diff --git a/tfhe/src/integer/backward_compatibility/ciphertext/mod.rs b/tfhe/src/integer/backward_compatibility/ciphertext/mod.rs
index f4e01140b..ac662abf3 100644
--- a/tfhe/src/integer/backward_compatibility/ciphertext/mod.rs
+++ b/tfhe/src/integer/backward_compatibility/ciphertext/mod.rs
@@ -5,6 +5,7 @@ use crate::integer::ciphertext::{
     CompressedModulusSwitchedSignedRadixCiphertext, DataKind, SquashedNoiseBooleanBlock,
     SquashedNoiseRadixCiphertext, SquashedNoiseSignedRadixCiphertext,
 };
+use crate::integer::server_key::CompressedKVStore;
 use crate::integer::BooleanBlock;
 #[cfg(feature = "zk-pok")]
 use crate::integer::ProvenCompactCiphertextList;
@@ -148,3 +149,8 @@ pub enum SquashedNoiseSignedRadixCiphertextVersions {
 pub enum SquashedNoiseBooleanBlockVersions {
     V0(SquashedNoiseBooleanBlock),
 }
+
+#[derive(VersionsDispatch)]
+pub enum CompressedKVStoreVersions<K> {
+    V0(CompressedKVStore<K>),
+}
diff --git a/tfhe/src/integer/server_key/mod.rs b/tfhe/src/integer/server_key/mod.rs
index d1212d681..761fbf848 100644
--- a/tfhe/src/integer/server_key/mod.rs
+++ b/tfhe/src/integer/server_key/mod.rs
@@ -7,7 +7,7 @@ pub(crate) mod crt;
 mod crt_parallel;
 pub(crate) mod radix;
 pub(crate) mod radix_parallel;
-pub use radix_parallel::kv_store::KVStore;
+pub use radix_parallel::kv_store::{CompressedKVStore, KVStore};
 
 use super::backward_compatibility::server_key::{CompressedServerKeyVersions, ServerKeyVersions};
 use crate::conformance::ParameterSetConformant;
diff --git a/tfhe/src/integer/server_key/radix_parallel/kv_store.rs b/tfhe/src/integer/server_key/radix_parallel/kv_store.rs
index 590e7987f..b13fc0b64 100644
--- a/tfhe/src/integer/server_key/radix_parallel/kv_store.rs
+++ b/tfhe/src/integer/server_key/radix_parallel/kv_store.rs
@@ -1,18 +1,37 @@
+use crate::integer::backward_compatibility::ciphertext::CompressedKVStoreVersions;
 use crate::integer::block_decomposition::{Decomposable, DecomposableInto};
+use crate::integer::ciphertext::{
+    CompressedCiphertextList, CompressedCiphertextListBuilder, Compressible, Expandable,
+};
+use crate::integer::compression_keys::{CompressionKey, DecompressionKey};
 use crate::integer::prelude::ServerKeyDefaultCMux;
 use crate::integer::{BooleanBlock, IntegerRadixCiphertext, ServerKey};
 use crate::prelude::CastInto;
 use rayon::prelude::*;
+use serde::{Deserialize, Serialize};
 use std::collections::HashMap;
+use std::fmt::Display;
 use std::hash::Hash;
 use std::num::NonZeroUsize;
+use tfhe_versionable::Versionize;
 
+/// The KVStore is a specialized encrypted HashMap
+///
+/// * Keys are clear numbers
+/// * Values are RadixCiphertext or SignedRadixCiphertext
+///
+/// It supports getting/modifying existing pairs of (key,value)
+/// using an encrypted key.
+///
+///
+/// To serialize a KVStore it must first be compressed with [KVStore::compress]
 pub struct KVStore<Key, Ct> {
     data: HashMap<Key, Ct>,
     block_count: Option<NonZeroUsize>,
 }
 
 impl<Key, Ct> KVStore<Key, Ct> {
+    /// Creates an empty KVStore
     pub fn new() -> Self {
         Self {
             data: HashMap::new(),
@@ -20,6 +39,10 @@ impl<Key, Ct> KVStore<Key, Ct> {
         }
     }
 
+    /// Returns the value stored for the key if any
+    ///
+    /// Key is in clear, see [ServerKey::kv_store_get] if you wish to
+    /// query using an encrypted key
     pub fn get(&self, key: &Key) -> Option<&Ct>
     where
         Key: Eq + Hash,
@@ -41,7 +64,7 @@ impl<Key, Ct> KVStore<Key, Ct> {
     /// values stored
     pub fn insert(&mut self, key: Key, value: Ct) -> Option<Ct>
     where
-        Key: PartialEq + Ord + Eq + Hash,
+        Key: PartialEq + Eq + Hash,
         Ct: IntegerRadixCiphertext,
     {
         let n_blocks = value.blocks().len();
@@ -61,10 +84,12 @@ impl<Key, Ct> KVStore<Key, Ct> {
         self.data.insert(key, value)
     }
 
+    /// Returns the number of key-value pairs currently stored
     pub fn len(&self) -> usize {
         self.data.len()
     }
 
+    /// Returns whether the store is empty
     pub fn is_empty(&self) -> bool {
         self.data.is_empty()
     }
@@ -352,3 +377,246 @@ impl ServerKey {
         (new_value, check_block)
     }
 }
+
+impl<Key, Ct> KVStore<Key, Ct>
+where
+    Key: Copy,
+    Ct: Compressible + Clone,
+{
+    /// Compress the KVStore to be able to serialize it
+    pub fn compress(&self, compression_key: &CompressionKey) -> CompressedKVStore<Key> {
+        let mut builder = CompressedCiphertextListBuilder::new();
+        let mut keys = Vec::with_capacity(self.data.len());
+        for (key, value) in self.data.iter() {
+            keys.push(*key);
+            builder.push(value.clone());
+        }
+
+        let values = builder.build(compression_key);
+
+        CompressedKVStore { keys, values }
+    }
+}
+
+/// Compressed KVStore
+///
+/// This type is the serializable and deserializable form of a KVStore
+#[derive(Serialize, Deserialize, Versionize)]
+#[versionize(CompressedKVStoreVersions)]
+pub struct CompressedKVStore<Key> {
+    keys: Vec<Key>,
+    values: CompressedCiphertextList,
+}
+
+impl<Key> CompressedKVStore<Key>
+where
+    Key: Copy + Display + Eq + Hash,
+{
+    /// Decompressed the KVStore
+    ///
+    /// Returns an error if:
+    /// * A key does not have a corresponding value
+    /// * A value (which is a radix ciphertext) does not have the same number of blocks as the
+    ///   others.
+    ///
+    /// Both these errors indicate corrupted or malformed data
+    pub fn decompress<Ct>(
+        &self,
+        decompression_key: &DecompressionKey,
+    ) -> crate::Result<KVStore<Key, Ct>>
+    where
+        Ct: Expandable + IntegerRadixCiphertext,
+    {
+        let mut block_count = None;
+        let mut store = KVStore::new();
+        for (i, key) in self.keys.iter().enumerate() {
+            let value: Ct = self
+                .values
+                .get(i, decompression_key)?
+                .ok_or_else(|| crate::error!("Missing value for key '{key}'"))?;
+
+            let n = *block_count.get_or_insert_with(|| value.blocks().len());
+
+            if n != value.blocks().len() {
+                return Err(crate::error!(
+                    "The value for key {key} does not have the same number \
+                        of blocks as other values. {} instead of {n}",
+                    value.blocks().len()
+                ));
+            }
+
+            let _ = store.insert(*key, value);
+        }
+
+        Ok(store)
+    }
+}
+
+macro_rules! impl_named_for_kv_store {
+    ($Key:ty) => {
+        impl crate::named::Named for CompressedKVStore<$Key> {
+            const NAME: &'static str =
+                concat!("integer::CompressedKVStore<", stringify!($Key), ">");
+        }
+    };
+}
+
+impl_named_for_kv_store!(u8);
+impl_named_for_kv_store!(u16);
+impl_named_for_kv_store!(u32);
+impl_named_for_kv_store!(u64);
+impl_named_for_kv_store!(u128);
+impl_named_for_kv_store!(i8);
+impl_named_for_kv_store!(i16);
+impl_named_for_kv_store!(i32);
+impl_named_for_kv_store!(i64);
+impl_named_for_kv_store!(i128);
+
+#[cfg(test)]
+mod tests {
+    use rand::Rng;
+
+    use super::*;
+    use crate::integer::{
+        gen_keys, ClientKey, IntegerKeyKind, RadixCiphertext, SignedRadixCiphertext,
+    };
+    use crate::shortint::parameters::test_params::{
+        TEST_COMP_PARAM_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M128,
+        TEST_PARAM_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M128,
+    };
+    use crate::shortint::ShortintParameterSet;
+
+    fn assert_store_unsigned_matches(
+        clear_store: &HashMap<u32, u64>,
+        kv_store: &KVStore<u32, RadixCiphertext>,
+        cks: &ClientKey,
+    ) {
+        assert_eq!(
+            clear_store.len(),
+            kv_store.len(),
+            "Clear and Encrypted stores do no have the same number of pairs"
+        );
+
+        for (key, value) in clear_store {
+            let ct = kv_store
+                .get(key)
+                .expect("Missing entry in decompressed KVStore");
+
+            let decrypted: u64 = cks.decrypt_radix(ct);
+            assert_eq!(
+                *value, decrypted,
+                "Invalid value stored for key '{key}', expected '{value}' got '{decrypted}'"
+            );
+        }
+    }
+
+    #[test]
+    fn test_compression_serialization_unsigned() {
+        let params = TEST_PARAM_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M128.into();
+
+        let (cks, _) = gen_keys::<ShortintParameterSet>(params, IntegerKeyKind::Radix);
+
+        let private_compression_key = cks
+            .new_compression_private_key(TEST_COMP_PARAM_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M128);
+
+        let (compression_key, decompression_key) =
+            cks.new_compression_decompression_keys(&private_compression_key);
+
+        let num_blocks = 32;
+        let num_keys = 100;
+
+        let mut rng = rand::thread_rng();
+
+        let mut clear_store = HashMap::new();
+        let mut kv_store = KVStore::new();
+        for _ in 0..num_keys {
+            let key = rng.gen::<u32>();
+            let value = rng.gen::<u64>();
+
+            let ct = cks.encrypt_radix(value, num_blocks);
+
+            let _ = clear_store.insert(key, value);
+            kv_store.insert(key, ct);
+        }
+
+        assert_store_unsigned_matches(&clear_store, &kv_store, &cks);
+
+        let compressed = kv_store.compress(&compression_key);
+        let kv_store = compressed.decompress(&decompression_key).unwrap();
+        assert_store_unsigned_matches(&clear_store, &kv_store, &cks);
+
+        let mut data = vec![];
+        crate::safe_serialization::safe_serialize(&compressed, &mut data, 1 << 20).unwrap();
+        let compressed: CompressedKVStore<u32> =
+            crate::safe_serialization::safe_deserialize(data.as_slice(), 1 << 20).unwrap();
+        let kv_store = compressed.decompress(&decompression_key).unwrap();
+        assert_store_unsigned_matches(&clear_store, &kv_store, &cks);
+    }
+
+    fn assert_store_signed_matches(
+        clear_store: &HashMap<u32, i64>,
+        kv_store: &KVStore<u32, SignedRadixCiphertext>,
+        cks: &ClientKey,
+    ) {
+        assert_eq!(
+            clear_store.len(),
+            kv_store.len(),
+            "Clear and Encrypted stores do no have the same number of pairs"
+        );
+
+        for (key, value) in clear_store {
+            let ct = kv_store
+                .get(key)
+                .expect("Missing entry in decompressed KVStore");
+
+            let decrypted: i64 = cks.decrypt_signed_radix(ct);
+            assert_eq!(
+                *value, decrypted,
+                "Invalid value stored for key '{key}', expected '{value}' got '{decrypted}'"
+            );
+        }
+    }
+
+    #[test]
+    fn test_compression_serialization_signed() {
+        let params = TEST_PARAM_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M128.into();
+
+        let (cks, _) = gen_keys::<ShortintParameterSet>(params, IntegerKeyKind::Radix);
+
+        let private_compression_key = cks
+            .new_compression_private_key(TEST_COMP_PARAM_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M128);
+
+        let (compression_key, decompression_key) =
+            cks.new_compression_decompression_keys(&private_compression_key);
+
+        let num_blocks = 32;
+        let num_keys = 100;
+
+        let mut rng = rand::thread_rng();
+
+        let mut clear_store = HashMap::new();
+        let mut kv_store = KVStore::new();
+        for _ in 0..num_keys {
+            let key = rng.gen::<u32>();
+            let value = rng.gen::<i64>();
+
+            let ct = cks.encrypt_signed_radix(value, num_blocks);
+
+            let _ = clear_store.insert(key, value);
+            kv_store.insert(key, ct);
+        }
+
+        assert_store_signed_matches(&clear_store, &kv_store, &cks);
+
+        let compressed = kv_store.compress(&compression_key);
+        let kv_store = compressed.decompress(&decompression_key).unwrap();
+        assert_store_signed_matches(&clear_store, &kv_store, &cks);
+
+        let mut data = vec![];
+        crate::safe_serialization::safe_serialize(&compressed, &mut data, 1 << 20).unwrap();
+        let compressed: CompressedKVStore<u32> =
+            crate::safe_serialization::safe_deserialize(data.as_slice(), 1 << 20).unwrap();
+        let kv_store = compressed.decompress(&decompression_key).unwrap();
+        assert_store_signed_matches(&clear_store, &kv_store, &cks);
+    }
+}
diff --git a/tfhe/src/integer/server_key/radix_parallel/tests_unsigned/test_kv_store.rs b/tfhe/src/integer/server_key/radix_parallel/tests_unsigned/test_kv_store.rs
index 0dfac00b5..51e1cf9f3 100644
--- a/tfhe/src/integer/server_key/radix_parallel/tests_unsigned/test_kv_store.rs
+++ b/tfhe/src/integer/server_key/radix_parallel/tests_unsigned/test_kv_store.rs
@@ -9,11 +9,101 @@ use crate::shortint::parameters::{TestParameters, *};
 use std::collections::BTreeMap;
 use std::sync::Arc;
 
-create_parameterized_test!(integer_default_kv_store_add);
-create_parameterized_test!(integer_default_kv_store_sub);
-create_parameterized_test!(integer_default_kv_store_mul);
-create_parameterized_test!(integer_default_kv_store_get_update);
-create_parameterized_test!(integer_default_kv_store_map);
+create_parameterized_test!(
+    integer_default_kv_store_add
+    {
+        coverage => {
+            COVERAGE_PARAM_MESSAGE_2_CARRY_2_KS_PBS,
+            COVERAGE_PARAM_MULTI_BIT_MESSAGE_2_CARRY_2_GROUP_2_KS_PBS
+        },
+        no_coverage => {
+            TEST_PARAM_MESSAGE_1_CARRY_1_KS_PBS_GAUSSIAN_2M128,
+            PARAM_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M128,
+            TEST_PARAM_MESSAGE_3_CARRY_3_KS_PBS_GAUSSIAN_2M128,
+            // 2M128 is too slow for 4_4, it is estimated to be 2x slower
+            TEST_PARAM_MESSAGE_4_CARRY_4_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_1_CARRY_1_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_2_CARRY_2_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_3_CARRY_3_KS_PBS_GAUSSIAN_2M64,
+        }
+    }
+);
+create_parameterized_test!(
+    integer_default_kv_store_sub
+      {
+        coverage => {
+            COVERAGE_PARAM_MESSAGE_2_CARRY_2_KS_PBS,
+            COVERAGE_PARAM_MULTI_BIT_MESSAGE_2_CARRY_2_GROUP_2_KS_PBS
+        },
+        no_coverage => {
+            TEST_PARAM_MESSAGE_1_CARRY_1_KS_PBS_GAUSSIAN_2M128,
+            PARAM_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M128,
+            TEST_PARAM_MESSAGE_3_CARRY_3_KS_PBS_GAUSSIAN_2M128,
+            // 2M128 is too slow for 4_4, it is estimated to be 2x slower
+            TEST_PARAM_MESSAGE_4_CARRY_4_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_1_CARRY_1_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_2_CARRY_2_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_3_CARRY_3_KS_PBS_GAUSSIAN_2M64,
+        }
+    }
+);
+create_parameterized_test!(
+    integer_default_kv_store_mul
+    {
+        coverage => {
+            COVERAGE_PARAM_MESSAGE_2_CARRY_2_KS_PBS,
+            COVERAGE_PARAM_MULTI_BIT_MESSAGE_2_CARRY_2_GROUP_2_KS_PBS
+        },
+        no_coverage => {
+            TEST_PARAM_MESSAGE_1_CARRY_1_KS_PBS_GAUSSIAN_2M128,
+            PARAM_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M128,
+            TEST_PARAM_MESSAGE_3_CARRY_3_KS_PBS_GAUSSIAN_2M128,
+            // 2M128 is too slow for 4_4, it is estimated to be 2x slower
+            TEST_PARAM_MESSAGE_4_CARRY_4_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_1_CARRY_1_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_2_CARRY_2_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_3_CARRY_3_KS_PBS_GAUSSIAN_2M64,
+        }
+    }
+);
+create_parameterized_test!(
+    integer_default_kv_store_get_update
+    {
+        coverage => {
+            COVERAGE_PARAM_MESSAGE_2_CARRY_2_KS_PBS,
+            COVERAGE_PARAM_MULTI_BIT_MESSAGE_2_CARRY_2_GROUP_2_KS_PBS
+        },
+        no_coverage => {
+            TEST_PARAM_MESSAGE_1_CARRY_1_KS_PBS_GAUSSIAN_2M128,
+            PARAM_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M128,
+            TEST_PARAM_MESSAGE_3_CARRY_3_KS_PBS_GAUSSIAN_2M128,
+            // 2M128 is too slow for 4_4, it is estimated to be 2x slower
+            TEST_PARAM_MESSAGE_4_CARRY_4_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_1_CARRY_1_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_2_CARRY_2_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_3_CARRY_3_KS_PBS_GAUSSIAN_2M64,
+        }
+    }
+);
+create_parameterized_test!(
+    integer_default_kv_store_map
+    {
+        coverage => {
+            COVERAGE_PARAM_MESSAGE_2_CARRY_2_KS_PBS,
+            COVERAGE_PARAM_MULTI_BIT_MESSAGE_2_CARRY_2_GROUP_2_KS_PBS
+        },
+        no_coverage => {
+            TEST_PARAM_MESSAGE_1_CARRY_1_KS_PBS_GAUSSIAN_2M128,
+            PARAM_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M128,
+            TEST_PARAM_MESSAGE_3_CARRY_3_KS_PBS_GAUSSIAN_2M128,
+            // 2M128 is too slow for 4_4, it is estimated to be 2x slower
+            TEST_PARAM_MESSAGE_4_CARRY_4_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_1_CARRY_1_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_2_CARRY_2_KS_PBS_GAUSSIAN_2M64,
+            TEST_PARAM_MULTI_BIT_GROUP_2_MESSAGE_3_CARRY_3_KS_PBS_GAUSSIAN_2M64,
+        }
+    }
+);
 
 fn integer_default_kv_store_add(params: impl Into<TestParameters>) {
     let executor = CpuFunctionExecutor::new(&ServerKey::kv_store_add_to_slot);