diff --git a/compilers/concrete-optimizer/concrete-optimizer-cpp/src/concrete-optimizer.rs b/compilers/concrete-optimizer/concrete-optimizer-cpp/src/concrete-optimizer.rs
index 480d86772..00a997055 100644
--- a/compilers/concrete-optimizer/concrete-optimizer-cpp/src/concrete-optimizer.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer-cpp/src/concrete-optimizer.rs
@@ -6,7 +6,8 @@ use concrete_optimizer::dag::operator::{
 };
 use concrete_optimizer::dag::unparametrized;
 use concrete_optimizer::optimization::config::{Config, SearchSpace};
-use concrete_optimizer::optimization::dag::multi_parameters::keys_spec;
+use concrete_optimizer::optimization::dag::multi_parameters::keys_spec::{self, CircuitSolution};
+use concrete_optimizer::optimization::dag::multi_parameters::optimize::optimize_to_circuit_solution;
 use concrete_optimizer::optimization::dag::solo_key::optimize_generic::{
     Encoding, Solution as DagSolution,
 };
@@ -164,60 +165,81 @@ impl From<DagSolution> for ffi::DagSolution {
     }
 }
 
-impl ffi::CircuitSolution {
-    fn of(sol: ffi::DagSolution, dag: &OperationDag) -> Self {
-        let big_key = ffi::SecretLweKey {
-            identifier: 0,
-            polynomial_size: sol.glwe_polynomial_size,
-            glwe_dimension: sol.glwe_dimension,
-            description: "big representation".into(),
-        };
-        let small_key = ffi::SecretLweKey {
-            identifier: 1,
-            polynomial_size: sol.internal_ks_output_lwe_dimension,
-            glwe_dimension: 1,
-            description: "small representation".into(),
-        };
-        let keyswitch_key = ffi::KeySwitchKey {
-            identifier: 0,
-            input_key: big_key.clone(),
-            output_key: small_key.clone(),
-            ks_decomposition_parameter: ffi::KsDecompositionParameters {
-                level: sol.ks_decomposition_level_count,
-                log2_base: sol.ks_decomposition_base_log,
-            },
-            description: "tlu keyswitch".into(),
-        };
-        let bootstrap_key = ffi::BootstrapKey {
-            identifier: 0,
-            input_key: small_key.clone(),
-            output_key: big_key.clone(),
-            br_decomposition_parameter: ffi::BrDecompositionParameters {
-                level: sol.br_decomposition_level_count,
-                log2_base: sol.br_decomposition_base_log,
-            },
-            description: "tlu bootsrap".into(),
-        };
-        let instruction_keys = ffi::InstructionKeys {
-            input_key: big_key.identifier,
-            tlu_keyswitch_key: keyswitch_key.identifier,
-            tlu_bootstrap_key: bootstrap_key.identifier,
-            output_key: big_key.identifier,
-            extra_conversion_keys: vec![],
-        };
-        let instructions_keys = vec![instruction_keys; dag.0.len()];
-        let circuit_keys = ffi::CircuitKeys {
-            secret_keys: [big_key, small_key].into(),
-            keyswitch_keys: [keyswitch_key].into(),
-            bootstrap_keys: [bootstrap_key].into(),
-            conversion_keyswitch_keys: [].into(),
-        };
-        ffi::CircuitSolution {
-            circuit_keys,
-            instructions_keys,
-            complexity: sol.complexity,
-            p_error: sol.p_error,
-            global_p_error: sol.global_p_error,
+fn convert_to_circuit_solution(sol: &ffi::DagSolution, dag: &OperationDag) -> ffi::CircuitSolution {
+    let big_key = ffi::SecretLweKey {
+        identifier: 0,
+        polynomial_size: sol.glwe_polynomial_size,
+        glwe_dimension: sol.glwe_dimension,
+        description: "big representation".into(),
+    };
+    let small_key = ffi::SecretLweKey {
+        identifier: 1,
+        polynomial_size: sol.internal_ks_output_lwe_dimension,
+        glwe_dimension: 1,
+        description: "small representation".into(),
+    };
+    let keyswitch_key = ffi::KeySwitchKey {
+        identifier: 0,
+        input_key: big_key.clone(),
+        output_key: small_key.clone(),
+        ks_decomposition_parameter: ffi::KsDecompositionParameters {
+            level: sol.ks_decomposition_level_count,
+            log2_base: sol.ks_decomposition_base_log,
+        },
+        description: "tlu keyswitch".into(),
+    };
+    let bootstrap_key = ffi::BootstrapKey {
+        identifier: 0,
+        input_key: small_key.clone(),
+        output_key: big_key.clone(),
+        br_decomposition_parameter: ffi::BrDecompositionParameters {
+            level: sol.br_decomposition_level_count,
+            log2_base: sol.br_decomposition_base_log,
+        },
+        description: "tlu bootstrap".into(),
+    };
+    let instruction_keys = ffi::InstructionKeys {
+        input_key: big_key.identifier,
+        tlu_keyswitch_key: keyswitch_key.identifier,
+        tlu_bootstrap_key: bootstrap_key.identifier,
+        output_key: big_key.identifier,
+        extra_conversion_keys: vec![],
+    };
+    let instructions_keys = vec![instruction_keys; dag.0.len()];
+    let circuit_keys = ffi::CircuitKeys {
+        secret_keys: [big_key, small_key].into(),
+        keyswitch_keys: [keyswitch_key].into(),
+        bootstrap_keys: [bootstrap_key].into(),
+        conversion_keyswitch_keys: [].into(),
+    };
+    let is_feasible = sol.p_error < 1.0;
+    let error_msg = if is_feasible {
+        ""
+    } else {
+        "No crypto-parameters for the given constraints"
+    }
+    .into();
+    ffi::CircuitSolution {
+        circuit_keys,
+        instructions_keys,
+        complexity: sol.complexity,
+        p_error: sol.p_error,
+        global_p_error: sol.global_p_error,
+        is_feasible,
+        error_msg,
+    }
+}
+
+impl From<CircuitSolution> for ffi::CircuitSolution {
+    fn from(v: CircuitSolution) -> Self {
+        Self {
+            circuit_keys: v.circuit_keys.into(),
+            instructions_keys: vec_into(v.instructions_keys),
+            complexity: v.complexity,
+            p_error: v.p_error,
+            global_p_error: v.global_p_error,
+            is_feasible: v.is_feasible,
+            error_msg: v.error_msg,
         }
     }
 }
@@ -230,7 +252,7 @@ impl ffi::CircuitSolution {
 
 impl From<KsDecompositionParameters> for ffi::KsDecompositionParameters {
     fn from(v: KsDecompositionParameters) -> Self {
-        ffi::KsDecompositionParameters {
+        Self {
             level: v.level,
             log2_base: v.log2_base,
         }
@@ -239,7 +261,7 @@ impl From<KsDecompositionParameters> for ffi::KsDecompositionParameters {
 
 impl From<BrDecompositionParameters> for ffi::BrDecompositionParameters {
     fn from(v: BrDecompositionParameters) -> Self {
-        ffi::BrDecompositionParameters {
+        Self {
             level: v.level,
             log2_base: v.log2_base,
         }
@@ -294,6 +316,18 @@ impl From<keys_spec::BootstrapKey> for ffi::BootstrapKey {
     }
 }
 
+impl From<keys_spec::InstructionKeys> for ffi::InstructionKeys {
+    fn from(v: keys_spec::InstructionKeys) -> Self {
+        Self {
+            input_key: v.input_key,
+            tlu_keyswitch_key: v.tlu_keyswitch_key,
+            tlu_bootstrap_key: v.tlu_bootstrap_key,
+            output_key: v.output_key,
+            extra_conversion_keys: v.extra_conversion_keys,
+        }
+    }
+}
+
 fn vec_into<F, T: std::convert::From<F>>(vec: Vec<F>) -> Vec<T> {
     vec.into_iter().map(|x| x.into()).collect()
 }
@@ -432,8 +466,22 @@ impl OperationDag {
     }
 
     fn optimize_multi(&self, options: ffi::Options) -> ffi::CircuitSolution {
-        let single_parameter = self.optimize(options);
-        ffi::CircuitSolution::of(single_parameter, self)
+        let processing_unit = processing_unit(options);
+        let config = Config {
+            security_level: options.security_level,
+            maximum_acceptable_error_probability: options.maximum_acceptable_error_probability,
+            ciphertext_modulus_log: 64,
+            complexity_model: &CpuComplexity::default(),
+        };
+        let search_space = SearchSpace::default(processing_unit);
+        let circuit_sol = optimize_to_circuit_solution(
+            &self.0,
+            config,
+            &search_space,
+            &caches_from(options),
+            &None,
+        );
+        circuit_sol.into()
     }
 }
 
@@ -480,6 +528,12 @@ mod ffi {
         #[namespace = "concrete_optimizer::utils"]
         fn convert_to_dag_solution(solution: &Solution) -> DagSolution;
 
+        #[namespace = "concrete_optimizer::utils"]
+        fn convert_to_circuit_solution(
+            solution: &DagSolution,
+            dag: &OperationDag,
+        ) -> CircuitSolution;
+
         type OperationDag;
 
         #[namespace = "concrete_optimizer::dag"]
@@ -685,6 +739,8 @@ mod ffi {
         pub complexity: f64,
         pub p_error: f64,
         pub global_p_error: f64,
+        pub is_feasible: bool,
+        pub error_msg: String,
     }
 }
 
diff --git a/compilers/concrete-optimizer/concrete-optimizer-cpp/src/cpp/concrete-optimizer.cpp b/compilers/concrete-optimizer/concrete-optimizer-cpp/src/cpp/concrete-optimizer.cpp
index 58b24b90f..24c69c22f 100644
--- a/compilers/concrete-optimizer/concrete-optimizer-cpp/src/cpp/concrete-optimizer.cpp
+++ b/compilers/concrete-optimizer/concrete-optimizer-cpp/src/cpp/concrete-optimizer.cpp
@@ -1188,6 +1188,8 @@ struct CircuitSolution final {
   double complexity;
   double p_error;
   double global_p_error;
+  bool is_feasible;
+  ::rust::String error_msg;
 
   ::rust::String dump() const noexcept;
   using IsRelocatable = ::std::true_type;
@@ -1204,6 +1206,8 @@ extern "C" {
 namespace utils {
 extern "C" {
 void concrete_optimizer$utils$cxxbridge1$convert_to_dag_solution(::concrete_optimizer::v0::Solution const &solution, ::concrete_optimizer::dag::DagSolution *return$) noexcept;
+
+void concrete_optimizer$utils$cxxbridge1$convert_to_circuit_solution(::concrete_optimizer::dag::DagSolution const &solution, ::concrete_optimizer::OperationDag const &dag, ::concrete_optimizer::dag::CircuitSolution *return$) noexcept;
 } // extern "C"
 } // namespace utils
 
@@ -1269,6 +1273,12 @@ namespace utils {
   concrete_optimizer$utils$cxxbridge1$convert_to_dag_solution(solution, &return$.value);
   return ::std::move(return$.value);
 }
+
+::concrete_optimizer::dag::CircuitSolution convert_to_circuit_solution(::concrete_optimizer::dag::DagSolution const &solution, ::concrete_optimizer::OperationDag const &dag) noexcept {
+  ::rust::MaybeUninit<::concrete_optimizer::dag::CircuitSolution> return$;
+  concrete_optimizer$utils$cxxbridge1$convert_to_circuit_solution(solution, dag, &return$.value);
+  return ::std::move(return$.value);
+}
 } // namespace utils
 
 ::std::size_t OperationDag::layout::size() noexcept {
diff --git a/compilers/concrete-optimizer/concrete-optimizer-cpp/src/cpp/concrete-optimizer.hpp b/compilers/concrete-optimizer/concrete-optimizer-cpp/src/cpp/concrete-optimizer.hpp
index 791d7750b..ddc053baa 100644
--- a/compilers/concrete-optimizer/concrete-optimizer-cpp/src/cpp/concrete-optimizer.hpp
+++ b/compilers/concrete-optimizer/concrete-optimizer-cpp/src/cpp/concrete-optimizer.hpp
@@ -1169,6 +1169,8 @@ struct CircuitSolution final {
   double complexity;
   double p_error;
   double global_p_error;
+  bool is_feasible;
+  ::rust::String error_msg;
 
   ::rust::String dump() const noexcept;
   using IsRelocatable = ::std::true_type;
@@ -1182,6 +1184,8 @@ namespace v0 {
 
 namespace utils {
 ::concrete_optimizer::dag::DagSolution convert_to_dag_solution(::concrete_optimizer::v0::Solution const &solution) noexcept;
+
+::concrete_optimizer::dag::CircuitSolution convert_to_circuit_solution(::concrete_optimizer::dag::DagSolution const &solution, ::concrete_optimizer::OperationDag const &dag) noexcept;
 } // namespace utils
 
 namespace dag {
diff --git a/compilers/concrete-optimizer/concrete-optimizer-cpp/tests/src/main.cpp b/compilers/concrete-optimizer/concrete-optimizer-cpp/tests/src/main.cpp
index eab317262..bffc73fba 100644
--- a/compilers/concrete-optimizer/concrete-optimizer-cpp/tests/src/main.cpp
+++ b/compilers/concrete-optimizer/concrete-optimizer-cpp/tests/src/main.cpp
@@ -109,7 +109,7 @@ void test_dag_lut_force_wop() {
   assert(!solution.crt_decomposition.empty());
 }
 
-void test_multi_parameters() {
+void test_multi_parameters_1_precision() {
   auto dag = concrete_optimizer::dag::empty();
 
   std::vector<uint64_t> shape = {3};
@@ -122,8 +122,53 @@ void test_multi_parameters() {
 
   auto options = default_options();
   auto circuit_solution = dag->optimize_multi(options);
-  auto secret_keys = circuit_solution.circuit_keys.keyswitch_keys;
-  assert(!secret_keys.empty());
+  assert(circuit_solution.is_feasible);
+  auto secret_keys = circuit_solution.circuit_keys.secret_keys;
+  assert(circuit_solution.circuit_keys.secret_keys.size() == 2);
+  assert(circuit_solution.circuit_keys.secret_keys[0].identifier == 0);
+  assert(circuit_solution.circuit_keys.secret_keys[1].identifier == 1);
+  assert(circuit_solution.circuit_keys.bootstrap_keys.size() == 1);
+  assert(circuit_solution.circuit_keys.keyswitch_keys.size() == 1);
+  assert(circuit_solution.circuit_keys.keyswitch_keys[0].identifier == 0);
+  assert(circuit_solution.circuit_keys.keyswitch_keys[0].identifier == 0);
+  assert(circuit_solution.circuit_keys.conversion_keyswitch_keys.size() == 0);
+}
+
+void test_multi_parameters_2_precision() {
+  auto dag = concrete_optimizer::dag::empty();
+
+  std::vector<uint64_t> shape = {3};
+
+  concrete_optimizer::dag::OperatorIndex input1 =
+      dag->add_input(PRECISION_8B, slice(shape));
+
+  concrete_optimizer::dag::OperatorIndex input2 =
+      dag->add_input(PRECISION_1B, slice(shape));
+
+
+  std::vector<u_int64_t> table = {};
+  auto lut1 = dag->add_lut(input1, slice(table), PRECISION_8B);
+  auto lut2 = dag->add_lut(input2, slice(table), PRECISION_8B);
+
+  std::vector<concrete_optimizer::dag::OperatorIndex> inputs = {lut1, lut2};
+
+  std::vector<int64_t> weight_vec = {1, 1};
+
+  rust::cxxbridge1::Box<concrete_optimizer::Weights> weights =
+      concrete_optimizer::weights::vector(slice(weight_vec));
+
+  dag->add_dot(slice(inputs), std::move(weights));
+
+  auto options = default_options();
+  auto circuit_solution = dag->optimize_multi(options);
+  assert(circuit_solution.is_feasible);
+  auto secret_keys = circuit_solution.circuit_keys.secret_keys;
+  assert(circuit_solution.circuit_keys.secret_keys.size() == 4);
+  assert(circuit_solution.circuit_keys.bootstrap_keys.size() == 2);
+  assert(circuit_solution.circuit_keys.keyswitch_keys.size() == 2); // 1 layer so less ks
+  std::string actual = circuit_solution.circuit_keys.conversion_keyswitch_keys[0].description.c_str();
+  std::string expected = "fks[1->0]";
+  assert(actual == expected);
 }
 
 int main() {
@@ -132,7 +177,8 @@ int main() {
   test_dag_lut();
   test_dag_lut_wop();
   test_dag_lut_force_wop();
-  test_multi_parameters();
+  test_multi_parameters_1_precision();
+  test_multi_parameters_2_precision();
 
   return 0;
 }
diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/regen.rs b/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/regen.rs
index 771903d54..d4a295216 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/regen.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/regen.rs
@@ -21,7 +21,7 @@ fn reindex_op_inputs(op: &Operator, old_index_to_new: &[usize]) -> Operator {
 pub(crate) fn regen(
     dag: &OperationDag,
     f: &mut dyn FnMut(usize, &Operator, &mut OperationDag) -> Option<OperatorIndex>,
-) -> OperationDag {
+) -> (OperationDag, Vec<Vec<OperatorIndex>>) {
     let mut regen_dag = OperationDag::new();
     let mut old_index_to_new = vec![];
     for (i, op) in dag.operators.iter().enumerate() {
@@ -37,5 +37,25 @@ pub(crate) fn regen(
             regen_dag.out_shapes.push(dag.out_shapes[i].clone());
         }
     }
-    regen_dag
+    (regen_dag, instructions_multi_map(&old_index_to_new))
+}
+
+fn instructions_multi_map(old_index_to_new: &[usize]) -> Vec<Vec<OperatorIndex>> {
+    let mut last_new_instr = None;
+    let mut result = vec![];
+    result.reserve_exact(old_index_to_new.len());
+    for &new_instr in old_index_to_new {
+        let start_from = last_new_instr.map_or(new_instr, |v: usize| v + 1);
+        if start_from <= new_instr {
+            result.push(
+                (start_from..=new_instr)
+                    .map(|i| OperatorIndex { i })
+                    .collect(),
+            );
+        } else {
+            result.push(vec![]);
+        }
+        last_new_instr = Some(new_instr);
+    }
+    result
 }
diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/round.rs b/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/round.rs
index ffbd73f38..04487ecef 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/round.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/round.rs
@@ -14,5 +14,11 @@ fn regen_round(_: usize, op: &Operator, dag: &mut OperationDag) -> Option<Operat
 }
 
 pub(crate) fn expand_round(dag: &OperationDag) -> OperationDag {
+    regen(dag, &mut regen_round).0
+}
+
+pub(crate) fn expand_round_and_index_map(
+    dag: &OperationDag,
+) -> (OperationDag, Vec<Vec<OperatorIndex>>) {
     regen(dag, &mut regen_round)
 }
diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/analyze.rs b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/analyze.rs
index f45933064..5567d3f1e 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/analyze.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/analyze.rs
@@ -3,7 +3,7 @@ use std::collections::HashSet;
 use crate::dag::operator::{
     dot_kind, DotKind, LevelledComplexity, Operator, OperatorIndex, Precision, Shape,
 };
-use crate::dag::rewrite::round::expand_round;
+use crate::dag::rewrite::round::expand_round_and_index_map;
 use crate::dag::unparametrized;
 use crate::optimization::config::NoiseBoundConfig;
 use crate::optimization::dag::multi_parameters::partitionning::partitionning_with_preferred;
@@ -17,6 +17,7 @@ use crate::optimization::dag::solo_key::analyze::{
 };
 
 use super::complexity::OperationsCount;
+use super::keys_spec;
 use super::operations_value::OperationsValue;
 use super::variance_constraint::VarianceConstraint;
 
@@ -41,6 +42,7 @@ pub struct AnalyzedDag {
     pub undominated_variance_constraints: Vec<VarianceConstraint>,
     pub operations_count_per_instrs: Vec<OperationsCount>,
     pub operations_count: OperationsCount,
+    pub instruction_rewrite_index: Vec<Vec<OperatorIndex>>,
     pub p_cut: PrecisionCut,
 }
 
@@ -50,7 +52,7 @@ pub fn analyze(
     p_cut: &Option<PrecisionCut>,
     default_partition: PartitionIndex,
 ) -> AnalyzedDag {
-    let dag = expand_round(dag);
+    let (dag, instruction_rewrite_index) = expand_round_and_index_map(dag);
     let levelled_complexity = LevelledComplexity::ZERO;
     // The precision cut is chosen to work well with rounded pbs
     // Note: this is temporary
@@ -72,6 +74,7 @@ pub fn analyze(
     let operations_count = sum_operations_count(&operations_count_per_instrs);
     AnalyzedDag {
         operators: dag.operators,
+        instruction_rewrite_index,
         nb_partitions,
         instrs_partition,
         out_variances,
@@ -84,6 +87,77 @@ pub fn analyze(
     }
 }
 
+pub fn original_instrs_partition(
+    dag: &AnalyzedDag,
+    keys: &keys_spec::ExpandedCircuitKeys,
+) -> Vec<keys_spec::InstructionKeys> {
+    let big_keys = &keys.big_secret_keys;
+    let ks_keys = &keys.keyswitch_keys;
+    let pbs_keys = &keys.bootstrap_keys;
+    let fks_keys = &keys.conversion_keyswitch_keys;
+    let mut result = vec![];
+    result.reserve_exact(dag.instruction_rewrite_index.len());
+    let unknown = keys_spec::Id::MAX;
+    for new_instructions in &dag.instruction_rewrite_index {
+        let mut partition = None;
+        let mut input_partition = None;
+        let mut tlu_keyswitch_key = None;
+        let mut tlu_bootstrap_key = None;
+        let mut conversion_key = None;
+        // let mut extra_conversion_keys = None;
+        for (i, new_instruction) in new_instructions.iter().enumerate() {
+            // focus on TLU information
+            let new_instr_part = &dag.instrs_partition[new_instruction.i];
+            if let Op::Lut { .. } = dag.operators[new_instruction.i] {
+                let ks_dst = new_instr_part.instruction_partition;
+                partition = Some(ks_dst);
+                #[allow(clippy::match_on_vec_items)]
+                let ks_src = match new_instr_part.inputs_transition[0] {
+                    Some(Transition::Internal { src_partition }) => src_partition,
+                    None => ks_dst,
+                    _ => unreachable!(),
+                };
+                input_partition = Some(ks_src);
+                let ks_key = ks_keys[ks_src][ks_dst].as_ref().unwrap().identifier;
+                let pbs_key = pbs_keys[ks_dst].identifier;
+                assert!(tlu_keyswitch_key.unwrap_or(ks_key) == ks_key);
+                assert!(tlu_bootstrap_key.unwrap_or(pbs_key) == pbs_key);
+                tlu_keyswitch_key = Some(ks_key);
+                tlu_bootstrap_key = Some(pbs_key);
+            }
+            if !new_instr_part.alternative_output_representation.is_empty() {
+                assert!(new_instr_part.alternative_output_representation.len() == 1);
+                let src = new_instr_part.instruction_partition;
+                let dst = *new_instr_part
+                    .alternative_output_representation
+                    .iter()
+                    .next()
+                    .unwrap();
+                let key = fks_keys[src][dst].as_ref().unwrap().identifier;
+                assert!(conversion_key.unwrap_or(key) == key);
+                conversion_key = Some(key);
+            }
+            // Only last instruction can have alternative conversion
+            assert!(
+                new_instr_part.alternative_output_representation.is_empty()
+                    || i == new_instructions.len() - 1
+            );
+        }
+        let partition =
+            partition.unwrap_or(dag.instrs_partition[new_instructions[0].i].instruction_partition);
+        let input_partition = input_partition.unwrap_or(partition);
+        let merged = keys_spec::InstructionKeys {
+            input_key: big_keys[input_partition].identifier,
+            tlu_keyswitch_key: tlu_keyswitch_key.unwrap_or(unknown),
+            tlu_bootstrap_key: tlu_bootstrap_key.unwrap_or(unknown),
+            output_key: big_keys[partition].identifier,
+            extra_conversion_keys: conversion_key.iter().copied().collect(),
+        };
+        result.push(merged);
+    }
+    result
+}
+
 fn out_variance(
     op: &unparametrized::UnparameterizedOperator,
     out_shapes: &[Shape],
diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/keys_spec.rs b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/keys_spec.rs
index 430240655..ea22e068e 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/keys_spec.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/keys_spec.rs
@@ -1,11 +1,13 @@
 use crate::parameters::{BrDecompositionParameters, KsDecompositionParameters};
 
-type Id = u64;
+use crate::optimization::dag::multi_parameters::optimize::MacroParameters;
+
+pub type Id = u64;
 /* An Id is unique per key type. Starting from 0 for the first key ... */
-type SecretLweKeyId = Id;
-type BootstrapKeyId = Id;
-type KeySwitchKeyId = Id;
-type ConversionKeySwitchKeyId = Id;
+pub type SecretLweKeyId = Id;
+pub type BootstrapKeyId = Id;
+pub type KeySwitchKeyId = Id;
+pub type ConversionKeySwitchKeyId = Id;
 
 #[derive(Debug, Clone)]
 pub struct SecretLweKey {
@@ -38,7 +40,7 @@ pub struct KeySwitchKey {
 
 #[derive(Debug, Clone)]
 pub struct ConversionKeySwitchKey {
-    /* Public conversion to make cyphertext with incompatible keys compatible.
+    /* Public conversion to make compatible ciphertext with incompatible keys.
     It's currently only between two big secret keys. */
     pub identifier: ConversionKeySwitchKeyId,
     pub input_key: SecretLweKey,
@@ -48,7 +50,7 @@ pub struct ConversionKeySwitchKey {
     pub description: String,
 }
 
-#[derive(Debug, Clone)]
+#[derive(Debug, Default, Clone)]
 pub struct CircuitKeys {
     /* All keys used in a circuit, sorted by Id for each key type */
     pub secret_keys: Vec<SecretLweKey>,
@@ -86,4 +88,129 @@ pub struct CircuitSolution {
     pub p_error: f64,
     /* result error rate, assuming any error will propagate to the result */
     pub global_p_error: f64,
+    pub is_feasible: bool,
+    pub error_msg: String,
+}
+
+pub struct ExpandedCircuitKeys {
+    pub big_secret_keys: Vec<SecretLweKey>,
+    pub small_secret_keys: Vec<SecretLweKey>,
+    pub keyswitch_keys: Vec<Vec<Option<KeySwitchKey>>>,
+    pub bootstrap_keys: Vec<BootstrapKey>,
+    pub conversion_keyswitch_keys: Vec<Vec<Option<ConversionKeySwitchKey>>>,
+}
+
+impl ExpandedCircuitKeys {
+    pub fn of(params: &super::optimize::Parameters) -> Self {
+        let nb_partitions = params.macro_params.len();
+        let big_secret_keys: Vec<_> = params
+            .macro_params
+            .iter()
+            .enumerate()
+            .map(|(i, v): (usize, &Option<MacroParameters>)| {
+                let glwe_params = v.unwrap().glwe_params;
+                SecretLweKey {
+                    identifier: i as Id,
+                    polynomial_size: glwe_params.polynomial_size(),
+                    glwe_dimension: glwe_params.glwe_dimension,
+                    description: format!("big-secret[{i}]"),
+                }
+            })
+            .collect();
+        let small_secret_keys: Vec<_> = params
+            .macro_params
+            .iter()
+            .enumerate()
+            .map(|(i, v): (usize, &Option<MacroParameters>)| {
+                let polynomial_size = v.unwrap().internal_dim;
+                SecretLweKey {
+                    identifier: (nb_partitions + i) as Id,
+                    polynomial_size,
+                    glwe_dimension: 1,
+                    description: format!("small-secret[{i}]"),
+                }
+            })
+            .collect();
+        let bootstrap_keys: Vec<_> = params
+            .micro_params
+            .pbs
+            .iter()
+            .enumerate()
+            .map(|(i, v): (usize, &Option<_>)| {
+                let br_decomposition_parameter = v.unwrap().decomp;
+                BootstrapKey {
+                    identifier: i as Id,
+                    input_key: small_secret_keys[i].clone(),
+                    output_key: big_secret_keys[i].clone(),
+                    br_decomposition_parameter,
+                    description: format!("pbs[{i}]"),
+                }
+            })
+            .collect();
+        let mut keyswitch_keys = vec![vec![None; nb_partitions]; nb_partitions];
+        let mut conversion_keyswitch_keys = vec![vec![None; nb_partitions]; nb_partitions];
+        let mut identifier_ks = 0 as Id;
+        let mut identifier_fks = 0 as Id;
+        #[allow(clippy::needless_range_loop)]
+        for src in 0..nb_partitions {
+            for dst in 0..nb_partitions {
+                let cross_key = |name: &str| {
+                    if src == dst {
+                        format!("{name}[{src}]")
+                    } else {
+                        format!("{name}[{src}->{dst}]")
+                    }
+                };
+                if let Some(ks) = params.micro_params.ks[src][dst] {
+                    let identifier = identifier_ks;
+                    keyswitch_keys[src][dst] = Some(KeySwitchKey {
+                        identifier,
+                        input_key: big_secret_keys[src].clone(),
+                        output_key: small_secret_keys[dst].clone(),
+                        ks_decomposition_parameter: ks.decomp,
+                        description: cross_key("ks"),
+                    });
+                    identifier_ks += 1;
+                }
+                if let Some(fks) = params.micro_params.fks[src][dst] {
+                    let identifier = identifier_fks;
+                    conversion_keyswitch_keys[src][dst] = Some(ConversionKeySwitchKey {
+                        identifier,
+                        input_key: big_secret_keys[src].clone(),
+                        output_key: big_secret_keys[dst].clone(),
+                        ks_decomposition_parameter: fks.decomp,
+                        fast_keyswitch: true,
+                        description: cross_key("fks"),
+                    });
+                    identifier_fks += 1;
+                }
+            }
+        }
+        Self {
+            big_secret_keys,
+            small_secret_keys,
+            keyswitch_keys,
+            bootstrap_keys,
+            conversion_keyswitch_keys,
+        }
+    }
+
+    pub fn compacted(self) -> CircuitKeys {
+        CircuitKeys {
+            secret_keys: [self.big_secret_keys, self.small_secret_keys].concat(),
+            keyswitch_keys: self
+                .keyswitch_keys
+                .into_iter()
+                .flatten()
+                .flatten()
+                .collect(),
+            bootstrap_keys: self.bootstrap_keys,
+            conversion_keyswitch_keys: self
+                .conversion_keyswitch_keys
+                .into_iter()
+                .flatten()
+                .flatten()
+                .collect(),
+        }
+    }
 }
diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/optimize.rs b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/optimize.rs
index f7f14dbe6..459436c0d 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/optimize.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/optimize.rs
@@ -17,19 +17,20 @@ use crate::optimization::dag::multi_parameters::complexity::Complexity;
 use crate::optimization::dag::multi_parameters::feasible::Feasible;
 use crate::optimization::dag::multi_parameters::partitions::PartitionIndex;
 use crate::optimization::dag::multi_parameters::precision_cut::PrecisionCut;
+use crate::optimization::dag::multi_parameters::{analyze, keys_spec};
 
 const DEBUG: bool = false;
 
 #[derive(Debug, Clone)]
 pub struct MicroParameters {
-    pbs: Vec<Option<CmuxComplexityNoise>>,
-    ks: Vec<Vec<Option<KsComplexityNoise>>>,
-    fks: Vec<Vec<Option<FksComplexityNoise>>>,
+    pub pbs: Vec<Option<CmuxComplexityNoise>>,
+    pub ks: Vec<Vec<Option<KsComplexityNoise>>>,
+    pub fks: Vec<Vec<Option<FksComplexityNoise>>>,
 }
 
 // Parameters optimized for 1 partition:
 //  the partition pbs, all used ks for all partitions, a much fks as partition
-pub struct PartialMicroParameters {
+struct PartialMicroParameters {
     pbs: CmuxComplexityNoise,
     ks: Vec<Vec<Option<KsComplexityNoise>>>,
     fks: Vec<Vec<Option<FksComplexityNoise>>>,
@@ -40,19 +41,19 @@ pub struct PartialMicroParameters {
 
 #[derive(Debug, Copy, Clone, Eq, PartialEq)]
 pub struct MacroParameters {
-    glwe_params: GlweParameters,
-    internal_dim: u64,
+    pub glwe_params: GlweParameters,
+    pub internal_dim: u64,
 }
 
 #[derive(Debug, Clone)]
 pub struct Parameters {
-    micro_params: MicroParameters,
-    macro_params: Vec<Option<MacroParameters>>,
+    pub micro_params: MicroParameters,
+    pub macro_params: Vec<Option<MacroParameters>>,
     is_lower_bound: bool,
     is_feasible: bool,
-    p_error: f64,
-    global_p_error: f64,
-    complexity: f64,
+    pub p_error: f64,
+    pub global_p_error: f64,
+    pub complexity: f64,
 }
 
 #[derive(Debug, Clone)]
@@ -792,7 +793,7 @@ pub fn optimize(
     persistent_caches: &PersistDecompCaches,
     p_cut: &Option<PrecisionCut>,
     default_partition: PartitionIndex,
-) -> Option<Parameters> {
+) -> Option<(AnalyzedDag, Parameters)> {
     let ciphertext_modulus_log = config.ciphertext_modulus_log;
     let security_level = config.security_level;
     let noise_config = NoiseBoundConfig {
@@ -904,7 +905,7 @@ pub fn optimize(
         &feasible,
         &complexity,
     );
-    Some(params)
+    Some((dag, params))
 }
 
 fn used_tlu_keyswitch(dag: &AnalyzedDag) -> Vec<Vec<bool>> {
@@ -1003,5 +1004,48 @@ fn sanity_check(
     }
 }
 
+pub fn optimize_to_circuit_solution(
+    dag: &unparametrized::OperationDag,
+    config: Config,
+    search_space: &SearchSpace,
+    persistent_caches: &PersistDecompCaches,
+    p_cut: &Option<PrecisionCut>,
+) -> keys_spec::CircuitSolution {
+    let default_partition = 0;
+    let dag_and_params = optimize(
+        dag,
+        config,
+        search_space,
+        persistent_caches,
+        p_cut,
+        default_partition,
+    );
+    #[allow(clippy::option_if_let_else)]
+    if let Some((dag, params)) = dag_and_params {
+        let ext_keys = keys_spec::ExpandedCircuitKeys::of(&params);
+        let instructions_keys = analyze::original_instrs_partition(&dag, &ext_keys);
+        let circuit_keys = ext_keys.compacted();
+        keys_spec::CircuitSolution {
+            circuit_keys,
+            instructions_keys,
+            complexity: params.complexity,
+            p_error: params.p_error,
+            global_p_error: params.global_p_error,
+            is_feasible: true,
+            error_msg: String::default(),
+        }
+    } else {
+        keys_spec::CircuitSolution {
+            circuit_keys: keys_spec::CircuitKeys::default(),
+            instructions_keys: vec![],
+            complexity: f64::INFINITY,
+            p_error: 1.0,
+            global_p_error: 1.0,
+            is_feasible: false,
+            error_msg: "No crypto-parameters for the given constraints".into(),
+        }
+    }
+}
+
 #[cfg(test)]
 include!("tests/test_optimize.rs");
diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/tests/test_optimize.rs b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/tests/test_optimize.rs
index 31d63aae7..a2c2a5823 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/tests/test_optimize.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/tests/test_optimize.rs
@@ -43,7 +43,7 @@ mod tests {
             &SHARED_CACHES,
             p_cut,
             default_partition,
-        )
+        ).map(|v| v.1)
     }
 
     fn optimize_single(dag: &unparametrized::OperationDag) -> Option<Parameters> {