[[Vc0]] to %[[Vc100]] step %[[Vc1]] iter_args(%[[Varg4:.*]] = %[[V0]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>) {
+//CHECK-NEXT:      %[[V3:.*]] = scf.for %[[Varg5:.*]] = %[[Vc0]] to %[[Vc4]] step %[[Vc1]] iter_args(%[[Varg6:.*]] = %[[Varg4]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>) {
+//CHECK-NEXT:        %[[V4:.*]] = scf.for %[[Varg7:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg8:.*]] = %[[Varg6]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>) {
+//CHECK-NEXT:          %[[V5:.*]] = scf.for %[[Varg9:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg10:.*]] = %[[Varg8]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>) {
 //CHECK-NEXT:            %[[Vextracted:.*]] = tensor.extract %[[Varg2]]{{\[}}%[[Varg5]]{{\]}} : tensor<4xi3>
 //CHECK-NEXT:            %[[Vc0_0:.*]] = arith.constant 0 : index
-//CHECK-NEXT:            %[[Vextracted_slice:.*]] = tensor.extract_slice %[[Varg10]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]], %[[Vc0_0]]{{\] \[1, 1, 1, 1, 5\] \[1, 1, 1, 1, 1\]}} : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>> to tensor<5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:            %[[Vextracted_slice:.*]] = tensor.extract_slice %[[Varg10]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]], %[[Vc0_0]]{{\] \[1, 1, 1, 1, 5\] \[1, 1, 1, 1, 1\]}} : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>> to tensor<5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:            %[[V6:.*]] = arith.extsi %[[Vextracted]] : i3 to i64
 //CHECK-NEXT:            %[[V7:.*]] = "TFHE.encode_plaintext_with_crt"(%[[V6]]) {mods = {{\[2, 3, 5, 7, 11\], modsProd}} = 2310 : i64} : (i64) -> tensor<5xi64>
-//CHECK-NEXT:            %[[V8:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:            %[[V8:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:            %[[Vc0_1:.*]] = arith.constant 0 : index
 //CHECK-NEXT:            %[[Vc1_2:.*]] = arith.constant 1 : index
 //CHECK-NEXT:            %[[Vc5:.*]] = arith.constant 5 : index
-//CHECK-NEXT:            %[[V9:.*]] = scf.for %[[Varg11:.*]] = %[[Vc0_1]] to %[[Vc5]] step %[[Vc1_2]] iter_args(%[[Varg12:.*]] = %[[V8]]) -> (tensor<5x!TFHE.glwe<{_,_,_}{2}>>) {
-//CHECK-NEXT:              %[[Vextracted_4:.*]] = tensor.extract %[[Vextracted_slice]]{{\[}}%[[Varg11]]{{\]}} : tensor<5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:            %[[V9:.*]] = scf.for %[[Varg11:.*]] = %[[Vc0_1]] to %[[Vc5]] step %[[Vc1_2]] iter_args(%[[Varg12:.*]] = %[[V8]]) -> (tensor<5x!TFHE.glwe<sk[?]>>) {
+//CHECK-NEXT:              %[[Vextracted_4:.*]] = tensor.extract %[[Vextracted_slice]]{{\[}}%[[Varg11]]{{\]}} : tensor<5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:              %[[Vextracted_5:.*]] = tensor.extract %[[V7]]{{\[}}%[[Varg11]]{{\]}} : tensor<5xi64>
-//CHECK-NEXT:              %[[V10:.*]] = "TFHE.add_glwe_int"(%[[Vextracted_4]], %[[Vextracted_5]]) : (!TFHE.glwe<{_,_,_}{2}>, i64) -> !TFHE.glwe<{_,_,_}{2}>
-//CHECK-NEXT:              %[[Vinserted:.*]] = tensor.insert %[[V10]] into %[[Varg12]]{{\[}}%[[Varg11]]{{\]}} : tensor<5x!TFHE.glwe<{_,_,_}{2}>>
-//CHECK-NEXT:              scf.yield %[[Vinserted]] : tensor<5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:              %[[V10:.*]] = "TFHE.add_glwe_int"(%[[Vextracted_4]], %[[Vextracted_5]]) : (!TFHE.glwe<sk[?]>, i64) -> !TFHE.glwe<sk[?]>
+//CHECK-NEXT:              %[[Vinserted:.*]] = tensor.insert %[[V10]] into %[[Varg12]]{{\[}}%[[Varg11]]{{\]}} : tensor<5x!TFHE.glwe<sk[?]>>
+//CHECK-NEXT:              scf.yield %[[Vinserted]] : tensor<5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:            }
 //CHECK-NEXT:            %[[Vc0_3:.*]] = arith.constant 0 : index
-//CHECK-NEXT:            %[[Vinserted_slice:.*]] = tensor.insert_slice %[[V9]] into %[[Varg10]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]], %[[Vc0_3]]{{\] \[1, 1, 1, 1, 5\] \[1, 1, 1, 1, 1\]}} : tensor<5x!TFHE.glwe<{_,_,_}{2}>> into tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
-//CHECK-NEXT:            scf.yield %[[Vinserted_slice]] : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:            %[[Vinserted_slice:.*]] = tensor.insert_slice %[[V9]] into %[[Varg10]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]], %[[Vc0_3]]{{\] \[1, 1, 1, 1, 5\] \[1, 1, 1, 1, 1\]}} : tensor<5x!TFHE.glwe<sk[?]>> into tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
+//CHECK-NEXT:            scf.yield %[[Vinserted_slice]] : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:          }
-//CHECK-NEXT:          scf.yield %[[V5]] : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:          scf.yield %[[V5]] : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:        }
-//CHECK-NEXT:        scf.yield %[[V4]] : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:        scf.yield %[[V4]] : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:      }
-//CHECK-NEXT:      scf.yield %[[V3]] : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:      scf.yield %[[V3]] : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:    }
-//CHECK-NEXT:    %[[V2:.*]] = scf.for %[[Varg3:.*]] = %[[Vc0]] to %[[Vc100]] step %[[Vc1]] iter_args(%[[Varg4:.*]] = %[[V1]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>) {
-//CHECK-NEXT:      %[[V3:.*]] = scf.for %[[Varg5:.*]] = %[[Vc0]] to %[[Vc4]] step %[[Vc1]] iter_args(%[[Varg6:.*]] = %[[Varg4]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>) {
-//CHECK-NEXT:        %[[V4:.*]] = scf.for %[[Varg7:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg8:.*]] = %[[Varg6]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>) {
-//CHECK-NEXT:          %[[V5:.*]] = scf.for %[[Varg9:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg10:.*]] = %[[Varg8]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>) {
-//CHECK-NEXT:            %[[V6:.*]] = scf.for %[[Varg11:.*]] = %[[Vc0]] to %[[Vc3]] step %[[Vc1]] iter_args(%[[Varg12:.*]] = %[[Varg10]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>) {
-//CHECK-NEXT:              %[[V7:.*]] = scf.for %[[Varg13:.*]] = %[[Vc0]] to %[[Vc14]] step %[[Vc1]] iter_args(%[[Varg14:.*]] = %[[Varg12]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>) {
-//CHECK-NEXT:                %[[V8:.*]] = scf.for %[[Varg15:.*]] = %[[Vc0]] to %[[Vc14]] step %[[Vc1]] iter_args(%[[Varg16:.*]] = %[[Varg14]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>) {
+//CHECK-NEXT:    %[[V2:.*]] = scf.for %[[Varg3:.*]] = %[[Vc0]] to %[[Vc100]] step %[[Vc1]] iter_args(%[[Varg4:.*]] = %[[V1]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>) {
+//CHECK-NEXT:      %[[V3:.*]] = scf.for %[[Varg5:.*]] = %[[Vc0]] to %[[Vc4]] step %[[Vc1]] iter_args(%[[Varg6:.*]] = %[[Varg4]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>) {
+//CHECK-NEXT:        %[[V4:.*]] = scf.for %[[Varg7:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg8:.*]] = %[[Varg6]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>) {
+//CHECK-NEXT:          %[[V5:.*]] = scf.for %[[Varg9:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg10:.*]] = %[[Varg8]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>) {
+//CHECK-NEXT:            %[[V6:.*]] = scf.for %[[Varg11:.*]] = %[[Vc0]] to %[[Vc3]] step %[[Vc1]] iter_args(%[[Varg12:.*]] = %[[Varg10]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>) {
+//CHECK-NEXT:              %[[V7:.*]] = scf.for %[[Varg13:.*]] = %[[Vc0]] to %[[Vc14]] step %[[Vc1]] iter_args(%[[Varg14:.*]] = %[[Varg12]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>) {
+//CHECK-NEXT:                %[[V8:.*]] = scf.for %[[Varg15:.*]] = %[[Vc0]] to %[[Vc14]] step %[[Vc1]] iter_args(%[[Varg16:.*]] = %[[Varg14]]) -> (tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>) {
 //CHECK-NEXT:                  %[[V9:.*]] = affine.apply #map(%[[Varg7]], %[[Varg13]])
 //CHECK-NEXT:                  %[[V10:.*]] = affine.apply #map(%[[Varg9]], %[[Varg15]])
 //CHECK-NEXT:                  %[[Vc0_0:.*]] = arith.constant 0 : index
-//CHECK-NEXT:                  %[[Vextracted_slice:.*]] = tensor.extract_slice %[[Varg0]]{{\[}}%[[Varg3]], %[[Varg11]], %[[V9]], %[[V10]], %[[Vc0_0]]{{\] \[1, 1, 1, 1, 5\] \[1, 1, 1, 1, 1\]}} : tensor<100x3x28x28x5x!TFHE.glwe<{_,_,_}{2}>> to tensor<5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:                  %[[Vextracted_slice:.*]] = tensor.extract_slice %[[Varg0]]{{\[}}%[[Varg3]], %[[Varg11]], %[[V9]], %[[V10]], %[[Vc0_0]]{{\] \[1, 1, 1, 1, 5\] \[1, 1, 1, 1, 1\]}} : tensor<100x3x28x28x5x!TFHE.glwe<sk[?]>> to tensor<5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:                  %[[Vextracted:.*]] = tensor.extract %[[Varg1]]{{\[}}%[[Varg5]], %[[Varg11]], %[[Varg13]], %[[Varg15]]{{\]}} : tensor<4x3x14x14xi3>
 //CHECK-NEXT:                  %[[Vc0_1:.*]] = arith.constant 0 : index
-//CHECK-NEXT:                  %[[Vextracted_slice_2:.*]] = tensor.extract_slice %[[Varg16]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]], %[[Vc0_1]]{{\] \[1, 1, 1, 1, 5\] \[1, 1, 1, 1, 1\]}} : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>> to tensor<5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:                  %[[Vextracted_slice_2:.*]] = tensor.extract_slice %[[Varg16]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]], %[[Vc0_1]]{{\] \[1, 1, 1, 1, 5\] \[1, 1, 1, 1, 1\]}} : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>> to tensor<5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:                  %[[V11:.*]] = arith.extsi %[[Vextracted]] : i3 to i64
-//CHECK-NEXT:                  %[[V12:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:                  %[[V12:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:                  %[[Vc0_3:.*]] = arith.constant 0 : index
 //CHECK-NEXT:                  %[[Vc1_4:.*]] = arith.constant 1 : index
 //CHECK-NEXT:                  %[[Vc5:.*]] = arith.constant 5 : index
-//CHECK-NEXT:                  %[[V13:.*]] = scf.for %[[Varg17:.*]] = %[[Vc0_3]] to %[[Vc5]] step %[[Vc1_4]] iter_args(%[[Varg18:.*]] = %[[V12]]) -> (tensor<5x!TFHE.glwe<{_,_,_}{2}>>) {
-//CHECK-NEXT:                    %[[Vextracted_9:.*]] = tensor.extract %[[Vextracted_slice]]{{\[}}%[[Varg17]]{{\]}} : tensor<5x!TFHE.glwe<{_,_,_}{2}>>
-//CHECK-NEXT:                    %[[V16:.*]] = "TFHE.mul_glwe_int"(%[[Vextracted_9]], %[[V11]]) : (!TFHE.glwe<{_,_,_}{2}>, i64) -> !TFHE.glwe<{_,_,_}{2}>
-//CHECK-NEXT:                    %[[Vinserted:.*]] = tensor.insert %[[V16]] into %[[Varg18]]{{\[}}%[[Varg17]]{{\]}} : tensor<5x!TFHE.glwe<{_,_,_}{2}>>
-//CHECK-NEXT:                    scf.yield %[[Vinserted]] : tensor<5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:                  %[[V13:.*]] = scf.for %[[Varg17:.*]] = %[[Vc0_3]] to %[[Vc5]] step %[[Vc1_4]] iter_args(%[[Varg18:.*]] = %[[V12]]) -> (tensor<5x!TFHE.glwe<sk[?]>>) {
+//CHECK-NEXT:                    %[[Vextracted_9:.*]] = tensor.extract %[[Vextracted_slice]]{{\[}}%[[Varg17]]{{\]}} : tensor<5x!TFHE.glwe<sk[?]>>
+//CHECK-NEXT:                    %[[V16:.*]] = "TFHE.mul_glwe_int"(%[[Vextracted_9]], %[[V11]]) : (!TFHE.glwe<sk[?]>, i64) -> !TFHE.glwe<sk[?]>
+//CHECK-NEXT:                    %[[Vinserted:.*]] = tensor.insert %[[V16]] into %[[Varg18]]{{\[}}%[[Varg17]]{{\]}} : tensor<5x!TFHE.glwe<sk[?]>>
+//CHECK-NEXT:                    scf.yield %[[Vinserted]] : tensor<5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:                  }
-//CHECK-NEXT:                  %[[V14:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:                  %[[V14:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:                  %[[Vc0_5:.*]] = arith.constant 0 : index
 //CHECK-NEXT:                  %[[Vc1_6:.*]] = arith.constant 1 : index
 //CHECK-NEXT:                  %[[Vc5_7:.*]] = arith.constant 5 : index
-//CHECK-NEXT:                  %[[V15:.*]] = scf.for %[[Varg17:.*]] = %[[Vc0_5]] to %[[Vc5_7]] step %[[Vc1_6]] iter_args(%[[Varg18:.*]] = %[[V14]]) -> (tensor<5x!TFHE.glwe<{_,_,_}{2}>>) {
-//CHECK-NEXT:                    %[[Vextracted_9:.*]] = tensor.extract %[[Vextracted_slice_2]]{{\[}}%[[Varg17]]{{\]}} : tensor<5x!TFHE.glwe<{_,_,_}{2}>>
-//CHECK-NEXT:                    %[[Vextracted_10:.*]] = tensor.extract %[[V13]]{{\[}}%[[Varg17]]{{\]}} : tensor<5x!TFHE.glwe<{_,_,_}{2}>>
-//CHECK-NEXT:                    %[[V16:.*]] = "TFHE.add_glwe"(%[[Vextracted_9]], %[[Vextracted_10]]) : (!TFHE.glwe<{_,_,_}{2}>, !TFHE.glwe<{_,_,_}{2}>) -> !TFHE.glwe<{_,_,_}{2}>
-//CHECK-NEXT:                    %[[Vinserted:.*]] = tensor.insert %[[V16]] into %[[Varg18]]{{\[}}%[[Varg17]]{{\]}} : tensor<5x!TFHE.glwe<{_,_,_}{2}>>
-//CHECK-NEXT:                    scf.yield %[[Vinserted]] : tensor<5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:                  %[[V15:.*]] = scf.for %[[Varg17:.*]] = %[[Vc0_5]] to %[[Vc5_7]] step %[[Vc1_6]] iter_args(%[[Varg18:.*]] = %[[V14]]) -> (tensor<5x!TFHE.glwe<sk[?]>>) {
+//CHECK-NEXT:                    %[[Vextracted_9:.*]] = tensor.extract %[[Vextracted_slice_2]]{{\[}}%[[Varg17]]{{\]}} : tensor<5x!TFHE.glwe<sk[?]>>
+//CHECK-NEXT:                    %[[Vextracted_10:.*]] = tensor.extract %[[V13]]{{\[}}%[[Varg17]]{{\]}} : tensor<5x!TFHE.glwe<sk[?]>>
+//CHECK-NEXT:                    %[[V16:.*]] = "TFHE.add_glwe"(%[[Vextracted_9]], %[[Vextracted_10]]) : (!TFHE.glwe<sk[?]>, !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
+//CHECK-NEXT:                    %[[Vinserted:.*]] = tensor.insert %[[V16]] into %[[Varg18]]{{\[}}%[[Varg17]]{{\]}} : tensor<5x!TFHE.glwe<sk[?]>>
+//CHECK-NEXT:                    scf.yield %[[Vinserted]] : tensor<5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:                  }
 //CHECK-NEXT:                  %[[Vc0_8:.*]] = arith.constant 0 : index
-//CHECK-NEXT:                  %[[Vinserted_slice:.*]] = tensor.insert_slice %[[V15]] into %[[Varg16]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]], %[[Vc0_8]]{{\] \[1, 1, 1, 1, 5\] \[1, 1, 1, 1, 1\]}} : tensor<5x!TFHE.glwe<{_,_,_}{2}>> into tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
-//CHECK-NEXT:                  scf.yield %[[Vinserted_slice]] : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:                  %[[Vinserted_slice:.*]] = tensor.insert_slice %[[V15]] into %[[Varg16]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]], %[[Vc0_8]]{{\] \[1, 1, 1, 1, 5\] \[1, 1, 1, 1, 1\]}} : tensor<5x!TFHE.glwe<sk[?]>> into tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
+//CHECK-NEXT:                  scf.yield %[[Vinserted_slice]] : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:                }
-//CHECK-NEXT:                scf.yield %[[V8]] : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:                scf.yield %[[V8]] : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:              }
-//CHECK-NEXT:              scf.yield %[[V7]] : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:              scf.yield %[[V7]] : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:            }
-//CHECK-NEXT:            scf.yield %[[V6]] : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:            scf.yield %[[V6]] : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:          }
-//CHECK-NEXT:          scf.yield %[[V5]] : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:          scf.yield %[[V5]] : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:        }
-//CHECK-NEXT:        scf.yield %[[V4]] : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:        scf.yield %[[V4]] : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:      }
-//CHECK-NEXT:      scf.yield %[[V3]] : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:      scf.yield %[[V3]] : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:    }
-//CHECK-NEXT:    return %[[V2]] : tensor<100x4x15x15x5x!TFHE.glwe<{_,_,_}{2}>>
+//CHECK-NEXT:    return %[[V2]] : tensor<100x4x15x15x5x!TFHE.glwe<sk[?]>>
 //CHECK-NEXT:  }
 func.func @conv2d(%input: tensor<100x3x28x28x!FHE.eint<2>>, %weight: tensor<4x3x14x14xi3>, %bias: tensor<4xi3>) -> tensor<100x4x15x15x!FHE.eint<2>> {
  %1 = "FHELinalg.conv2d"(%input, %weight, %bias){strides = dense<[1,1]> : tensor<2xi64>, dilations = dense<[1,1]> : tensor<2xi64>, padding = dense<[0, 0, 0, 0]> : tensor<4xi64>}: (tensor<100x3x28x28x!FHE.eint<2>>, tensor<4x3x14x14xi3>, tensor<4xi3>) -> tensor<100x4x15x15x!FHE.eint<2>>
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/mul_eint_int.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/mul_eint_int.mlir
@@ -1,19 +1,19 @@
 // RUN: concretecompiler --optimize-tfhe=false --action=dump-tfhe %s --large-integer-crt-decomposition=2,3,5,7,11 --large-integer-circuit-bootstrap=2,9 --large-integer-packing-keyswitch=694,1024,4,9 --v0-parameter=2,10,693,4,9,7,2 2>&1| FileCheck %s

-// CHECK:  func.func @mul_eint_int(%[[Varg0:.*]]: tensor<5x!TFHE.glwe<{_,_,_}{7}>>) -> tensor<5x!TFHE.glwe<{_,_,_}{7}>> {
+// CHECK:  func.func @mul_eint_int(%[[Varg0:.*]]: tensor<5x!TFHE.glwe<sk[?]>>) -> tensor<5x!TFHE.glwe<sk[?]>> {
 // CHECK-NEXT:    %[[Vc2_i8:.*]] = arith.constant 2 : i8
 // CHECK-NEXT:    %[[V0:.*]] = arith.extsi %[[Vc2_i8]] : i8 to i64
-// CHECK-NEXT:    %[[V1:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT:    %[[V1:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:    %[[Vc0:.*]] = arith.constant 0 : index
 // CHECK-NEXT:    %[[Vc1:.*]] = arith.constant 1 : index
 // CHECK-NEXT:    %[[Vc5:.*]] = arith.constant 5 : index
-// CHECK-NEXT:    %[[V2:.*]] = scf.for %[[Varg1:.*]] = %[[Vc0]] to %[[Vc5]] step %[[Vc1]] iter_args(%[[Varg2:.*]] = %[[V1]]) -> (tensor<5x!TFHE.glwe<{_,_,_}{7}>>) {
-// CHECK-NEXT:      %[[V3:.*]] = tensor.extract %[[Varg0]][%[[Varg1]]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
-// CHECK-NEXT:      %[[V4:.*]] = "TFHE.mul_glwe_int"(%[[V3]], %[[V0]]) : (!TFHE.glwe<{_,_,_}{7}>, i64) -> !TFHE.glwe<{_,_,_}{7}>
-// CHECK-NEXT:      %[[V5:.*]] = tensor.insert %[[V4]] into %[[Varg2]][%[[Varg1]]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
-// CHECK-NEXT:      scf.yield %[[V5]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT:    %[[V2:.*]] = scf.for %[[Varg1:.*]] = %[[Vc0]] to %[[Vc5]] step %[[Vc1]] iter_args(%[[Varg2:.*]] = %[[V1]]) -> (tensor<5x!TFHE.glwe<sk[?]>>) {
+// CHECK-NEXT:      %[[V3:.*]] = tensor.extract %[[Varg0]][%[[Varg1]]] : tensor<5x!TFHE.glwe<sk[?]>>
+// CHECK-NEXT:      %[[V4:.*]] = "TFHE.mul_glwe_int"(%[[V3]], %[[V0]]) : (!TFHE.glwe<sk[?]>, i64) -> !TFHE.glwe<sk[?]>
+// CHECK-NEXT:      %[[V5:.*]] = tensor.insert %[[V4]] into %[[Varg2]][%[[Varg1]]] : tensor<5x!TFHE.glwe<sk[?]>>
+// CHECK-NEXT:      scf.yield %[[V5]] : tensor<5x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:    }
-// CHECK-NEXT:    return %[[V2]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT:    return %[[V2]] : tensor<5x!TFHE.glwe<sk[?]>>
 func.func @mul_eint_int(%arg0: !FHE.eint<7>) -> !FHE.eint<7> {
  %0 = arith.constant 2 : i8
  %1 = "FHE.mul_eint_int"(%arg0, %0): (!FHE.eint<7>, i8) -> (!FHE.eint<7>)
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/neg_eint.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/neg_eint.mlir
@@ -1,17 +1,17 @@
 // RUN: concretecompiler --optimize-tfhe=false --action=dump-tfhe %s --large-integer-crt-decomposition=2,3,5,7,11 --large-integer-circuit-bootstrap=2,9 --large-integer-packing-keyswitch=694,1024,4,9 --v0-parameter=2,10,693,4,9,7,2 2>&1| FileCheck %s

-// CHECK:  func.func @neg_eint(%[[Varg0:.*]]: tensor<5x!TFHE.glwe<{_,_,_}{7}>>) -> tensor<5x!TFHE.glwe<{_,_,_}{7}>> {
-// CHECK-NEXT:    %[[V0:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK:  func.func @neg_eint(%[[Varg0:.*]]: tensor<5x!TFHE.glwe<sk[?]>>) -> tensor<5x!TFHE.glwe<sk[?]>> {
+// CHECK-NEXT:    %[[V0:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:    %[[Vc0:.*]] = arith.constant 0 : index
 // CHECK-NEXT:    %[[Vc1:.*]] = arith.constant 1 : index
 // CHECK-NEXT:    %[[Vc5:.*]] = arith.constant 5 : index
-// CHECK-NEXT:    %[[V1:.*]] = scf.for %[[Varg1:.*]] = %[[Vc0]] to %[[Vc5]] step %[[Vc1]] iter_args(%[[Varg2:.*]] = %[[V0]]) -> (tensor<5x!TFHE.glwe<{_,_,_}{7}>>) {
-// CHECK-NEXT:      %[[V2:.*]] = tensor.extract %[[Varg0]][%[[Varg1]]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
-// CHECK-NEXT:      %[[V3:.*]] = "TFHE.neg_glwe"(%[[V2]]) : (!TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}>
-// CHECK-NEXT:      %[[V4:.*]] = tensor.insert %[[V3]] into %[[Varg2]][%[[Varg1]]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
-// CHECK-NEXT:      scf.yield %[[V4]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT:    %[[V1:.*]] = scf.for %[[Varg1:.*]] = %[[Vc0]] to %[[Vc5]] step %[[Vc1]] iter_args(%[[Varg2:.*]] = %[[V0]]) -> (tensor<5x!TFHE.glwe<sk[?]>>) {
+// CHECK-NEXT:      %[[V2:.*]] = tensor.extract %[[Varg0]][%[[Varg1]]] : tensor<5x!TFHE.glwe<sk[?]>>
+// CHECK-NEXT:      %[[V3:.*]] = "TFHE.neg_glwe"(%[[V2]]) : (!TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
+// CHECK-NEXT:      %[[V4:.*]] = tensor.insert %[[V3]] into %[[Varg2]][%[[Varg1]]] : tensor<5x!TFHE.glwe<sk[?]>>
+// CHECK-NEXT:      scf.yield %[[V4]] : tensor<5x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:    }
-// CHECK-NEXT:    return %[[V1]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT:    return %[[V1]] : tensor<5x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:  }
 func.func @neg_eint(%arg0: !FHE.eint<7>) -> !FHE.eint<7> {
  %1 = "FHE.neg_eint"(%arg0): (!FHE.eint<7>) -> (!FHE.eint<7>)
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/sub_int_eint.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHECrt/sub_int_eint.mlir
@@ -1,24 +1,25 @@
 // RUN: concretecompiler --optimize-tfhe=false --action=dump-tfhe %s --large-integer-crt-decomposition=2,3,5,7,11 --large-integer-circuit-bootstrap=2,9 --large-integer-packing-keyswitch=694,1024,4,9 --v0-parameter=2,10,693,4,9,7,2 2>&1| FileCheck %s

-// CHECK:  func.func @sub_int_eint(%[[Varg0:.*]]: tensor<5x!TFHE.glwe<{_,_,_}{7}>>) -> tensor<5x!TFHE.glwe<{_,_,_}{7}>> {
+// CHECK:  func.func @sub_int_eint(%[[Varg0:.*]]: tensor<5x!TFHE.glwe<sk[?]>>) -> tensor<5x!TFHE.glwe<sk[?]>> {
 // CHECK-NEXT:    %[[Vc1_i8:.*]] = arith.constant 1 : i8
 // CHECK-NEXT:    %[[V0:.*]] = arith.extsi %[[Vc1_i8]] : i8 to i64
 // CHECK-NEXT:    %[[V1:.*]] = "TFHE.encode_plaintext_with_crt"(%[[V0]]) {mods = [2, 3, 5, 7, 11], modsProd = 2310 : i64} : (i64) -> tensor<5xi64>
-// CHECK-NEXT:    %[[V2:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT:    %[[V2:.*]] = bufferization.alloc_tensor() : tensor<5x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:    %[[Vc0:.*]] = arith.constant 0 : index
 // CHECK-NEXT:    %[[Vc1:.*]] = arith.constant 1 : index
 // CHECK-NEXT:    %[[Vc5:.*]] = arith.constant 5 : index
-// CHECK-NEXT:    %[[V3:.*]] = scf.for %[[Varg1:.*]] = %[[Vc0]] to %[[Vc5]] step %[[Vc1]] iter_args(%[[Varg2:.*]] = %[[V2]]) -> (tensor<5x!TFHE.glwe<{_,_,_}{7}>>) {
-// CHECK-NEXT:      %[[V4:.*]] = tensor.extract %[[Varg0]][%[[Varg1]]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT:    %[[V3:.*]] = scf.for %[[Varg1:.*]] = %[[Vc0]] to %[[Vc5]] step %[[Vc1]] iter_args(%[[Varg2:.*]] = %[[V2]]) -> (tensor<5x!TFHE.glwe<sk[?]>>) {
+// CHECK-NEXT:      %[[V4:.*]] = tensor.extract %[[Varg0]][%[[Varg1]]] : tensor<5x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:      %[[V5:.*]] = tensor.extract %[[V1]][%[[Varg1]]] : tensor<5xi64>
-// CHECK-NEXT:      %[[V6:.*]] = "TFHE.sub_int_glwe"(%[[V5]], %[[V4]]) : (i64, !TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}>
-// CHECK-NEXT:      %[[V7:.*]] = tensor.insert %[[V6]] into %[[Varg2]][%[[Varg1]]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
-// CHECK-NEXT:      scf.yield %[[V7]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT:      %[[V6:.*]] = "TFHE.sub_int_glwe"(%[[V5]], %[[V4]]) : (i64, !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
+// CHECK-NEXT:      %[[V7:.*]] = tensor.insert %[[V6]] into %[[Varg2]][%[[Varg1]]] : tensor<5x!TFHE.glwe<sk[?]>>
+// CHECK-NEXT:      scf.yield %[[V7]] : tensor<5x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:    }
-// CHECK-NEXT:    return %[[V3]] : tensor<5x!TFHE.glwe<{_,_,_}{7}>>
+// CHECK-NEXT:    return %[[V3]] : tensor<5x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:  }
 func.func @sub_int_eint(%arg0: !FHE.eint<7>) -> !FHE.eint<7> {
  %0 = arith.constant 1 : i8
  %1 = "FHE.sub_int_eint"(%0, %arg0): (i8, !FHE.eint<7>) -> (!FHE.eint<7>)
  return %1: !FHE.eint<7>
 }
+
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/add_eint.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/add_eint.mlir
@@ -1,9 +1,9 @@
 // RUN: concretecompiler %s --optimize-tfhe=false --action=dump-tfhe 2>&1| FileCheck %s

-// CHECK-LABEL: func.func @add_eint(%arg0: !TFHE.glwe<{_,_,_}{7}>, %arg1: !TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}>
+// CHECK-LABEL: func.func @add_eint(%arg0: !TFHE.glwe<sk[?]>, %arg1: !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
 func.func @add_eint(%arg0: !FHE.eint<7>, %arg1: !FHE.eint<7>) -> !FHE.eint<7> {
-  // CHECK-NEXT: %[[V1:.*]] = "TFHE.add_glwe"(%arg0, %arg1) : (!TFHE.glwe<{_,_,_}{7}>, !TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}>
-  // CHECK-NEXT: return %[[V1]] : !TFHE.glwe<{_,_,_}{7}>
+  // CHECK-NEXT: %[[V1:.*]] = "TFHE.add_glwe"(%arg0, %arg1) : (!TFHE.glwe<sk[?]>, !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
+  // CHECK-NEXT: return %[[V1]] : !TFHE.glwe<sk[?]>

  %1 = "FHE.add_eint"(%arg0, %arg1): (!FHE.eint<7>, !FHE.eint<7>) -> (!FHE.eint<7>)
  return %1: !FHE.eint<7>
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/add_eint_int.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/add_eint_int.mlir
@@ -1,13 +1,13 @@
 // RUN: concretecompiler %s --optimize-tfhe=false --action=dump-tfhe 2>&1| FileCheck %s

-// CHECK-LABEL: func.func @add_eint_int(%arg0: !TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}>
+// CHECK-LABEL: func.func @add_eint_int(%arg0: !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
 func.func @add_eint_int(%arg0: !FHE.eint<7>) -> !FHE.eint<7> {
  // CHECK-NEXT:  %c1_i8 = arith.constant 1 : i8
  // CHECK-NEXT:  %0 = arith.extsi %c1_i8 : i8 to i64
  // CHECK-NEXT:  %c56_i64 = arith.constant 56 : i64
  // CHECK-NEXT:  %1 = arith.shli %0, %c56_i64 : i64
-  // CHECK-NEXT:  %2 = "TFHE.add_glwe_int"(%arg0, %1) : (!TFHE.glwe<{_,_,_}{7}>, i64) -> !TFHE.glwe<{_,_,_}{7}>
-  // CHECK-NEXT:  return %2 : !TFHE.glwe<{_,_,_}{7}>
+  // CHECK-NEXT:  %2 = "TFHE.add_glwe_int"(%arg0, %1) : (!TFHE.glwe<sk[?]>, i64) -> !TFHE.glwe<sk[?]>
+  // CHECK-NEXT:  return %2 : !TFHE.glwe<sk[?]>


  %0 = arith.constant 1 : i8
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/apply_univariate.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/apply_univariate.mlir
@@ -1,10 +1,10 @@
 // RUN: concretecompiler %s --optimize-tfhe=false --action=dump-tfhe 2>&1| FileCheck %s

-// CHECK: func.func @apply_lookup_table(%arg0: !TFHE.glwe<{_,_,_}{2}>, %arg1: tensor<4xi64>) -> !TFHE.glwe<{_,_,_}{3}> {
+// CHECK: func.func @apply_lookup_table(%arg0: !TFHE.glwe<sk[?]>, %arg1: tensor<4xi64>) -> !TFHE.glwe<sk[?]> {
 // CHECK-NEXT: %0 = "TFHE.encode_expand_lut_for_bootstrap"(%arg1) {isSigned = false, outputBits = 3 : i32, polySize = 256 : i32} : (tensor<4xi64>) -> tensor<256xi64>
-// CHECK-NEXT: %1 = "TFHE.keyswitch_glwe"(%arg0) {baseLog = -1 : i32, level = -1 : i32} : (!TFHE.glwe<{_,_,_}{2}>) -> !TFHE.glwe<{_,_,_}{2}>
-// CHECK-NEXT: %2 = "TFHE.bootstrap_glwe"(%1, %0) {baseLog = -1 : i32, glweDimension = -1 : i32, level = -1 : i32, polySize = -1 : i32} : (!TFHE.glwe<{_,_,_}{2}>, tensor<256xi64>) -> !TFHE.glwe<{_,_,_}{3}>
-// CHECK-NEXT: return %2 : !TFHE.glwe<{_,_,_}{3}>
+// CHECK-NEXT: %1 = "TFHE.keyswitch_glwe"(%arg0) {key = #TFHE.ksk<sk[?], sk[?], -1, -1>} : (!TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
+// CHECK-NEXT: %2 = "TFHE.bootstrap_glwe"(%1, %0) {key = #TFHE.bsk<sk[?], sk[?], -1, -1, -1, -1>} : (!TFHE.glwe<sk[?]>, tensor<256xi64>) -> !TFHE.glwe<sk[?]>
+// CHECK-NEXT: return %2 : !TFHE.glwe<sk[?]>
 func.func @apply_lookup_table(%arg0: !FHE.eint<2>, %arg1: tensor<4xi64>) -> !FHE.eint<3> {
  %1 = "FHE.apply_lookup_table"(%arg0, %arg1): (!FHE.eint<2>, tensor<4xi64>) -> (!FHE.eint<3>)
  return %1: !FHE.eint<3>
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/apply_univariate_cst.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/apply_univariate_cst.mlir
@@ -1,12 +1,12 @@
 // RUN: concretecompiler %s --optimize-tfhe=false --action=dump-tfhe 2>&1| FileCheck %s

-//CHECK: func.func @apply_lookup_table_cst(%[[A0:.*]]: !TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}> {
+//CHECK: func.func @apply_lookup_table_cst(%[[A0:.*]]: !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]> {

 //CHECK-NEXT: %cst = arith.constant dense<"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tensor<128xi64>
 //CHECK-NEXT: %0 = "TFHE.encode_expand_lut_for_bootstrap"(%cst) {isSigned = false, outputBits = 7 : i32, polySize = 8192 : i32} : (tensor<128xi64>) -> tensor<8192xi64>
-//CHECK-NEXT: %1 = "TFHE.keyswitch_glwe"(%arg0) {baseLog = -1 : i32, level = -1 : i32} : (!TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}>
-//CHECK-NEXT: %2 = "TFHE.bootstrap_glwe"(%1, %0) {baseLog = -1 : i32, glweDimension = -1 : i32, level = -1 : i32, polySize = -1 : i32} : (!TFHE.glwe<{_,_,_}{7}>, tensor<8192xi64>) -> !TFHE.glwe<{_,_,_}{7}>
-//CHECK-NEXT: return %2 : !TFHE.glwe<{_,_,_}{7}>
+//CHECK-NEXT: %1 = "TFHE.keyswitch_glwe"(%arg0) {key = #TFHE.ksk<sk[?], sk[?], -1, -1>} : (!TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
+//CHECK-NEXT: %2 = "TFHE.bootstrap_glwe"(%1, %0) {key = #TFHE.bsk<sk[?], sk[?], -1, -1, -1, -1>} : (!TFHE.glwe<sk[?]>, tensor<8192xi64>) -> !TFHE.glwe<sk[?]>
+//CHECK-NEXT: return %2 : !TFHE.glwe<sk[?]>
 func.func @apply_lookup_table_cst(%arg0: !FHE.eint<7>) -> !FHE.eint<7> {
  %tlu = arith.constant dense<[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127]> : tensor<128xi64>
  %1 = "FHE.apply_lookup_table"(%arg0, %tlu): (!FHE.eint<7>, tensor<128xi64>) -> (!FHE.eint<7>)
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/conv2d.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/conv2d.mlir
@@ -1,6 +1,6 @@
 // RUN: concretecompiler %s --optimize-tfhe=false --action=dump-tfhe 2>&1| FileCheck %s

-// CHECK: func.func @conv2d(%[[Varg0:.*]]: tensor<100x3x28x28x!TFHE.glwe<{_,_,_}{2}>>, %[[Varg1:.*]]: tensor<4x3x14x14xi3>, %[[Varg2:.*]]: tensor<4xi3>) -> tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>> {
+// CHECK: func.func @conv2d(%[[Varg0:.*]]: tensor<100x3x28x28x!TFHE.glwe<sk[?]>>, %[[Varg1:.*]]: tensor<4x3x14x14xi3>, %[[Varg2:.*]]: tensor<4xi3>) -> tensor<100x4x15x15x!TFHE.glwe<sk[?]>> {
 // CHECK-NEXT:    %[[Vc0:.*]] = arith.constant 0 : index
 // CHECK-NEXT:    %[[Vc100:.*]] = arith.constant 100 : index
 // CHECK-NEXT:    %[[Vc1:.*]] = arith.constant 1 : index
@@ -8,57 +8,57 @@
 // CHECK-NEXT:    %[[Vc15:.*]] = arith.constant 15 : index
 // CHECK-NEXT:    %[[Vc3:.*]] = arith.constant 3 : index
 // CHECK-NEXT:    %[[Vc14:.*]] = arith.constant 14 : index
-// CHECK-NEXT:    %[[V0:.*]] = "TFHE.zero_tensor"() : () -> tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
-// CHECK-NEXT:    %[[V1:.*]] = scf.for %[[Varg3:.*]] = %[[Vc0]] to %[[Vc100]] step %[[Vc1]] iter_args(%[[Varg4:.*]] = %[[V0]]) -> (tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>) {
-// CHECK-NEXT:      %[[V3:.*]] = scf.for %[[Varg5:.*]] = %[[Vc0]] to %[[Vc4]] step %[[Vc1]] iter_args(%[[Varg6:.*]] = %[[Varg4]]) -> (tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>) {
-// CHECK-NEXT:        %[[V4:.*]] = scf.for %[[Varg7:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg8:.*]] = %[[Varg6]]) -> (tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>) {
-// CHECK-NEXT:          %[[V5:.*]] = scf.for %[[Varg9:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg10:.*]] = %[[Varg8]]) -> (tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>) {
+// CHECK-NEXT:    %[[V0:.*]] = "TFHE.zero_tensor"() : () -> tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
+// CHECK-NEXT:    %[[V1:.*]] = scf.for %[[Varg3:.*]] = %[[Vc0]] to %[[Vc100]] step %[[Vc1]] iter_args(%[[Varg4:.*]] = %[[V0]]) -> (tensor<100x4x15x15x!TFHE.glwe<sk[?]>>) {
+// CHECK-NEXT:      %[[V3:.*]] = scf.for %[[Varg5:.*]] = %[[Vc0]] to %[[Vc4]] step %[[Vc1]] iter_args(%[[Varg6:.*]] = %[[Varg4]]) -> (tensor<100x4x15x15x!TFHE.glwe<sk[?]>>) {
+// CHECK-NEXT:        %[[V4:.*]] = scf.for %[[Varg7:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg8:.*]] = %[[Varg6]]) -> (tensor<100x4x15x15x!TFHE.glwe<sk[?]>>) {
+// CHECK-NEXT:          %[[V5:.*]] = scf.for %[[Varg9:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg10:.*]] = %[[Varg8]]) -> (tensor<100x4x15x15x!TFHE.glwe<sk[?]>>) {
 // CHECK-NEXT:            %[[Vextracted:.*]] = tensor.extract %[[Varg2]]{{\[}}%[[Varg5]]{{\]}} : tensor<4xi3>
-// CHECK-NEXT:            %[[Vextracted_0:.*]] = tensor.extract %[[Varg10]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]]{{\]}} : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:            %[[Vextracted_0:.*]] = tensor.extract %[[Varg10]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]]{{\]}} : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:            %[[V6:.*]] = arith.extsi %[[Vextracted]] : i3 to i64
 // CHECK-NEXT:            %[[Vc61_i64:.*]] = arith.constant 61 : i64
 // CHECK-NEXT:            %[[V7:.*]] = arith.shli %[[V6]], %[[Vc61_i64]] : i64
-// CHECK-NEXT:            %[[V8:.*]] = "TFHE.add_glwe_int"(%[[Vextracted_0]], %[[V7]]) : (!TFHE.glwe<{_,_,_}{2}>, i64) -> !TFHE.glwe<{_,_,_}{2}>
-// CHECK-NEXT:            %[[Vinserted:.*]] = tensor.insert %[[V8]] into %[[Varg10]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]]{{\]}} : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
-// CHECK-NEXT:            scf.yield %[[Vinserted]] : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:            %[[V8:.*]] = "TFHE.add_glwe_int"(%[[Vextracted_0]], %[[V7]]) : (!TFHE.glwe<sk[?]>, i64) -> !TFHE.glwe<sk[?]>
+// CHECK-NEXT:            %[[Vinserted:.*]] = tensor.insert %[[V8]] into %[[Varg10]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]]{{\]}} : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
+// CHECK-NEXT:            scf.yield %[[Vinserted]] : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:          }
-// CHECK-NEXT:          scf.yield %[[V5]] : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:          scf.yield %[[V5]] : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:        }
-// CHECK-NEXT:        scf.yield %[[V4]] : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:        scf.yield %[[V4]] : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:      }
-// CHECK-NEXT:      scf.yield %[[V3]] : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:      scf.yield %[[V3]] : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:    }
-// CHECK-NEXT:    %[[V2:.*]] = scf.for %[[Varg3:.*]] = %[[Vc0]] to %[[Vc100]] step %[[Vc1]] iter_args(%[[Varg4:.*]] = %[[V1]]) -> (tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>) {
-// CHECK-NEXT:      %[[V3:.*]] = scf.for %[[Varg5:.*]] = %[[Vc0]] to %[[Vc4]] step %[[Vc1]] iter_args(%[[Varg6:.*]] = %[[Varg4]]) -> (tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>) {
-// CHECK-NEXT:        %[[V4:.*]] = scf.for %[[Varg7:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg8:.*]] = %[[Varg6]]) -> (tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>) {
-// CHECK-NEXT:          %[[V5:.*]] = scf.for %[[Varg9:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg10:.*]] = %[[Varg8]]) -> (tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>) {
-// CHECK-NEXT:            %[[V6:.*]] = scf.for %[[Varg11:.*]] = %[[Vc0]] to %[[Vc3]] step %[[Vc1]] iter_args(%[[Varg12:.*]] = %[[Varg10]]) -> (tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>) {
-// CHECK-NEXT:              %[[V7:.*]] = scf.for %[[Varg13:.*]] = %[[Vc0]] to %[[Vc14]] step %[[Vc1]] iter_args(%[[Varg14:.*]] = %[[Varg12]]) -> (tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>) {
-// CHECK-NEXT:                %[[V8:.*]] = scf.for %[[Varg15:.*]] = %[[Vc0]] to %[[Vc14]] step %[[Vc1]] iter_args(%[[Varg16:.*]] = %[[Varg14]]) -> (tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>) {
+// CHECK-NEXT:    %[[V2:.*]] = scf.for %[[Varg3:.*]] = %[[Vc0]] to %[[Vc100]] step %[[Vc1]] iter_args(%[[Varg4:.*]] = %[[V1]]) -> (tensor<100x4x15x15x!TFHE.glwe<sk[?]>>) {
+// CHECK-NEXT:      %[[V3:.*]] = scf.for %[[Varg5:.*]] = %[[Vc0]] to %[[Vc4]] step %[[Vc1]] iter_args(%[[Varg6:.*]] = %[[Varg4]]) -> (tensor<100x4x15x15x!TFHE.glwe<sk[?]>>) {
+// CHECK-NEXT:        %[[V4:.*]] = scf.for %[[Varg7:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg8:.*]] = %[[Varg6]]) -> (tensor<100x4x15x15x!TFHE.glwe<sk[?]>>) {
+// CHECK-NEXT:          %[[V5:.*]] = scf.for %[[Varg9:.*]] = %[[Vc0]] to %[[Vc15]] step %[[Vc1]] iter_args(%[[Varg10:.*]] = %[[Varg8]]) -> (tensor<100x4x15x15x!TFHE.glwe<sk[?]>>) {
+// CHECK-NEXT:            %[[V6:.*]] = scf.for %[[Varg11:.*]] = %[[Vc0]] to %[[Vc3]] step %[[Vc1]] iter_args(%[[Varg12:.*]] = %[[Varg10]]) -> (tensor<100x4x15x15x!TFHE.glwe<sk[?]>>) {
+// CHECK-NEXT:              %[[V7:.*]] = scf.for %[[Varg13:.*]] = %[[Vc0]] to %[[Vc14]] step %[[Vc1]] iter_args(%[[Varg14:.*]] = %[[Varg12]]) -> (tensor<100x4x15x15x!TFHE.glwe<sk[?]>>) {
+// CHECK-NEXT:                %[[V8:.*]] = scf.for %[[Varg15:.*]] = %[[Vc0]] to %[[Vc14]] step %[[Vc1]] iter_args(%[[Varg16:.*]] = %[[Varg14]]) -> (tensor<100x4x15x15x!TFHE.glwe<sk[?]>>) {
 // CHECK-NEXT:                  %[[V9:.*]] = affine.apply #map(%[[Varg7]], %[[Varg13]])
 // CHECK-NEXT:                  %[[V10:.*]] = affine.apply #map(%[[Varg9]], %[[Varg15]])
-// CHECK-NEXT:                  %[[Vextracted:.*]] = tensor.extract %[[Varg0]]{{\[}}%[[Varg3]], %[[Varg11]], %[[V9]], %[[V10]]{{\]}} : tensor<100x3x28x28x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:                  %[[Vextracted:.*]] = tensor.extract %[[Varg0]]{{\[}}%[[Varg3]], %[[Varg11]], %[[V9]], %[[V10]]{{\]}} : tensor<100x3x28x28x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:                  %[[Vextracted_0:.*]] = tensor.extract %[[Varg1]]{{\[}}%[[Varg5]], %[[Varg11]], %[[Varg13]], %[[Varg15]]{{\]}} : tensor<4x3x14x14xi3>
-// CHECK-NEXT:                  %[[Vextracted_1:.*]] = tensor.extract %[[Varg16]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]]{{\]}} : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:                  %[[Vextracted_1:.*]] = tensor.extract %[[Varg16]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]]{{\]}} : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:                  %[[V11:.*]] = arith.extsi %[[Vextracted_0]] : i3 to i64
-// CHECK-NEXT:                  %[[V12:.*]] = "TFHE.mul_glwe_int"(%[[Vextracted]], %[[V11]]) : (!TFHE.glwe<{_,_,_}{2}>, i64) -> !TFHE.glwe<{_,_,_}{2}>
-// CHECK-NEXT:                  %[[V13:.*]] = "TFHE.add_glwe"(%[[Vextracted_1]], %[[V12]]) : (!TFHE.glwe<{_,_,_}{2}>, !TFHE.glwe<{_,_,_}{2}>) -> !TFHE.glwe<{_,_,_}{2}>
-// CHECK-NEXT:                  %[[Vinserted:.*]] = tensor.insert %[[V13]] into %[[Varg16]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]]{{\]}} : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
-// CHECK-NEXT:                  scf.yield %[[Vinserted]] : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:                  %[[V12:.*]] = "TFHE.mul_glwe_int"(%[[Vextracted]], %[[V11]]) : (!TFHE.glwe<sk[?]>, i64) -> !TFHE.glwe<sk[?]>
+// CHECK-NEXT:                  %[[V13:.*]] = "TFHE.add_glwe"(%[[Vextracted_1]], %[[V12]]) : (!TFHE.glwe<sk[?]>, !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
+// CHECK-NEXT:                  %[[Vinserted:.*]] = tensor.insert %[[V13]] into %[[Varg16]]{{\[}}%[[Varg3]], %[[Varg5]], %[[Varg7]], %[[Varg9]]{{\]}} : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
+// CHECK-NEXT:                  scf.yield %[[Vinserted]] : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:                }
-// CHECK-NEXT:                scf.yield %[[V8]] : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:                scf.yield %[[V8]] : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:              }
-// CHECK-NEXT:              scf.yield %[[V7]] : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:              scf.yield %[[V7]] : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:            }
-// CHECK-NEXT:            scf.yield %[[V6]] : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:            scf.yield %[[V6]] : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:          }
-// CHECK-NEXT:          scf.yield %[[V5]] : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:          scf.yield %[[V5]] : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:        }
-// CHECK-NEXT:        scf.yield %[[V4]] : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:        scf.yield %[[V4]] : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:      }
-// CHECK-NEXT:      scf.yield %[[V3]] : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:      scf.yield %[[V3]] : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:    }
-// CHECK-NEXT:    return %[[V2]] : tensor<100x4x15x15x!TFHE.glwe<{_,_,_}{2}>>
+// CHECK-NEXT:    return %[[V2]] : tensor<100x4x15x15x!TFHE.glwe<sk[?]>>
 // CHECK-NEXT:   }
 func.func @conv2d(%input: tensor<100x3x28x28x!FHE.eint<2>>, %weight: tensor<4x3x14x14xi3>, %bias: tensor<4xi3>) -> tensor<100x4x15x15x!FHE.eint<2>> {
  %1 = "FHELinalg.conv2d"(%input, %weight, %bias){strides = dense<[1,1]> : tensor<2xi64>, dilations = dense<[1,1]> : tensor<2xi64>, padding = dense<[0, 0, 0, 0]> : tensor<4xi64>}: (tensor<100x3x28x28x!FHE.eint<2>>, tensor<4x3x14x14xi3>, tensor<4xi3>) -> tensor<100x4x15x15x!FHE.eint<2>>
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/mul_eint_int.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/mul_eint_int.mlir
@@ -1,11 +1,11 @@
 // RUN: concretecompiler %s --optimize-tfhe=false --action=dump-tfhe 2>&1| FileCheck %s

-// CHECK-LABEL: func.func @mul_eint_int(%arg0: !TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}>
+// CHECK-LABEL: func.func @mul_eint_int(%arg0: !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
 func.func @mul_eint_int(%arg0: !FHE.eint<7>) -> !FHE.eint<7> {
  // CHECK-NEXT:  %c2_i8 = arith.constant 2 : i8
  // CHECK-NEXT:  %0 = arith.extsi %c2_i8 : i8 to i64
-  // CHECK-NEXT:  %1 = "TFHE.mul_glwe_int"(%arg0, %0) : (!TFHE.glwe<{_,_,_}{7}>, i64) -> !TFHE.glwe<{_,_,_}{7}>
-  // CHECK-NEXT:  return %1 : !TFHE.glwe<{_,_,_}{7}>
+  // CHECK-NEXT:  %1 = "TFHE.mul_glwe_int"(%arg0, %0) : (!TFHE.glwe<sk[?]>, i64) -> !TFHE.glwe<sk[?]>
+  // CHECK-NEXT:  return %1 : !TFHE.glwe<sk[?]>

  %0 = arith.constant 2 : i8
  %1 = "FHE.mul_eint_int"(%arg0, %0): (!FHE.eint<7>, i8) -> (!FHE.eint<7>)
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/neg_eint.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/neg_eint.mlir
@@ -1,18 +1,18 @@
 // RUN: concretecompiler %s --optimize-tfhe=false --action=dump-tfhe 2>&1| FileCheck %s

-// CHECK-LABEL: func.func @neg_eint(%arg0: !TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}>
+// CHECK-LABEL: func.func @neg_eint(%arg0: !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
 func.func @neg_eint(%arg0: !FHE.eint<7>) -> !FHE.eint<7> {
-  // CHECK-NEXT:  %0 = "TFHE.neg_glwe"(%arg0) : (!TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}>
-  // CHECK-NEXT:  return %0 : !TFHE.glwe<{_,_,_}{7}>
+  // CHECK-NEXT:  %0 = "TFHE.neg_glwe"(%arg0) : (!TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
+  // CHECK-NEXT:  return %0 : !TFHE.glwe<sk[?]>

  %1 = "FHE.neg_eint"(%arg0): (!FHE.eint<7>) -> (!FHE.eint<7>)
  return %1: !FHE.eint<7>
 }

-// CHECK-LABEL: func.func @not(%arg0: !TFHE.glwe<{_,_,_}{2}>) -> !TFHE.glwe<{_,_,_}{2}>
+// CHECK-LABEL: func.func @not(%arg0: !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
 func.func @not(%arg0: !FHE.ebool) -> !FHE.ebool {
-  // CHECK-NEXT:  %0 = "TFHE.neg_glwe"(%arg0) : (!TFHE.glwe<{_,_,_}{2}>) -> !TFHE.glwe<{_,_,_}{2}>
-  // CHECK-NEXT:  return %0 : !TFHE.glwe<{_,_,_}{2}>
+  // CHECK-NEXT:  %0 = "TFHE.neg_glwe"(%arg0) : (!TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
+  // CHECK-NEXT:  return %0 : !TFHE.glwe<sk[?]>
  %1 = "FHE.not"(%arg0) : (!FHE.ebool) -> !FHE.ebool
  return %1: !FHE.ebool
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/sub_int_eint.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/FHEToTFHEScalar/sub_int_eint.mlir
@@ -1,13 +1,13 @@
 // RUN: concretecompiler %s --optimize-tfhe=false  --action=dump-tfhe 2>&1| FileCheck %s

-// CHECK-LABEL: func.func @sub_int_eint(%arg0: !TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}>
+// CHECK-LABEL: func.func @sub_int_eint(%arg0: !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
 func.func @sub_int_eint(%arg0: !FHE.eint<7>) -> !FHE.eint<7> {
    // CHECK-NEXT: %c1_i8 = arith.constant 1 : i8
    // CHECK-NEXT: %0 = arith.extsi %c1_i8 : i8 to i64
    // CHECK-NEXT: %c56_i64 = arith.constant 56 : i64
    // CHECK-NEXT: %1 = arith.shli %0, %c56_i64 : i64
-    // CHECK-NEXT: %2 = "TFHE.sub_int_glwe"(%1, %arg0) : (i64, !TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}>
-    // CHECK-NEXT: return %2 : !TFHE.glwe<{_,_,_}{7}>
+    // CHECK-NEXT: %2 = "TFHE.sub_int_glwe"(%1, %arg0) : (i64, !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
+    // CHECK-NEXT: return %2 : !TFHE.glwe<sk[?]>

  %0 = arith.constant 1 : i8
  %1 = "FHE.sub_int_eint"(%0, %arg0): (i8, !FHE.eint<7>) -> (!FHE.eint<7>)
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEGlobalParametrization/pbs_ks_bs.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEGlobalParametrization/pbs_ks_bs.mlir
@@ -1,14 +1,14 @@
 // RUN: concretecompiler --passes tfhe-global-parametrization --action=dump-std --optimizer-v0 --v0-parameter=2,10,750,1,23,3,4 --v0-constraint=4,0 %s 2>&1| FileCheck %s

-//CHECK: func.func @main(%[[A0:.*]]: !TFHE.glwe<{2048,1,64}{4}>) -> !TFHE.glwe<{2048,1,64}{4}> {
-//CHECK:   %cst = arith.constant dense<[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]> : tensor<16xi64>
-//CHECK:   %[[V1:.*]] = "TFHE.keyswitch_glwe"(%[[A0]]) {baseLog = 4 : i32, level = 3 : i32} : (!TFHE.glwe<{2048,1,64}{4}>) -> !TFHE.glwe<{750,1,64}{4}>
-//CHECK:   %[[V2:.*]] = "TFHE.bootstrap_glwe"(%[[V1]], %cst) {baseLog = 23 : i32, glweDimension = 2 : i32, level = 1 : i32, polySize = 1024 : i32} : (!TFHE.glwe<{750,1,64}{4}>, tensor<16xi64>) -> !TFHE.glwe<{2048,1,64}{4}>
-//CHECK:   return %[[V2]] : !TFHE.glwe<{2048,1,64}{4}>
-//CHECK: }
-func.func @main(%arg0: !TFHE.glwe<{_,_,_}{4}>) -> !TFHE.glwe<{_,_,_}{4}> {
+//CHECK: func.func @main(%[[A0:.*]]: !TFHE.glwe<sk[1]<1,2048>>) -> !TFHE.glwe<sk[1]<1,2048>> {
+//CHECK-NEXT:   %cst = arith.constant dense<[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]> : tensor<16xi64>
+//CHECK-NEXT:   %[[V1:.*]] = "TFHE.keyswitch_glwe"(%[[A0]]) {key = #TFHE.ksk<sk[1]<1,2048>, sk[3]<1,750>, 3, 4>} : (!TFHE.glwe<sk[1]<1,2048>>) -> !TFHE.glwe<sk[3]<1,750>>
+//CHECK-NEXT:   %[[V2:.*]] = "TFHE.bootstrap_glwe"(%[[V1]], %cst) {key = #TFHE.bsk<sk[3]<1,750>, sk[1]<1,2048>, 1024, 2, 1, 23>} : (!TFHE.glwe<sk[3]<1,750>>, tensor<16xi64>) -> !TFHE.glwe<sk[1]<1,2048>>
+//CHECK-NEXT:   return %[[V2]] : !TFHE.glwe<sk[1]<1,2048>>
+//CHECK-NEXT: }
+func.func @main(%arg0: !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]> {
  %cst = arith.constant dense<[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]> : tensor<16xi64>
-  %1 = "TFHE.keyswitch_glwe"(%arg0) {baseLog = -1 : i32, level = -1 : i32} : (!TFHE.glwe<{_,_,_}{4}>) -> !TFHE.glwe<{_,_,_}{4}>
-  %2 = "TFHE.bootstrap_glwe"(%1, %cst) {baseLog = -1 : i32, glweDimension = -1 : i32, level = -1 : i32, polySize = -1 : i32} : (!TFHE.glwe<{_,_,_}{4}>, tensor<16xi64>) -> !TFHE.glwe<{_,_,_}{4}>
-  return %2 : !TFHE.glwe<{_,_,_}{4}>
+  %1 = "TFHE.keyswitch_glwe"(%arg0) {key = #TFHE.ksk<sk[?], sk[?], -1, -1>} : (!TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
+  %2 = "TFHE.bootstrap_glwe"(%1, %cst) {key = #TFHE.bsk<sk[?], sk[?], -1, -1, -1, -1>} : (!TFHE.glwe<sk[?]>, tensor<16xi64>) -> !TFHE.glwe<sk[?]>
+  return %2 : !TFHE.glwe<sk[?]>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/add_glwe.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/add_glwe.mlir
@@ -1,10 +1,10 @@
 // RUN: concretecompiler --passes tfhe-to-concrete --action=dump-concrete %s 2>&1| FileCheck %s

 // CHECK-LABEL: func.func @add_glwe(%arg0: tensor<2049xi64>, %arg1: tensor<2049xi64>) -> tensor<2049xi64>
-func.func @add_glwe(%arg0: !TFHE.glwe<{2048,1,64}{7}>, %arg1: !TFHE.glwe<{2048,1,64}{7}>) -> !TFHE.glwe<{2048,1,64}{7}> {
+func.func @add_glwe(%arg0: !TFHE.glwe<sk[1]<1,2048>>, %arg1: !TFHE.glwe<sk[1]<1,2048>>) -> !TFHE.glwe<sk[1]<1,2048>> {
  // CHECK-NEXT: %[[V1:.*]] = "Concrete.add_lwe_tensor"(%arg0, %arg1) : (tensor<2049xi64>, tensor<2049xi64>) -> tensor<2049xi64>
  // CHECK-NEXT: return %[[V1]] : tensor<2049xi64>

-  %0 = "TFHE.add_glwe"(%arg0, %arg1): (!TFHE.glwe<{2048,1,64}{7}>, !TFHE.glwe<{2048,1,64}{7}>) -> (!TFHE.glwe<{2048,1,64}{7}>)
-  return %0: !TFHE.glwe<{2048,1,64}{7}>
+  %0 = "TFHE.add_glwe"(%arg0, %arg1): (!TFHE.glwe<sk[1]<1,2048>>, !TFHE.glwe<sk[1]<1,2048>>) -> (!TFHE.glwe<sk[1]<1,2048>>)
+  return %0: !TFHE.glwe<sk[1]<1,2048>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/add_glwe_int.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/add_glwe_int.mlir
@@ -5,10 +5,10 @@
 //CHECK:   %[[V0:.*]] = "Concrete.add_plaintext_lwe_tensor"(%[[A0]], %c1_i64) : (tensor<1025xi64>, i64) -> tensor<1025xi64>
 //CHECK:   return %[[V0]] : tensor<1025xi64>
 //CHECK: }
-func.func @add_glwe_const_int(%arg0: !TFHE.glwe<{1024,1,64}{7}>) -> !TFHE.glwe<{1024,1,64}{7}> {
+func.func @add_glwe_const_int(%arg0: !TFHE.glwe<sk[1]<1,1024>>) -> !TFHE.glwe<sk[1]<1,1024>> {
  %0 = arith.constant 1 : i64
-  %1 = "TFHE.add_glwe_int"(%arg0, %0): (!TFHE.glwe<{1024,1,64}{7}>, i64) -> (!TFHE.glwe<{1024,1,64}{7}>)
-  return %1: !TFHE.glwe<{1024,1,64}{7}>
+  %1 = "TFHE.add_glwe_int"(%arg0, %0): (!TFHE.glwe<sk[1]<1,1024>>, i64) -> (!TFHE.glwe<sk[1]<1,1024>>)
+  return %1: !TFHE.glwe<sk[1]<1,1024>>
 }


@@ -16,7 +16,7 @@ func.func @add_glwe_const_int(%arg0: !TFHE.glwe<{1024,1,64}{7}>) -> !TFHE.glwe<{
 //CHECK:   %[[V0:.*]] = "Concrete.add_plaintext_lwe_tensor"(%[[A0]], %[[A1]]) : (tensor<1025xi64>, i64) -> tensor<1025xi64>
 //CHECK:   return %[[V0]] : tensor<1025xi64>
 //CHECK: }
-func.func @add_glwe_int(%arg0: !TFHE.glwe<{1024,1,64}{4}>, %arg1: i64) -> !TFHE.glwe<{1024,1,64}{4}> {
-  %1 = "TFHE.add_glwe_int"(%arg0, %arg1): (!TFHE.glwe<{1024,1,64}{4}>, i64) -> (!TFHE.glwe<{1024,1,64}{4}>)
-  return %1: !TFHE.glwe<{1024,1,64}{4}>
+func.func @add_glwe_int(%arg0: !TFHE.glwe<sk[1]<1,1024>>, %arg1: i64) -> !TFHE.glwe<sk[1]<1,1024>> {
+  %1 = "TFHE.add_glwe_int"(%arg0, %arg1): (!TFHE.glwe<sk[1]<1,1024>>, i64) -> (!TFHE.glwe<sk[1]<1,1024>>)
+  return %1: !TFHE.glwe<sk[1]<1,1024>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/bootstrap.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/bootstrap.mlir
@@ -1,12 +1,12 @@
 // RUN: concretecompiler --passes tfhe-to-concrete --action=dump-concrete %s 2>&1| FileCheck %s

 //CHECK: func.func @bootstrap_lwe(%[[A0:.*]]: tensor<601xi64>) -> tensor<1025xi64> {
-//CHECK:   %cst = arith.constant dense<"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tensor<128xi64>
-//CHECK:   %[[V1:.*]] = "Concrete.bootstrap_lwe_tensor"(%arg0, %cst) {baseLog = 1 : i32, glweDimension = 1 : i32, inputLweDim = 600 : i32, level = 3 : i32, polySize = 1024 : i32} : (tensor<601xi64>, tensor<128xi64>) -> tensor<1025xi64>
-//CHECK:   return %[[V1]] : tensor<1025xi64>
-//CHECK: }
-func.func @bootstrap_lwe(%ciphertext: !TFHE.glwe<{600,1,64}{7}>) -> !TFHE.glwe<{1024,1,64}{4}> {
+//CHECK-NEXT:   %cst = arith.constant dense<"0x00000000000000000100000000000000020000000000000003000000000000000400000000000000050000000000000006000000000000000700000000000000080000000000000009000000000000000A000000000000000B000000000000000C000000000000000D000000000000000E000000000000000F0000000000000010000000000000001100000000000000120000000000000013000000000000001400000000000000150000000000000016000000000000001700000000000000180000000000000019000000000000001A000000000000001B000000000000001C000000000000001D000000000000001E000000000000001F0000000000000020000000000000002100000000000000220000000000000023000000000000002400000000000000250000000000000026000000000000002700000000000000280000000000000029000000000000002A000000000000002B000000000000002C000000000000002D000000000000002E000000000000002F0000000000000030000000000000003100000000000000320000000000000033000000000000003400000000000000350000000000000036000000000000003700000000000000380000000000000039000000000000003A000000000000003B000000000000003C000000000000003D000000000000003E000000000000003F0000000000000040000000000000004100000000000000420000000000000043000000000000004400000000000000450000000000000046000000000000004700000000000000480000000000000049000000000000004A000000000000004B000000000000004C000000000000004D000000000000004E000000000000004F0000000000000050000000000000005100000000000000520000000000000053000000000000005400000000000000550000000000000056000000000000005700000000000000580000000000000059000000000000005A000000000000005B000000000000005C000000000000005D000000000000005E000000000000005F0000000000000060000000000000006100000000000000620000000000000063000000000000006400000000000000650000000000000066000000000000006700000000000000680000000000000069000000000000006A000000000000006B000000000000006C000000000000006D000000000000006E000000000000006F0000000000000070000000000000007100000000000000720000000000000073000000000000007400000000000000750000000000000076000000000000007700000000000000780000000000000079000000000000007A000000000000007B000000000000007C000000000000007D000000000000007E000000000000007F00000000000000"> : tensor<128xi64>
+//CHECK-NEXT:   %[[V1:.*]] = "Concrete.bootstrap_lwe_tensor"(%arg0, %cst) {baseLog = 1 : i32, glweDimension = 1 : i32, inputLweDim = 600 : i32, level = 3 : i32, polySize = 1024 : i32} : (tensor<601xi64>, tensor<128xi64>) -> tensor<1025xi64>
+//CHECK-NEXT:   return %[[V1]] : tensor<1025xi64>
+//CHECK-NEXT: }
+func.func @bootstrap_lwe(%ciphertext: !TFHE.glwe<sk[1]<1,600>>) -> !TFHE.glwe<sk[5]<1,1024>> {
  %cst = arith.constant dense<"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tensor<128xi64>
-  %bootstraped = "TFHE.bootstrap_glwe"(%ciphertext, %cst) {baseLog = 1 : i32, glweDimension = 1 : i32, level = 3 : i32, polySize = 1024 : i32} : (!TFHE.glwe<{600,1,64}{7}>, tensor<128xi64>) -> !TFHE.glwe<{1024,1,64}{4}>
-  return %bootstraped : !TFHE.glwe<{1024,1,64}{4}>
+  %bootstraped = "TFHE.bootstrap_glwe"(%ciphertext, %cst) {key = #TFHE.bsk<sk[1]<1,600>, sk[1]<1,1024>, 1024, 1, 3, 1>}: (!TFHE.glwe<sk[1]<1,600>>, tensor<128xi64>) -> !TFHE.glwe<sk[5]<1,1024>>
+  return %bootstraped : !TFHE.glwe<sk[5]<1,1024>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/keyswitch.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/keyswitch.mlir
@@ -4,7 +4,7 @@
 // CHECK-NEXT:   %[[V0:.*]] = "Concrete.keyswitch_lwe_tensor"(%[[A0]]) {baseLog = 3 : i32, level = 2 : i32, lwe_dim_in = 1024 : i32, lwe_dim_out = 567 : i32} : (tensor<1025xi64>) -> tensor<568xi64>
 // CHECK-NEXT:   return %[[V0]] : tensor<568xi64>
 // CHECK-NEXT: }
-func.func @keyswitch_glwe(%arg0: !TFHE.glwe<{1024,1,64}{2}>) -> !TFHE.glwe<{567,1,64}{2}> {
-  %0 = "TFHE.keyswitch_glwe"(%arg0) {baseLog = 3 : i32, level = 2 : i32} : (!TFHE.glwe<{1024,1,64}{2}>) -> !TFHE.glwe<{567,1,64}{2}>
-  return %0 : !TFHE.glwe<{567,1,64}{2}>
+func.func @keyswitch_glwe(%arg0: !TFHE.glwe<sk[1]<1,1024>>) -> !TFHE.glwe<sk[3]<1,567>> {
+  %0 = "TFHE.keyswitch_glwe"(%arg0) {key = #TFHE.ksk<sk[1]<1,1024>, sk[3]<1,567>, 2, 3>} : (!TFHE.glwe<sk[1]<1,1024>>) -> !TFHE.glwe<sk[3]<1,567>>
+  return %0 : !TFHE.glwe<sk[3]<1,567>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/mul_glwe_int.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/mul_glwe_int.mlir
@@ -5,10 +5,10 @@
 //CHECK:   %[[V0:.*]] = "Concrete.mul_cleartext_lwe_tensor"(%[[A0]], %c1_i64) : (tensor<1025xi64>, i64) -> tensor<1025xi64>
 //CHECK:   return %[[V0]] : tensor<1025xi64>
 //CHECK: }
-func.func @mul_glwe_const_int(%arg0: !TFHE.glwe<{1024,1,64}{7}>) -> !TFHE.glwe<{1024,1,64}{7}> {
+func.func @mul_glwe_const_int(%arg0: !TFHE.glwe<sk[1]<1,1024>>) -> !TFHE.glwe<sk[1]<1,1024>> {
  %0 = arith.constant 1 : i64
-  %1 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<{1024,1,64}{7}>, i64) -> (!TFHE.glwe<{1024,1,64}{7}>)
-  return %1: !TFHE.glwe<{1024,1,64}{7}>
+  %1 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<sk[1]<1,1024>>, i64) -> (!TFHE.glwe<sk[1]<1,1024>>)
+  return %1: !TFHE.glwe<sk[1]<1,1024>>
 }


@@ -16,7 +16,7 @@ func.func @mul_glwe_const_int(%arg0: !TFHE.glwe<{1024,1,64}{7}>) -> !TFHE.glwe<{
 //CHECK:   %[[V0:.*]] = "Concrete.mul_cleartext_lwe_tensor"(%[[A0]], %[[A1]]) : (tensor<1025xi64>, i64) -> tensor<1025xi64>
 //CHECK:   return %[[V0]] : tensor<1025xi64>
 //CHECK: }
-func.func @mul_glwe_int(%arg0: !TFHE.glwe<{1024,1,64}{4}>, %arg1: i64) -> !TFHE.glwe<{1024,1,64}{4}> {
-  %1 = "TFHE.mul_glwe_int"(%arg0, %arg1): (!TFHE.glwe<{1024,1,64}{4}>, i64) -> (!TFHE.glwe<{1024,1,64}{4}>)
-  return %1: !TFHE.glwe<{1024,1,64}{4}>
+func.func @mul_glwe_int(%arg0: !TFHE.glwe<sk[1]<1,1024>>, %arg1: i64) -> !TFHE.glwe<sk[1]<1,1024>> {
+  %1 = "TFHE.mul_glwe_int"(%arg0, %arg1): (!TFHE.glwe<sk[1]<1,1024>>, i64) -> (!TFHE.glwe<sk[1]<1,1024>>)
+  return %1: !TFHE.glwe<sk[1]<1,1024>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/neg_glwe.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/neg_glwe.mlir
@@ -1,9 +1,9 @@
 // RUN: concretecompiler --passes tfhe-to-concrete --action=dump-concrete %s 2>&1| FileCheck %s

 // CHECK-LABEL: func.func @neg_glwe(%arg0: tensor<1025xi64>) -> tensor<1025xi64>
-func.func @neg_glwe(%arg0: !TFHE.glwe<{1024,1,64}{4}>) -> !TFHE.glwe<{1024,1,64}{4}> {
+func.func @neg_glwe(%arg0: !TFHE.glwe<sk[1]<1,1024>>) -> !TFHE.glwe<sk[1]<1,1024>> {
  // CHECK-NEXT: %[[V1:.*]] = "Concrete.negate_lwe_tensor"(%arg0) : (tensor<1025xi64>) -> tensor<1025xi64>
  // CHECK-NEXT: return %[[V1]] : tensor<1025xi64>
-  %1 = "TFHE.neg_glwe"(%arg0): (!TFHE.glwe<{1024,1,64}{4}>) -> (!TFHE.glwe<{1024,1,64}{4}>)
-  return %1: !TFHE.glwe<{1024,1,64}{4}>
+  %1 = "TFHE.neg_glwe"(%arg0): (!TFHE.glwe<sk[1]<1,1024>>) -> (!TFHE.glwe<sk[1]<1,1024>>)
+  return %1: !TFHE.glwe<sk[1]<1,1024>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/sub_int_glwe.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/sub_int_glwe.mlir
@@ -6,10 +6,10 @@
 //CHECK:   %[[V1:.*]] = "Concrete.add_plaintext_lwe_tensor"(%[[V0]], %c1_i64) : (tensor<1025xi64>, i64) -> tensor<1025xi64>
 //CHECK:   return %[[V1]] : tensor<1025xi64>
 //CHECK: }
-func.func @sub_const_int_glwe(%arg0: !TFHE.glwe<{1024,1,64}{7}>) -> !TFHE.glwe<{1024,1,64}{7}> {
+func.func @sub_const_int_glwe(%arg0: !TFHE.glwe<sk[1]<1,1024>>) -> !TFHE.glwe<sk[1]<1,1024>> {
  %0 = arith.constant 1 : i64
-  %1 = "TFHE.sub_int_glwe"(%0, %arg0): (i64, !TFHE.glwe<{1024,1,64}{7}>) -> (!TFHE.glwe<{1024,1,64}{7}>)
-  return %1: !TFHE.glwe<{1024,1,64}{7}>
+  %1 = "TFHE.sub_int_glwe"(%0, %arg0): (i64, !TFHE.glwe<sk[1]<1,1024>>) -> (!TFHE.glwe<sk[1]<1,1024>>)
+  return %1: !TFHE.glwe<sk[1]<1,1024>>
 }

 //CHECK: func.func @sub_int_glwe(%[[A0:.*]]: tensor<1025xi64>, %[[A1:.*]]: i64) -> tensor<1025xi64> {
@@ -17,7 +17,7 @@ func.func @sub_const_int_glwe(%arg0: !TFHE.glwe<{1024,1,64}{7}>) -> !TFHE.glwe<{
 //CHECK:   %[[V1:.*]] = "Concrete.add_plaintext_lwe_tensor"(%[[V0]], %[[A1]]) : (tensor<1025xi64>, i64) -> tensor<1025xi64>
 //CHECK:   return %[[V1]] : tensor<1025xi64>
 //CHECK: }
-func.func @sub_int_glwe(%arg0: !TFHE.glwe<{1024,1,64}{4}>, %arg1: i64) -> !TFHE.glwe<{1024,1,64}{4}> {
-  %1 = "TFHE.sub_int_glwe"(%arg1, %arg0): (i64, !TFHE.glwe<{1024,1,64}{4}>) -> (!TFHE.glwe<{1024,1,64}{4}>)
-  return %1: !TFHE.glwe<{1024,1,64}{4}>
+func.func @sub_int_glwe(%arg0: !TFHE.glwe<sk[1]<1,1024>>, %arg1: i64) -> !TFHE.glwe<sk[1]<1,1024>> {
+  %1 = "TFHE.sub_int_glwe"(%arg1, %arg0): (i64, !TFHE.glwe<sk[1]<1,1024>>) -> (!TFHE.glwe<sk[1]<1,1024>>)
+  return %1: !TFHE.glwe<sk[1]<1,1024>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/tensor_exapand_collapse_shape.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/tensor_exapand_collapse_shape.mlir
@@ -4,9 +4,9 @@
 //CHECK:   %[[V0:.*]] = tensor.collapse_shape %[[A0]] [[_:\[\[0, 1, 2, 3, 4\], \[5\]\]]] : tensor<2x3x4x5x6x1025xi64> into tensor<720x1025xi64>
 //CHECK:   return %[[V0]] : tensor<720x1025xi64>
 //CHECK: }
-func.func @tensor_collapse_shape(%arg0: tensor<2x3x4x5x6x!TFHE.glwe<{1024, 1, 64}{4}>>) -> tensor<720x!TFHE.glwe<{1024, 1, 64}{4}>> {
-    %0 = tensor.collapse_shape %arg0 [[0, 1, 2, 3, 4]]  {MANP = 1 : ui1}: tensor<2x3x4x5x6x!TFHE.glwe<{1024, 1, 64}{4}>> into tensor<720x!TFHE.glwe<{1024, 1, 64}{4}>>
-    return %0 : tensor<720x!TFHE.glwe<{1024, 1, 64}{4}>>
+func.func @tensor_collapse_shape(%arg0: tensor<2x3x4x5x6x!TFHE.glwe<sk[1]<1,1024>>>) -> tensor<720x!TFHE.glwe<sk[1]<1,1024>>> {
+    %0 = tensor.collapse_shape %arg0 [[0, 1, 2, 3, 4]]  {MANP = 1 : ui1}: tensor<2x3x4x5x6x!TFHE.glwe<sk[1]<1,1024>>> into tensor<720x!TFHE.glwe<sk[1]<1,1024>>>
+    return %0 : tensor<720x!TFHE.glwe<sk[1]<1,1024>>>
 }

 // -----
@@ -15,10 +15,10 @@ func.func @tensor_collapse_shape(%arg0: tensor<2x3x4x5x6x!TFHE.glwe<{1024, 1, 64
 //CHECK:   %[[V1:.*]] = tensor.expand_shape %[[V0]] [[_:\[\[0, 1\], \[2\]\]]] : tensor<30x1025xi64> into tensor<5x6x1025xi64>
 //CHECK:   return %[[V1]] : tensor<5x6x1025xi64>
 //CHECK: }
-func.func @tensor_collatenspse_shape(%arg0: tensor<2x3x5x!TFHE.glwe<{1024, 1, 64}{4}>>) -> tensor<5x6x!TFHE.glwe<{1024, 1, 64}{4}>> {
-    %0 = tensor.collapse_shape %arg0 [[0, 1, 2]]  {MANP = 1 : ui1}: tensor<2x3x5x!TFHE.glwe<{1024, 1, 64}{4}>> into tensor<30x!TFHE.glwe<{1024, 1, 64}{4}>>
-    %1 = tensor.expand_shape %0 [[0, 1]]  {MANP = 1 : ui1}: tensor<30x!TFHE.glwe<{1024, 1, 64}{4}>> into tensor<5x6x!TFHE.glwe<{1024, 1, 64}{4}>>
-    return %1 : tensor<5x6x!TFHE.glwe<{1024, 1, 64}{4}>>
+func.func @tensor_collatenspse_shape(%arg0: tensor<2x3x5x!TFHE.glwe<sk[1]<1,1024>>>) -> tensor<5x6x!TFHE.glwe<sk[1]<1,1024>>> {
+    %0 = tensor.collapse_shape %arg0 [[0, 1, 2]]  {MANP = 1 : ui1}: tensor<2x3x5x!TFHE.glwe<sk[1]<1,1024>>> into tensor<30x!TFHE.glwe<sk[1]<1,1024>>>
+    %1 = tensor.expand_shape %0 [[0, 1]]  {MANP = 1 : ui1}: tensor<30x!TFHE.glwe<sk[1]<1,1024>>> into tensor<5x6x!TFHE.glwe<sk[1]<1,1024>>>
+    return %1 : tensor<5x6x!TFHE.glwe<sk[1]<1,1024>>>
 }

 // -----
@@ -26,9 +26,9 @@ func.func @tensor_collatenspse_shape(%arg0: tensor<2x3x5x!TFHE.glwe<{1024, 1, 64
 //CHECK:   %[[V0:.*]] = tensor.collapse_shape %[[A0]] [[_:\[\[0, 1\], \[2\], \[3, 4\], \[5\]\]]] : tensor<2x3x2x3x4x1025xi64> into tensor<6x2x12x1025xi64>
 //CHECK:   return %[[V0]] : tensor<6x2x12x1025xi64>
 //CHECK: }
-func.func @tensor_collatenspse_shape(%arg0: tensor<2x3x2x3x4x!TFHE.glwe<{1024, 1, 64}{4}>>) -> tensor<6x2x12x!TFHE.glwe<{1024, 1, 64}{4}>> {
-    %0 = tensor.collapse_shape %arg0 [[0, 1], [2], [3, 4]]  {MANP = 1 : ui1}: tensor<2x3x2x3x4x!TFHE.glwe<{1024, 1, 64}{4}>> into tensor<6x2x12x!TFHE.glwe<{1024, 1, 64}{4}>>
-    return %0 : tensor<6x2x12x!TFHE.glwe<{1024, 1, 64}{4}>>
+func.func @tensor_collatenspse_shape(%arg0: tensor<2x3x2x3x4x!TFHE.glwe<sk[1]<1,1024>>>) -> tensor<6x2x12x!TFHE.glwe<sk[1]<1,1024>>> {
+    %0 = tensor.collapse_shape %arg0 [[0, 1], [2], [3, 4]]  {MANP = 1 : ui1}: tensor<2x3x2x3x4x!TFHE.glwe<sk[1]<1,1024>>> into tensor<6x2x12x!TFHE.glwe<sk[1]<1,1024>>>
+    return %0 : tensor<6x2x12x!TFHE.glwe<sk[1]<1,1024>>>
 }

 // -----
@@ -36,7 +36,7 @@ func.func @tensor_collatenspse_shape(%arg0: tensor<2x3x2x3x4x!TFHE.glwe<{1024, 1
 //CHECK:   %[[V0:.*]] = tensor.expand_shape %[[A0]] [[_:\[\[0, 1\], \[2\]\]]] : tensor<30x1025xi64> into tensor<5x6x1025xi64>
 //CHECK:   return %[[V0]] : tensor<5x6x1025xi64>
 //CHECK: }
-func.func @tensor_expand_shape_crt(%arg0: tensor<30x!TFHE.glwe<{1024, 1, 64}{4}>>) -> tensor<5x6x!TFHE.glwe<{1024, 1, 64}{4}>> {
-    %0 = tensor.expand_shape %arg0 [[0, 1]]  {MANP = 1 : ui1}: tensor<30x!TFHE.glwe<{1024, 1, 64}{4}>> into tensor<5x6x!TFHE.glwe<{1024, 1, 64}{4}>>
-    return %0 : tensor<5x6x!TFHE.glwe<{1024, 1, 64}{4}>>
+func.func @tensor_expand_shape_crt(%arg0: tensor<30x!TFHE.glwe<sk[1]<1,1024>>>) -> tensor<5x6x!TFHE.glwe<sk[1]<1,1024>>> {
+    %0 = tensor.expand_shape %arg0 [[0, 1]]  {MANP = 1 : ui1}: tensor<30x!TFHE.glwe<sk[1]<1,1024>>> into tensor<5x6x!TFHE.glwe<sk[1]<1,1024>>>
+    return %0 : tensor<5x6x!TFHE.glwe<sk[1]<1,1024>>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/tensor_from_elements.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/tensor_from_elements.mlir
@@ -10,9 +10,9 @@
 // CHECK:   %[[V6:.*]] = tensor.insert_slice %[[A5]] into %[[V5]][5, 0] [1, 2049] [1, 1] : tensor<2049xi64> into tensor<6x2049xi64>
 // CHECK:   return %[[V6]] : tensor<6x2049xi64>
 // CHECK: }
-func.func @main(%arg0 : !TFHE.glwe<{2048, 1, 64}{4}>, %arg1 : !TFHE.glwe<{2048, 1, 64}{4}>, %arg2 : !TFHE.glwe<{2048, 1, 64}{4}>, %arg3 : !TFHE.glwe<{2048, 1, 64}{4}>, %arg4 : !TFHE.glwe<{2048, 1, 64}{4}>, %arg5 : !TFHE.glwe<{2048, 1, 64}{4}>) -> tensor<6x!TFHE.glwe<{2048, 1, 64}{4}>> {
-  %0 = tensor.from_elements %arg0, %arg1, %arg2, %arg3, %arg4, %arg5 : tensor<6x!TFHE.glwe<{2048, 1, 64}{4}>>
-  return %0 : tensor<6x!TFHE.glwe<{2048, 1, 64}{4}>>
+func.func @main(%arg0 : !TFHE.glwe<sk[1]<1,2048>>, %arg1 : !TFHE.glwe<sk[1]<1,2048>>, %arg2 : !TFHE.glwe<sk[1]<1,2048>>, %arg3 : !TFHE.glwe<sk[1]<1,2048>>, %arg4 : !TFHE.glwe<sk[1]<1,2048>>, %arg5 : !TFHE.glwe<sk[1]<1,2048>>) -> tensor<6x!TFHE.glwe<sk[1]<1,2048>>> {
+  %0 = tensor.from_elements %arg0, %arg1, %arg2, %arg3, %arg4, %arg5 : tensor<6x!TFHE.glwe<sk[1]<1,2048>>>
+  return %0 : tensor<6x!TFHE.glwe<sk[1]<1,2048>>>
 }

 // -----
@@ -27,7 +27,7 @@ func.func @main(%arg0 : !TFHE.glwe<{2048, 1, 64}{4}>, %arg1 : !TFHE.glwe<{2048,
 // CHECK:   %[[V6:.*]] = tensor.insert_slice %[[A5]] into %[[V5]][1, 2, 0] [1, 1, 2049] [1, 1, 1] : tensor<2049xi64> into tensor<2x3x2049xi64>
 // CHECK:   return %[[V6]] : tensor<2x3x2049xi64>
 // CHECK: }
-func.func @main(%arg0 : !TFHE.glwe<{2048, 1, 64}{4}>, %arg1 : !TFHE.glwe<{2048, 1, 64}{4}>, %arg2 : !TFHE.glwe<{2048, 1, 64}{4}>, %arg3 : !TFHE.glwe<{2048, 1, 64}{4}>, %arg4 : !TFHE.glwe<{2048, 1, 64}{4}>, %arg5 : !TFHE.glwe<{2048, 1, 64}{4}>) -> tensor<2x3x!TFHE.glwe<{2048, 1, 64}{4}>> {
-  %0 = tensor.from_elements %arg0, %arg1, %arg2, %arg3, %arg4, %arg5 : tensor<2x3x!TFHE.glwe<{2048, 1, 64}{4}>>
-  return %0 : tensor<2x3x!TFHE.glwe<{2048, 1, 64}{4}>>
+func.func @main(%arg0 : !TFHE.glwe<sk[1]<1,2048>>, %arg1 : !TFHE.glwe<sk[1]<1,2048>>, %arg2 : !TFHE.glwe<sk[1]<1,2048>>, %arg3 : !TFHE.glwe<sk[1]<1,2048>>, %arg4 : !TFHE.glwe<sk[1]<1,2048>>, %arg5 : !TFHE.glwe<sk[1]<1,2048>>) -> tensor<2x3x!TFHE.glwe<sk[1]<1,2048>>> {
+  %0 = tensor.from_elements %arg0, %arg1, %arg2, %arg3, %arg4, %arg5 : tensor<2x3x!TFHE.glwe<sk[1]<1,2048>>>
+  return %0 : tensor<2x3x!TFHE.glwe<sk[1]<1,2048>>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/tensor_identity.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Conversion/TFHEToConcrete/tensor_identity.mlir
@@ -3,6 +3,6 @@
 // CHECK: func.func @tensor_identity(%arg0: tensor<2x3x4x1025xi64>) -> tensor<2x3x4x1025xi64> {
 // CHECK-NEXT:   return %arg0 : tensor<2x3x4x1025xi64>
 // CHECK-NEXT: }
-func.func @tensor_identity(%arg0: tensor<2x3x4x!TFHE.glwe<{1024, 1, 64}{7}>>) -> tensor<2x3x4x!TFHE.glwe<{1024, 1, 64}{7}>> {
-    return %arg0 : tensor<2x3x4x!TFHE.glwe<{1024, 1, 64}{7}>>
+func.func @tensor_identity(%arg0: tensor<2x3x4x!TFHE.glwe<sk[1]<1,1024>>>) -> tensor<2x3x4x!TFHE.glwe<sk[1]<1,1024>>> {
+    return %arg0 : tensor<2x3x4x!TFHE.glwe<sk[1]<1,1024>>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/no_optimization.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/no_optimization.mlir
@@ -1,12 +1,12 @@
 // RUN: concretecompiler --passes tfhe-optimization --optimize-tfhe=false --action=dump-tfhe %s 2>&1| FileCheck %s

-//CHECK: func.func @mul_cleartext_glwe_ciphertext_0(%[[A0:.*]]: !TFHE.glwe<{1,527,64}{7}>) -> !TFHE.glwe<{1,527,64}{7}> {
+//CHECK: func.func @mul_cleartext_glwe_ciphertext_0(%[[A0:.*]]: !TFHE.glwe<sk[1]<527,1>>) -> !TFHE.glwe<sk[1]<527,1>> {
 //CHECK:   %c0_i64 = arith.constant 0 : i64
-//CHECK:   %[[V0:.*]] = "TFHE.mul_glwe_int"(%[[A0]], %c0_i64) : (!TFHE.glwe<{1,527,64}{7}>, i64) -> !TFHE.glwe<{1,527,64}{7}>
-//CHECK:   return %[[V0]] : !TFHE.glwe<{1,527,64}{7}>
+//CHECK:   %[[V0:.*]] = "TFHE.mul_glwe_int"(%[[A0]], %c0_i64) : (!TFHE.glwe<sk[1]<527,1>>, i64) -> !TFHE.glwe<sk[1]<527,1>>
+//CHECK:   return %[[V0]] : !TFHE.glwe<sk[1]<527,1>>
 //CHECK: }
-func.func @mul_cleartext_glwe_ciphertext_0(%arg0: !TFHE.glwe<{1,527,64}{7}>) -> !TFHE.glwe<{1,527,64}{7}> {
+func.func @mul_cleartext_glwe_ciphertext_0(%arg0: !TFHE.glwe<sk[1]<527,1>>) -> !TFHE.glwe<sk[1]<527,1>> {
  %0 = arith.constant 0 : i64
-  %2 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<{1,527,64}{7}>, i64) -> (!TFHE.glwe<{1,527,64}{7}>)
-  return %2: !TFHE.glwe<{1,527,64}{7}>
+  %2 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<sk[1]<527,1>>, i64) -> (!TFHE.glwe<sk[1]<527,1>>)
+  return %2: !TFHE.glwe<sk[1]<527,1>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_add_glwe.invalid.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_add_glwe.invalid.mlir
@@ -1,35 +1,35 @@
 // RUN: concretecompiler --split-input-file --verify-diagnostics --action=roundtrip %s

 // GLWE dimension parameter result
-func.func @add_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>, %arg1: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{512,12,64}{7}> {
-  // expected-error @+1 {{'TFHE.add_glwe' op should have the same GLWE 'dimension' parameter}}
-  %1 = "TFHE.add_glwe"(%arg0, %arg1): (!TFHE.glwe<{1024,12,64}{7}>, !TFHE.glwe<{1024,12,64}{7}>) -> (!TFHE.glwe<{512,12,64}{7}>)
-  return %1: !TFHE.glwe<{512,12,64}{7}>
+func.func @add_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>, %arg1: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,512>> {
+  // expected-error @+1 {{'TFHE.add_glwe' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.add_glwe"(%arg0, %arg1): (!TFHE.glwe<sk[1]<12,1024>>, !TFHE.glwe<sk[1]<12,1024>>) -> (!TFHE.glwe<sk[1]<12,512>>)
+  return %1: !TFHE.glwe<sk[1]<12,512>>
 }

 // -----

 // GLWE dimension parameter inputs
-func.func @add_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>, %arg1: !TFHE.glwe<{512,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}> {
-  // expected-error @+1 {{'TFHE.add_glwe' op should have the same GLWE 'dimension' parameter}}
-  %1 = "TFHE.add_glwe"(%arg0, %arg1): (!TFHE.glwe<{1024,12,64}{7}>, !TFHE.glwe<{512,12,64}{7}>) -> (!TFHE.glwe<{1024,12,64}{7}>)
-  return %1: !TFHE.glwe<{1024,12,64}{7}>
+func.func @add_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>, %arg1: !TFHE.glwe<sk[1]<12,512>>) -> !TFHE.glwe<sk[1]<12,1024>> {
+  // expected-error @+1 {{'TFHE.add_glwe' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.add_glwe"(%arg0, %arg1): (!TFHE.glwe<sk[1]<12,1024>>, !TFHE.glwe<sk[1]<12,512>>) -> (!TFHE.glwe<sk[1]<12,1024>>)
+  return %1: !TFHE.glwe<sk[1]<12,1024>>
 }

 // -----

 // GLWE polynomialSize parameter result
-func.func @add_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>, %arg1: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,11,64}{7}> {
-  // expected-error @+1 {{'TFHE.add_glwe' op should have the same GLWE 'polynomialSize' parameter}}
-  %1 = "TFHE.add_glwe"(%arg0, %arg1): (!TFHE.glwe<{1024,12,64}{7}>, !TFHE.glwe<{1024,12,64}{7}>) -> (!TFHE.glwe<{1024,11,64}{7}>)
-  return %1: !TFHE.glwe<{1024,11,64}{7}>
+func.func @add_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>, %arg1: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<11,1024>> {
+  // expected-error @+1 {{'TFHE.add_glwe' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.add_glwe"(%arg0, %arg1): (!TFHE.glwe<sk[1]<12,1024>>, !TFHE.glwe<sk[1]<12,1024>>) -> (!TFHE.glwe<sk[1]<11,1024>>)
+  return %1: !TFHE.glwe<sk[1]<11,1024>>
 }

 // -----

 // GLWE polynomialSize parameter inputs
-func.func @add_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>, %arg1: !TFHE.glwe<{1024,11,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}> {
-  // expected-error @+1 {{'TFHE.add_glwe' op should have the same GLWE 'polynomialSize' parameter}}
-  %1 = "TFHE.add_glwe"(%arg0, %arg1): (!TFHE.glwe<{1024,12,64}{7}>, !TFHE.glwe<{1024,11,64}{7}>) -> (!TFHE.glwe<{1024,12,64}{7}>)
-  return %1: !TFHE.glwe<{1024,12,64}{7}>
+func.func @add_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>, %arg1: !TFHE.glwe<sk[1]<11,1024>>) -> !TFHE.glwe<sk[1]<12,1024>> {
+  // expected-error @+1 {{'TFHE.add_glwe' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.add_glwe"(%arg0, %arg1): (!TFHE.glwe<sk[1]<12,1024>>, !TFHE.glwe<sk[1]<11,1024>>) -> (!TFHE.glwe<sk[1]<12,1024>>)
+  return %1: !TFHE.glwe<sk[1]<12,1024>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_add_glwe.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_add_glwe.mlir
@@ -1,10 +1,10 @@
 // RUN: concretecompiler --action=roundtrip %s 2>&1| FileCheck %s

-// CHECK-LABEL: func.func @add_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>, %arg1: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}>
-func.func @add_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>, %arg1: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}> {
-  // CHECK-NEXT: %[[V1:.*]] = "TFHE.add_glwe"(%arg0, %arg1) : (!TFHE.glwe<{1024,12,64}{7}>, !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}>
-  // CHECK-NEXT: return %[[V1]] : !TFHE.glwe<{1024,12,64}{7}>
+// CHECK-LABEL: func.func @add_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>, %arg1: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>>
+func.func @add_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>, %arg1: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>> {
+  // CHECK-NEXT: %[[V1:.*]] = "TFHE.add_glwe"(%arg0, %arg1) : (!TFHE.glwe<sk[1]<12,1024>>, !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>>
+  // CHECK-NEXT: return %[[V1]] : !TFHE.glwe<sk[1]<12,1024>>

-  %0 = "TFHE.add_glwe"(%arg0, %arg1): (!TFHE.glwe<{1024,12,64}{7}>, !TFHE.glwe<{1024,12,64}{7}>) -> (!TFHE.glwe<{1024,12,64}{7}>)
-  return %0: !TFHE.glwe<{1024,12,64}{7}>
+  %0 = "TFHE.add_glwe"(%arg0, %arg1): (!TFHE.glwe<sk[1]<12,1024>>, !TFHE.glwe<sk[1]<12,1024>>) -> (!TFHE.glwe<sk[1]<12,1024>>)
+  return %0: !TFHE.glwe<sk[1]<12,1024>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_add_glwe_int.invalid.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_add_glwe_int.invalid.mlir
@@ -1,29 +1,29 @@
 // RUN: concretecompiler --split-input-file --verify-diagnostics --action=roundtrip %s

-// GLWE p parameter
-func.func @add_glwe_int(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{6}> {
+// GLWE id parameter
+func.func @add_glwe_int(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[2]<12,1024>> {
  %0 = arith.constant 1 : i8
-  // expected-error @+1 {{'TFHE.add_glwe_int' op should have the same GLWE 'p' parameter}}
-  %1 = "TFHE.add_glwe_int"(%arg0, %0): (!TFHE.glwe<{1024,12,64}{7}>, i8) -> (!TFHE.glwe<{1024,12,64}{6}>)
-  return %1: !TFHE.glwe<{1024,12,64}{6}>
+  // expected-error @+1 {{'TFHE.add_glwe_int' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.add_glwe_int"(%arg0, %0): (!TFHE.glwe<sk[1]<12,1024>>, i8) -> (!TFHE.glwe<sk[2]<12,1024>>)
+  return %1: !TFHE.glwe<sk[2]<12,1024>>
 }

 // -----

 // GLWE dimension parameter
-func.func @add_glwe_int(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{512,12,64}{7}> {
+func.func @add_glwe_int(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,512>> {
  %0 = arith.constant 1 : i8
-  // expected-error @+1 {{'TFHE.add_glwe_int' op should have the same GLWE 'dimension' parameter}}
-  %1 = "TFHE.add_glwe_int"(%arg0, %0): (!TFHE.glwe<{1024,12,64}{7}>, i8) -> (!TFHE.glwe<{512,12,64}{7}>)
-  return %1: !TFHE.glwe<{512,12,64}{7}>
+  // expected-error @+1 {{'TFHE.add_glwe_int' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.add_glwe_int"(%arg0, %0): (!TFHE.glwe<sk[1]<12,1024>>, i8) -> (!TFHE.glwe<sk[1]<12,512>>)
+  return %1: !TFHE.glwe<sk[1]<12,512>>
 }

 // -----

 // GLWE polynomialSize parameter
-func.func @add_glwe_int(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,11,64}{7}> {
+func.func @add_glwe_int(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<11,1024>> {
  %0 = arith.constant 1 : i8
-  // expected-error @+1 {{'TFHE.add_glwe_int' op should have the same GLWE 'polynomialSize' parameter}}
-  %1 = "TFHE.add_glwe_int"(%arg0, %0): (!TFHE.glwe<{1024,12,64}{7}>, i8) -> (!TFHE.glwe<{1024,11,64}{7}>)
-  return %1: !TFHE.glwe<{1024,11,64}{7}>
+  // expected-error @+1 {{'TFHE.add_glwe_int' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.add_glwe_int"(%arg0, %0): (!TFHE.glwe<sk[1]<12,1024>>, i8) -> (!TFHE.glwe<sk[1]<11,1024>>)
+  return %1: !TFHE.glwe<sk[1]<11,1024>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_add_glwe_int.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_add_glwe_int.mlir
@@ -1,12 +1,12 @@
 // RUN: concretecompiler --action=roundtrip %s  2>&1| FileCheck %s

-// CHECK-LABEL: func.func @add_glwe_int(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}>
-func.func @add_glwe_int(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}> {
+// CHECK-LABEL: func.func @add_glwe_int(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>>
+func.func @add_glwe_int(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>> {
  // CHECK-NEXT: %[[V1:.*]] = arith.constant 1 : i64
-  // CHECK-NEXT: %[[V2:.*]] = "TFHE.add_glwe_int"(%arg0, %[[V1]]) : (!TFHE.glwe<{1024,12,64}{7}>, i64) -> !TFHE.glwe<{1024,12,64}{7}>
-  // CHECK-NEXT: return %[[V2]] : !TFHE.glwe<{1024,12,64}{7}>
+  // CHECK-NEXT: %[[V2:.*]] = "TFHE.add_glwe_int"(%arg0, %[[V1]]) : (!TFHE.glwe<sk[1]<12,1024>>, i64) -> !TFHE.glwe<sk[1]<12,1024>>
+  // CHECK-NEXT: return %[[V2]] : !TFHE.glwe<sk[1]<12,1024>>

  %0 = arith.constant 1 : i64
-  %1 = "TFHE.add_glwe_int"(%arg0, %0): (!TFHE.glwe<{1024,12,64}{7}>, i64) -> (!TFHE.glwe<{1024,12,64}{7}>)
-  return %1: !TFHE.glwe<{1024,12,64}{7}>
+  %1 = "TFHE.add_glwe_int"(%arg0, %0): (!TFHE.glwe<sk[1]<12,1024>>, i64) -> (!TFHE.glwe<sk[1]<12,1024>>)
+  return %1: !TFHE.glwe<sk[1]<12,1024>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_mul_glwe_int.invalid.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_mul_glwe_int.invalid.mlir
@@ -1,29 +1,29 @@
 // RUN: concretecompiler --split-input-file --verify-diagnostics --action=roundtrip %s

 // GLWE p parameter
-func.func @mul_glwe_int(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{6}> {
+func.func @mul_glwe_int(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[2]<12,1024>> {
  %0 = arith.constant 1 : i8
-  // expected-error @+1 {{'TFHE.mul_glwe_int' op should have the same GLWE 'p' parameter}}
-  %1 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<{1024,12,64}{7}>, i8) -> (!TFHE.glwe<{1024,12,64}{6}>)
-  return %1: !TFHE.glwe<{1024,12,64}{6}>
+  // expected-error @+1 {{'TFHE.mul_glwe_int' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<sk[1]<12,1024>>, i8) -> (!TFHE.glwe<sk[2]<12,1024>>)
+  return %1: !TFHE.glwe<sk[2]<12,1024>>
 }

 // -----

 // GLWE dimension parameter
-func.func @mul_glwe_int(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{512,12,64}{7}> {
+func.func @mul_glwe_int(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,512>> {
  %0 = arith.constant 1 : i8
-  // expected-error @+1 {{'TFHE.mul_glwe_int' op should have the same GLWE 'dimension' parameter}}
-  %1 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<{1024,12,64}{7}>, i8) -> (!TFHE.glwe<{512,12,64}{7}>)
-  return %1: !TFHE.glwe<{512,12,64}{7}>
+  // expected-error @+1 {{'TFHE.mul_glwe_int' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<sk[1]<12,1024>>, i8) -> (!TFHE.glwe<sk[1]<12,512>>)
+  return %1: !TFHE.glwe<sk[1]<12,512>>
 }

 // -----

 // GLWE polynomialSize parameter
-func.func @mul_glwe_int(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,11,64}{7}> {
+func.func @mul_glwe_int(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<11,1024>> {
  %0 = arith.constant 1 : i8
-  // expected-error @+1 {{'TFHE.mul_glwe_int' op should have the same GLWE 'polynomialSize' parameter}}
-  %1 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<{1024,12,64}{7}>, i8) -> (!TFHE.glwe<{1024,11,64}{7}>)
-  return %1: !TFHE.glwe<{1024,11,64}{7}>
+  // expected-error @+1 {{'TFHE.mul_glwe_int' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<sk[1]<12,1024>>, i8) -> (!TFHE.glwe<sk[1]<11,1024>>)
+  return %1: !TFHE.glwe<sk[1]<11,1024>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_mul_glwe_int.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_mul_glwe_int.mlir
@@ -1,12 +1,12 @@
 // RUN: concretecompiler --action=roundtrip %s 2>&1| FileCheck %s

-// CHECK-LABEL: func.func @mul_glwe_int(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}>
-func.func @mul_glwe_int(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}> {
+// CHECK-LABEL: func.func @mul_glwe_int(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>>
+func.func @mul_glwe_int(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>> {
  // CHECK-NEXT: %[[V1:.*]] = arith.constant 1 : i64
-  // CHECK-NEXT: %[[V2:.*]] = "TFHE.mul_glwe_int"(%arg0, %[[V1]]) : (!TFHE.glwe<{1024,12,64}{7}>, i64) -> !TFHE.glwe<{1024,12,64}{7}>
-  // CHECK-NEXT: return %[[V2]] : !TFHE.glwe<{1024,12,64}{7}>
+  // CHECK-NEXT: %[[V2:.*]] = "TFHE.mul_glwe_int"(%arg0, %[[V1]]) : (!TFHE.glwe<sk[1]<12,1024>>, i64) -> !TFHE.glwe<sk[1]<12,1024>>
+  // CHECK-NEXT: return %[[V2]] : !TFHE.glwe<sk[1]<12,1024>>

  %0 = arith.constant 1 : i64
-  %1 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<{1024,12,64}{7}>, i64) -> (!TFHE.glwe<{1024,12,64}{7}>)
-  return %1: !TFHE.glwe<{1024,12,64}{7}>
+  %1 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<sk[1]<12,1024>>, i64) -> (!TFHE.glwe<sk[1]<12,1024>>)
+  return %1: !TFHE.glwe<sk[1]<12,1024>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_neg_glwe.invalid.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_neg_glwe.invalid.mlir
@@ -1,36 +1,26 @@
 // RUN: concretecompiler --split-input-file --verify-diagnostics --action=roundtrip %s

-// GLWE p parameter
-func.func @neg_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{6}> {
-  // expected-error @+1 {{'TFHE.neg_glwe' op should have the same GLWE 'p' parameter}}
-  %1 = "TFHE.neg_glwe"(%arg0): (!TFHE.glwe<{1024,12,64}{7}>) -> (!TFHE.glwe<{1024,12,64}{6}>)
-  return %1: !TFHE.glwe<{1024,12,64}{6}>
+// GLWE id parameter
+func.func @neg_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[2]<12,1024>> {
+  // expected-error @+1 {{'TFHE.neg_glwe' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.neg_glwe"(%arg0): (!TFHE.glwe<sk[1]<12,1024>>) -> (!TFHE.glwe<sk[2]<12,1024>>)
+  return %1: !TFHE.glwe<sk[2]<12,1024>>
 }

 // -----

 // GLWE dimension parameter
-func.func @neg_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{512,12,64}{7}> {
-  // expected-error @+1 {{'TFHE.neg_glwe' op should have the same GLWE 'dimension' parameter}}
-  %1 = "TFHE.neg_glwe"(%arg0): (!TFHE.glwe<{1024,12,64}{7}>) -> (!TFHE.glwe<{512,12,64}{7}>)
-  return %1: !TFHE.glwe<{512,12,64}{7}>
+func.func @neg_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,512>> {
+  // expected-error @+1 {{'TFHE.neg_glwe' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.neg_glwe"(%arg0): (!TFHE.glwe<sk[1]<12,1024>>) -> (!TFHE.glwe<sk[1]<12,512>>)
+  return %1: !TFHE.glwe<sk[1]<12,512>>
 }

 // -----

 // GLWE polynomialSize parameter
-func.func @neg_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,11,64}{7}> {
-  // expected-error @+1 {{'TFHE.neg_glwe' op should have the same GLWE 'polynomialSize' parameter}}
-  %1 = "TFHE.neg_glwe"(%arg0): (!TFHE.glwe<{1024,12,64}{7}>) -> (!TFHE.glwe<{1024,11,64}{7}>)
-  return %1: !TFHE.glwe<{1024,11,64}{7}>
+func.func @neg_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<11,1024>> {
+  // expected-error @+1 {{'TFHE.neg_glwe' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.neg_glwe"(%arg0): (!TFHE.glwe<sk[1]<12,1024>>) -> (!TFHE.glwe<sk[1]<11,1024>>)
+  return %1: !TFHE.glwe<sk[1]<11,1024>>
 }
-
-// -----
-
-// integer width doesn't match GLWE parameter
-func.func @neg_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,11,64}{7}> {
-  // expected-error @+1 {{'TFHE.neg_glwe' op should have the same GLWE 'polynomialSize' parameter}}
-  %1 = "TFHE.neg_glwe"(%arg0): (!TFHE.glwe<{1024,12,64}{7}>) -> (!TFHE.glwe<{1024,11,64}{7}>)
-  return %1: !TFHE.glwe<{1024,11,64}{7}>
-}
-
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_neg_glwe.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_neg_glwe.mlir
@@ -1,10 +1,10 @@
 // RUN: concretecompiler --action=roundtrip %s 2>&1| FileCheck %s

-// CHECK-LABEL: func.func @neg_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}>
-func.func @neg_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}> {
-  // CHECK-NEXT: %[[V1:.*]] = "TFHE.neg_glwe"(%arg0) : (!TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}>
-  // CHECK-NEXT: return %[[V1]] : !TFHE.glwe<{1024,12,64}{7}>
+// CHECK-LABEL: func.func @neg_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>>
+func.func @neg_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>> {
+  // CHECK-NEXT: %[[V1:.*]] = "TFHE.neg_glwe"(%arg0) : (!TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>>
+  // CHECK-NEXT: return %[[V1]] : !TFHE.glwe<sk[1]<12,1024>>

-  %1 = "TFHE.neg_glwe"(%arg0): (!TFHE.glwe<{1024,12,64}{7}>) -> (!TFHE.glwe<{1024,12,64}{7}>)
-  return %1: !TFHE.glwe<{1024,12,64}{7}>
+  %1 = "TFHE.neg_glwe"(%arg0): (!TFHE.glwe<sk[1]<12,1024>>) -> (!TFHE.glwe<sk[1]<12,1024>>)
+  return %1: !TFHE.glwe<sk[1]<12,1024>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_sub_int_glwe.invalid.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_sub_int_glwe.invalid.mlir
@@ -1,41 +1,30 @@
 // RUN: concretecompiler --split-input-file --verify-diagnostics --action=roundtrip %s

-// GLWE p parameter
-func.func @sub_int_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{6}> {
+// GLWE id parameter
+func.func @sub_int_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[2]<12,1024>> {
  %0 = arith.constant 1 : i8
-  // expected-error @+1 {{'TFHE.sub_int_glwe' op should have the same GLWE 'p' parameter}}
-  %1 = "TFHE.sub_int_glwe"(%0, %arg0): (i8, !TFHE.glwe<{1024,12,64}{7}>) -> (!TFHE.glwe<{1024,12,64}{6}>)
-  return %1: !TFHE.glwe<{1024,12,64}{6}>
+  // expected-error @+1 {{'TFHE.sub_int_glwe' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.sub_int_glwe"(%0, %arg0): (i8, !TFHE.glwe<sk[1]<12,1024>>) -> (!TFHE.glwe<sk[2]<12,1024>>)
+  return %1: !TFHE.glwe<sk[2]<12,1024>>
 }

 // -----

 // GLWE dimension parameter
-func.func @sub_int_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{512,12,64}{7}> {
+func.func @sub_int_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,512>> {
  %0 = arith.constant 1 : i8
-  // expected-error @+1 {{'TFHE.sub_int_glwe' op should have the same GLWE 'dimension' parameter}}
-  %1 = "TFHE.sub_int_glwe"(%0, %arg0): (i8, !TFHE.glwe<{1024,12,64}{7}>) -> (!TFHE.glwe<{512,12,64}{7}>)
-  return %1: !TFHE.glwe<{512,12,64}{7}>
+  // expected-error @+1 {{'TFHE.sub_int_glwe' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.sub_int_glwe"(%0, %arg0): (i8, !TFHE.glwe<sk[1]<12,1024>>) -> (!TFHE.glwe<sk[1]<12,512>>)
+  return %1: !TFHE.glwe<sk[1]<12,512>>
 }

 // -----

 // GLWE polynomialSize parameter
-func.func @sub_int_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,11,64}{7}> {
+func.func @sub_int_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<11,1024>> {
  %0 = arith.constant 1 : i8
-  // expected-error @+1 {{'TFHE.sub_int_glwe' op should have the same GLWE 'polynomialSize' parameter}}
-  %1 = "TFHE.sub_int_glwe"(%0, %arg0): (i8, !TFHE.glwe<{1024,12,64}{7}>) -> (!TFHE.glwe<{1024,11,64}{7}>)
-  return %1: !TFHE.glwe<{1024,11,64}{7}>
-}
-
-
-// -----
-
-// integer width doesn't match GLWE parameter
-func.func @sub_int_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,11,64}{7}> {
-  %0 = arith.constant 1 : i8
-  // expected-error @+1 {{'TFHE.sub_int_glwe' op should have the same GLWE 'polynomialSize' parameter}}
-  %1 = "TFHE.sub_int_glwe"(%0, %arg0): (i8, !TFHE.glwe<{1024,12,64}{7}>) -> (!TFHE.glwe<{1024,11,64}{7}>)
-  return %1: !TFHE.glwe<{1024,11,64}{7}>
+  // expected-error @+1 {{'TFHE.sub_int_glwe' op should have the same GLWE Secret Key}}
+  %1 = "TFHE.sub_int_glwe"(%0, %arg0): (i8, !TFHE.glwe<sk[1]<12,1024>>) -> (!TFHE.glwe<sk[1]<11,1024>>)
+  return %1: !TFHE.glwe<sk[1]<11,1024>>
 }

--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_sub_int_glwe.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/op_sub_int_glwe.mlir
@@ -1,12 +1,12 @@
 // RUN: concretecompiler --action=roundtrip %s 2>&1| FileCheck %s

-// CHECK-LABEL: func.func @sub_int_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}>
-func.func @sub_int_glwe(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}> {
+// CHECK-LABEL: func.func @sub_int_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>>
+func.func @sub_int_glwe(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>> {
  // CHECK-NEXT: %[[V1:.*]] = arith.constant 1 : i64
-  // CHECK-NEXT: %[[V2:.*]] = "TFHE.sub_int_glwe"(%[[V1]], %arg0) : (i64, !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}>
-  // CHECK-NEXT: return %[[V2]] : !TFHE.glwe<{1024,12,64}{7}>
+  // CHECK-NEXT: %[[V2:.*]] = "TFHE.sub_int_glwe"(%[[V1]], %arg0) : (i64, !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>>
+  // CHECK-NEXT: return %[[V2]] : !TFHE.glwe<sk[1]<12,1024>>

  %0 = arith.constant 1 : i64
-  %1 = "TFHE.sub_int_glwe"(%0, %arg0): (i64, !TFHE.glwe<{1024,12,64}{7}>) -> (!TFHE.glwe<{1024,12,64}{7}>)
-  return %1: !TFHE.glwe<{1024,12,64}{7}>
+  %1 = "TFHE.sub_int_glwe"(%0, %arg0): (i64, !TFHE.glwe<sk[1]<12,1024>>) -> (!TFHE.glwe<sk[1]<12,1024>>)
+  return %1: !TFHE.glwe<sk[1]<12,1024>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/ops.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/ops.mlir
@@ -1,18 +1,18 @@
 // RUN: concretecompiler --action=roundtrip %s 2>&1| FileCheck %s

-// CHECK: func.func @keyswitch_glwe(%[[A0:.*]]: !TFHE.glwe<{1,1024,64}{7}>) -> !TFHE.glwe<{1,527,64}{7}>
-func.func @keyswitch_glwe(%arg0: !TFHE.glwe<{1,1024,64}{7}>) -> !TFHE.glwe<{1,527,64}{7}> {
-  // CHECK-NEXT: %[[V0:.*]] = "TFHE.keyswitch_glwe"(%[[A0]]) {baseLog = 2 : i32, level = 3 : i32} : (!TFHE.glwe<{1,1024,64}{7}>) -> !TFHE.glwe<{1,527,64}{7}>
-  // CHECK-NEXT: return %[[V0]] : !TFHE.glwe<{1,527,64}{7}
-  %0 = "TFHE.keyswitch_glwe"(%arg0) {baseLog = 2 : i32, level = 3 : i32} : (!TFHE.glwe<{1,1024,64}{7}>) -> !TFHE.glwe<{1,527,64}{7}>
-  return %0: !TFHE.glwe<{1,527,64}{7}>
+// CHECK: func.func @keyswitch_glwe(%[[A0:.*]]: !TFHE.glwe<sk[1]<1024,1>>) -> !TFHE.glwe<sk[1]<527,1>> {
+func.func @keyswitch_glwe(%arg0: !TFHE.glwe<sk[1]<1024,1>>) -> !TFHE.glwe<sk[1]<527,1>> {
+  // CHECK-NEXT: %[[V0:.*]] = "TFHE.keyswitch_glwe"(%[[A0]]) {key = #TFHE.ksk<sk[1]<1024,1>, sk[1]<527,1>, 4, 4>} : (!TFHE.glwe<sk[1]<1024,1>>) -> !TFHE.glwe<sk[1]<527,1>>
+  // CHECK-NEXT: return %[[V0]] : !TFHE.glwe<sk[1]<527,1>>
+  %0 = "TFHE.keyswitch_glwe"(%arg0) {key=#TFHE.ksk<sk[1]<1024,1>,sk[1]<527,1>,4,4>} : (!TFHE.glwe<sk[1]<1024,1>>) -> !TFHE.glwe<sk[1]<527,1>>
+  return %0: !TFHE.glwe<sk[1]<527,1>>
 }

-// CHECK: func.func @bootstrap_glwe(%[[GLWE:.*]]: !TFHE.glwe<{1,527,64}{7}>, %[[LUT:.*]]: tensor<128xi64>) -> !TFHE.glwe<{1,1024,64}{7}>
-func.func @bootstrap_glwe(%glwe: !TFHE.glwe<{1,527,64}{7}>, %lut: tensor<128xi64>) -> !TFHE.glwe<{1,1024,64}{7}> {
-    // CHECK-NEXT: %[[V0:.*]] = "TFHE.bootstrap_glwe"(%[[GLWE]], %[[LUT]]) {baseLog = 2 : i32, glweDimension = 1 : i32, inputLweDim = 527 : i32, level = 3 : i32, polySize = 2048 : i32} : (!TFHE.glwe<{1,527,64}{7}>, tensor<128xi64>) -> !TFHE.glwe<{1,1024,64}{7}>
-    // CHECK-NEXT: return %[[V0]] : !TFHE.glwe<{1,1024,64}{7}>
-    %0 = "TFHE.bootstrap_glwe"(%glwe, %lut) {baseLog = 2 : i32, glweDimension = 1 : i32, inputLweDim = 527 : i32, level = 3 : i32, polySize = 2048 : i32} : (!TFHE.glwe<{1,527,64}{7}>, tensor<128xi64>) -> !TFHE.glwe<{1,1024,64}{7}>
-    return %0 : !TFHE.glwe<{1,1024,64}{7}>
+// CHECK: func.func @bootstrap_glwe(%[[GLWE:.*]]: !TFHE.glwe<sk[1]<527,1>>, %[[LUT:.*]]: tensor<128xi64>) -> !TFHE.glwe<sk[1]<1024,1>> {
+func.func @bootstrap_glwe(%glwe: !TFHE.glwe<sk[1]<527,1>>, %lut: tensor<128xi64>) -> !TFHE.glwe<sk[1]<1024,1>> {
+    // CHECK-NEXT: %[[V0:.*]] = "TFHE.bootstrap_glwe"(%[[GLWE]], %[[LUT]]) {key = #TFHE.bsk<sk[1]<527,1>, sk[1]<1024,1>, 512, 2, 4, 4>} : (!TFHE.glwe<sk[1]<527,1>>, tensor<128xi64>) -> !TFHE.glwe<sk[1]<1024,1>>
+    // CHECK-NEXT: return %[[V0]] : !TFHE.glwe<sk[1]<1024,1>>
+    %0 = "TFHE.bootstrap_glwe"(%glwe, %lut) {key=#TFHE.bsk<sk[1]<527,1>,sk[1]<1024,1>,512,2,4,4>} : (!TFHE.glwe<sk[1]<527,1>>, tensor<128xi64>) -> !TFHE.glwe<sk[1]<1024,1>>
+    return %0 : !TFHE.glwe<sk[1]<1024,1>>
 }

--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/optimization.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/optimization.mlir
@@ -1,31 +1,31 @@
 // RUN: concretecompiler --passes tfhe-optimization --action=dump-tfhe %s 2>&1| FileCheck %s


-// CHECK-LABEL: func.func @mul_cleartext_lwe_ciphertext(%arg0: !TFHE.glwe<{1,527,64}{7}>, %arg1: i64) -> !TFHE.glwe<{1,527,64}{7}>
-func.func @mul_cleartext_lwe_ciphertext(%arg0: !TFHE.glwe<{1,527,64}{7}>, %arg1: i64) -> !TFHE.glwe<{1,527,64}{7}> {
-  // CHECK-NEXT: %[[V1:.*]] = "TFHE.mul_glwe_int"(%arg0, %arg1) : (!TFHE.glwe<{1,527,64}{7}>, i64) -> !TFHE.glwe<{1,527,64}{7}>
-  // CHECK-NEXT: return %[[V1]] : !TFHE.glwe<{1,527,64}{7}>
+// CHECK-LABEL: func.func @mul_cleartext_lwe_ciphertext(%arg0: !TFHE.glwe<sk[1]<527,1>>, %arg1: i64) -> !TFHE.glwe<sk[1]<527,1>>
+func.func @mul_cleartext_lwe_ciphertext(%arg0: !TFHE.glwe<sk[1]<527,1>>, %arg1: i64) -> !TFHE.glwe<sk[1]<527,1>> {
+  // CHECK-NEXT: %[[V1:.*]] = "TFHE.mul_glwe_int"(%arg0, %arg1) : (!TFHE.glwe<sk[1]<527,1>>, i64) -> !TFHE.glwe<sk[1]<527,1>>
+  // CHECK-NEXT: return %[[V1]] : !TFHE.glwe<sk[1]<527,1>>

-  %1 = "TFHE.mul_glwe_int"(%arg0, %arg1): (!TFHE.glwe<{1,527,64}{7}>, i64) -> (!TFHE.glwe<{1,527,64}{7}>)
-  return %1: !TFHE.glwe<{1,527,64}{7}>
+  %1 = "TFHE.mul_glwe_int"(%arg0, %arg1): (!TFHE.glwe<sk[1]<527,1>>, i64) -> (!TFHE.glwe<sk[1]<527,1>>)
+  return %1: !TFHE.glwe<sk[1]<527,1>>
 }

-// CHECK-LABEL: func.func @mul_cleartext_lwe_ciphertext_0(%arg0: !TFHE.glwe<{1,527,64}{7}>) -> !TFHE.glwe<{1,527,64}{7}>
-func.func @mul_cleartext_lwe_ciphertext_0(%arg0: !TFHE.glwe<{1,527,64}{7}>) -> !TFHE.glwe<{1,527,64}{7}> {
-  // CHECK-NEXT: %[[V1:.*]] = "TFHE.zero"() : () -> !TFHE.glwe<{1,527,64}{7}>
-  // CHECK-NEXT: return %[[V1]] : !TFHE.glwe<{1,527,64}{7}>
+// CHECK-LABEL: func.func @mul_cleartext_lwe_ciphertext_0(%arg0: !TFHE.glwe<sk[1]<527,1>>) -> !TFHE.glwe<sk[1]<527,1>>
+func.func @mul_cleartext_lwe_ciphertext_0(%arg0: !TFHE.glwe<sk[1]<527,1>>) -> !TFHE.glwe<sk[1]<527,1>> {
+  // CHECK-NEXT: %[[V1:.*]] = "TFHE.zero"() : () -> !TFHE.glwe<sk[1]<527,1>>
+  // CHECK-NEXT: return %[[V1]] : !TFHE.glwe<sk[1]<527,1>>

  %0 = arith.constant 0 : i64
-  %2 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<{1,527,64}{7}>, i64) -> (!TFHE.glwe<{1,527,64}{7}>)
-  return %2: !TFHE.glwe<{1,527,64}{7}>
+  %2 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<sk[1]<527,1>>, i64) -> (!TFHE.glwe<sk[1]<527,1>>)
+  return %2: !TFHE.glwe<sk[1]<527,1>>
 }

-// CHECK-LABEL: func.func @mul_cleartext_lwe_ciphertext_minus_1(%arg0: !TFHE.glwe<{1,527,64}{7}>) -> !TFHE.glwe<{1,527,64}{7}>
-func.func @mul_cleartext_lwe_ciphertext_minus_1(%arg0: !TFHE.glwe<{1,527,64}{7}>) -> !TFHE.glwe<{1,527,64}{7}> {
-  // CHECK-NEXT: %[[V1:.*]] = "TFHE.neg_glwe"(%arg0) : (!TFHE.glwe<{1,527,64}{7}>) -> !TFHE.glwe<{1,527,64}{7}>
-  // CHECK-NEXT: return %[[V1]] : !TFHE.glwe<{1,527,64}{7}>
+// CHECK-LABEL: func.func @mul_cleartext_lwe_ciphertext_minus_1(%arg0: !TFHE.glwe<sk[1]<527,1>>) -> !TFHE.glwe<sk[1]<527,1>>
+func.func @mul_cleartext_lwe_ciphertext_minus_1(%arg0: !TFHE.glwe<sk[1]<527,1>>) -> !TFHE.glwe<sk[1]<527,1>> {
+  // CHECK-NEXT: %[[V1:.*]] = "TFHE.neg_glwe"(%arg0) : (!TFHE.glwe<sk[1]<527,1>>) -> !TFHE.glwe<sk[1]<527,1>>
+  // CHECK-NEXT: return %[[V1]] : !TFHE.glwe<sk[1]<527,1>>

  %0 = arith.constant -1 : i64
-  %2 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<{1,527,64}{7}>, i64) -> (!TFHE.glwe<{1,527,64}{7}>)
-  return %2: !TFHE.glwe<{1,527,64}{7}>
+  %2 = "TFHE.mul_glwe_int"(%arg0, %0): (!TFHE.glwe<sk[1]<527,1>>, i64) -> (!TFHE.glwe<sk[1]<527,1>>)
+  return %2: !TFHE.glwe<sk[1]<527,1>>
 }
--- a/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/types_glwe.mlir
+++ b/compilers/concrete-compiler/compiler/tests/check_tests/Dialect/TFHE/types_glwe.mlir
@@ -1,13 +1,15 @@
 // RUN: concretecompiler %s --action=roundtrip 2>&1| FileCheck %s

-// CHECK-LABEL: func.func @glwe_0(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}>
-func.func @glwe_0(%arg0: !TFHE.glwe<{1024,12,64}{7}>) -> !TFHE.glwe<{1024,12,64}{7}> {
-  // CHECK-LABEL: return %arg0 : !TFHE.glwe<{1024,12,64}{7}>
-  return %arg0: !TFHE.glwe<{1024,12,64}{7}>
+// CHECK-LABEL: func.func @glwe_0(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>>
+func.func @glwe_0(%arg0: !TFHE.glwe<sk[1]<12,1024>>) -> !TFHE.glwe<sk[1]<12,1024>> {
+  // CHECK-LABEL: return %arg0 : !TFHE.glwe<sk[1]<12,1024>>
+  return %arg0: !TFHE.glwe<sk[1]<12,1024>>
 }

-// CHECK-LABEL: func.func @glwe_1(%arg0: !TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}>
-func.func @glwe_1(%arg0: !TFHE.glwe<{_,_,_}{7}>) -> !TFHE.glwe<{_,_,_}{7}> {
-  // CHECK-LABEL: return %arg0 : !TFHE.glwe<{_,_,_}{7}>
-  return %arg0: !TFHE.glwe<{_,_,_}{7}>
+// -----
+
+// CHECK-LABEL: func.func @glwe_1(%arg0: !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]>
+func.func @glwe_1(%arg0: !TFHE.glwe<sk[?]>) -> !TFHE.glwe<sk[?]> {
+  // CHECK-LABEL: return %arg0 : !TFHE.glwe<sk[?]>
+  return %arg0: !TFHE.glwe<sk[?]>
 }