diff --git a/Cargo.toml b/Cargo.toml
index fc3ac1c..89e6a79 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -17,9 +17,11 @@ halo2_proofs = { git = "https://github.com/scroll-tech/halo2.git", branch = "scr
 [features]
 # Use an implementation using fewer rows (8) per permutation.
 short = []
+cached = []
 # printout the layout of circuits for demo and some unittests
 print_layout = ["halo2_proofs/dev-graph"]
 legacy = []
+default = ["short","cached"]
 
 [dev-dependencies]
 rand = "0.8"
@@ -32,6 +34,10 @@ subtle = "2"
 name = "hash"
 harness = false
 
+[[bench]]
+name = "synthesis"
+harness = false
+
 [profile.test]
 opt-level = 3
 debug-assertions = true
diff --git a/benches/synthesis.rs b/benches/synthesis.rs
new file mode 100644
index 0000000..4f7c442
--- /dev/null
+++ b/benches/synthesis.rs
@@ -0,0 +1,70 @@
+#[macro_use]
+extern crate bencher;
+use bencher::Bencher;
+
+use halo2_proofs::dev::MockProver;
+use halo2_proofs::halo2curves::{bn256::Fr as Fp, group::ff::PrimeField};
+use halo2_proofs::{
+    circuit::{Layouter, SimpleFloorPlanner},
+    plonk::{Circuit, ConstraintSystem, Error},
+};
+use poseidon_circuit::{hash::*, DEFAULT_STEP};
+
+struct TestCircuit(PoseidonHashTable<Fp>, usize);
+
+// test circuit derived from table data
+impl Circuit<Fp> for TestCircuit {
+    type Config = PoseidonHashConfig<Fp>;
+    type FloorPlanner = SimpleFloorPlanner;
+
+    fn without_witnesses(&self) -> Self {
+        Self(PoseidonHashTable::default(), self.1)
+    }
+
+    fn configure(meta: &mut ConstraintSystem<Fp>) -> Self::Config {
+        let hash_tbl = [0; 5].map(|_| meta.advice_column());
+        let q_enable = meta.fixed_column();
+        SpongeConfig::configure_sub(meta, (q_enable, hash_tbl), DEFAULT_STEP)
+    }
+
+    fn synthesize(
+        &self,
+        config: Self::Config,
+        mut layouter: impl Layouter<Fp>,
+    ) -> Result<(), Error> {
+        let chip = PoseidonHashChip::<Fp, DEFAULT_STEP>::construct(config, &self.0, self.1);
+        chip.load(&mut layouter)
+    }
+}
+
+fn synthesis(bench: &mut Bencher) {
+    let message1 = [
+        Fp::from_str_vartime("1").unwrap(),
+        Fp::from_str_vartime("2").unwrap(),
+    ];
+    let message2 = [
+        Fp::from_str_vartime("0").unwrap(),
+        Fp::from_str_vartime("1").unwrap(),
+    ];
+
+    let k = 12;
+    let circuit = TestCircuit(
+        PoseidonHashTable {
+            inputs: vec![message1, message2],
+            ..Default::default()
+        },
+        500,
+    );
+
+    bench.iter(|| {
+        MockProver::run(k, &circuit, vec![]).unwrap();
+    });
+}
+
+fn synthesis_limited(bench: &mut Bencher) {
+    bench.bench_n(1, synthesis);
+}
+
+benchmark_group!(syth_bench, synthesis_limited);
+
+benchmark_main!(syth_bench);
diff --git a/src/poseidon/septidon/full_round.rs b/src/poseidon/septidon/full_round.rs
index 5f0c349..756c2a4 100644
--- a/src/poseidon/septidon/full_round.rs
+++ b/src/poseidon/septidon/full_round.rs
@@ -1,7 +1,7 @@
 use super::loop_chip::LoopBody;
-use super::params::{mds, CachedConstants};
+use super::params::{calc::matmul, CachedConstants};
 use super::state::{Cell, FullState, SBox};
-use super::util::{join_values, matmul, query, split_values};
+use super::util::{join_values, query, split_values};
 use halo2_proofs::circuit::{Region, Value};
 //use halo2_proofs::halo2curves::bn256::Fr as F;
 use halo2_proofs::plonk::{ConstraintSystem, Error, Expression, VirtualCells};
@@ -27,7 +27,7 @@ impl FullRoundChip {
         meta: &mut VirtualCells<'_, F>,
     ) -> [Expression<F>; 3] {
         let sbox_out = self.0.map(|sbox: &SBox| sbox.output_expr(meta));
-        matmul::expr(mds(), sbox_out)
+        matmul::expr(sbox_out)
     }
 
     pub fn input_cells(&self) -> [Cell; 3] {
@@ -47,7 +47,7 @@ impl FullRoundChip {
             let sbox: &SBox = &self.0 .0[i];
             sbox_out[i] = sbox.assign(region, offset, round_constants[i], input[i])?;
         }
-        let output = join_values(sbox_out).map(|sbox_out| matmul::value(mds(), sbox_out));
+        let output = join_values(sbox_out).map(|sbox_out| matmul::value(sbox_out));
         Ok(split_values(output))
     }
 }
diff --git a/src/poseidon/septidon/params.rs b/src/poseidon/septidon/params.rs
index 823f2bb..cb0c263 100644
--- a/src/poseidon/septidon/params.rs
+++ b/src/poseidon/septidon/params.rs
@@ -12,32 +12,149 @@ pub trait CachedConstants: P128Pow5T3Constants {
     fn cached_mds() -> &'static Mds<Self>;
     /// cached inversed mds
     fn cached_mds_inv() -> &'static Mds<Self>;
+    /// cached pow5 calc result
+    fn cached_pow5(self) -> (Self, Option<Self>) {
+        (self, None)
+    }
+    /// cached muladd calc result
+    fn cached_muladd(vector: [Self; 3]) -> ([Self; 3], Option<[Self; 3]>) {
+        (vector, None)
+    }
 }
 
-pub mod sbox {
-    use super::super::util::pow_5;
-    use halo2_proofs::arithmetic::FieldExt;
+/// Wrap Fr as Hash key
+#[derive(Eq, PartialEq, Debug, Hash)]
+pub struct KeyConstant<T: CachedConstants>(T);
+
+pub mod calc {
+    use super::CachedConstants;
     use halo2_proofs::plonk::Expression;
 
-    pub fn expr<F: FieldExt>(input: Expression<F>, round_constant: Expression<F>) -> Expression<F> {
-        pow_5::expr(input + round_constant)
+    pub mod sbox {
+        use super::super::super::util::pow_5;
+        use super::*;
+        pub fn expr<F: CachedConstants>(
+            input: Expression<F>,
+            round_constant: Expression<F>,
+        ) -> Expression<F> {
+            pow_5::expr(input + round_constant)
+        }
+
+        pub fn value<F: CachedConstants>(input: F, round_constant: F) -> F {
+            let val_added = input + round_constant;
+            let (val_added, ret) = val_added.cached_pow5();
+            ret.unwrap_or_else(|| pow_5::value(val_added))
+        }
     }
 
-    pub fn value<F: FieldExt>(input: F, round_constant: F) -> F {
-        pow_5::value(input + round_constant)
+    pub mod matmul {
+        use super::super::super::util::matmul;
+        use super::*;
+
+        /// Multiply a vector of expressions by a constant matrix.
+        pub fn expr<F: CachedConstants>(vector: [Expression<F>; 3]) -> [Expression<F>; 3] {
+            matmul::expr(F::cached_mds(), vector)
+        }
+
+        /// Multiply a vector of values by a constant matrix.
+        pub fn value<F: CachedConstants>(vector: [F; 3]) -> [F; 3] {
+            let (vector, ret) = F::cached_muladd(vector);
+            ret.unwrap_or_else(|| matmul::value(F::cached_mds(), vector))
+        }
     }
 }
 
 pub type Mds<F> = MdsT<F, 3>;
 
 mod bn254 {
-    use super::{CachedConstants, Mds};
+    use super::super::util::{matmul, pow_5};
+    use super::*;
     use crate::poseidon::primitives::{P128Pow5T3Compact, Spec};
     use halo2_proofs::halo2curves::bn256::Fr as F;
     use lazy_static::lazy_static;
+    use std::iter;
+
+    type Pow5CacheMap = std::collections::HashMap<KeyConstant<F>, F>;
+    type MulAddCacheMap = std::collections::HashMap<[KeyConstant<F>; 3], [F; 3]>;
+
     lazy_static! {
         // Cache the round constants and the MDS matrix (and unused inverse MDS matrix).
         static ref CONSTANTS: (Vec<[F; 3]>, Mds<F>, Mds<F>) =  P128Pow5T3Compact::<F>::constants();
+        pub static ref POW5_CONSTANTS: Pow5CacheMap =  {
+
+            let r_f = P128Pow5T3Compact::<F>::full_rounds() / 2;
+            let r_p = P128Pow5T3Compact::<F>::partial_rounds();
+            let mds = &CONSTANTS.1;
+
+            let full_round = |ret: &mut Pow5CacheMap, state: &mut [F; 3], rcs: &[F; 3]| {
+                for (word, rc) in state.iter_mut().zip(rcs.iter()) {
+                    let key = KeyConstant(*word + rc);
+                    *word = pow_5::value(*word + rc);
+                    ret.insert(key, *word);
+                }
+                *state = matmul::value(mds, *state);
+            };
+
+            let part_round = |ret: &mut Pow5CacheMap, state: &mut [F; 3], rcs: &[F; 3]| {
+                // In a partial round, the S-box is only applied to the first state word.
+                // and the compact constants has only first rc is not zero
+                let key = KeyConstant(state[0]+rcs[0]);
+                state[0] = pow_5::value(state[0]+rcs[0]);
+                ret.insert(key, state[0]);
+                *state = matmul::value(mds, *state);
+            };
+
+            let (ret, _) = iter::empty()
+            .chain(iter::repeat(&full_round as &dyn Fn(&mut Pow5CacheMap, &mut [F; 3], &[F; 3])).take(r_f))
+            .chain(iter::repeat(&part_round as &dyn Fn(&mut Pow5CacheMap, &mut [F; 3], &[F; 3])).take(r_p))
+            .chain(iter::repeat(&full_round as &dyn Fn(&mut Pow5CacheMap, &mut [F; 3], &[F; 3])).take(r_f))
+            .zip(CONSTANTS.0.iter())
+            .fold((Pow5CacheMap::new(), [F::zero();3]), |(mut ret, mut state), (round, rcs)| {
+                round(&mut ret, &mut state, rcs);
+                (ret, state)
+            });
+
+            //let mut t_state = [F::zero(); 3];
+            //crate::poseidon::primitives::permute::<F, P128Pow5T3Compact<F>, 3, 2>(&mut t_state, mds, &CONSTANTS.0);
+            //assert_eq!(t_state, state);
+            ret
+        };
+        static ref MULADD_CONSTANTS: MulAddCacheMap =  {
+            let r_f = P128Pow5T3Compact::<F>::full_rounds() / 2;
+            let r_p = P128Pow5T3Compact::<F>::partial_rounds();
+            let mds = &CONSTANTS.1;
+
+            let full_round = |ret: &mut MulAddCacheMap, state: &mut [F; 3], rcs: &[F; 3]| {
+                for (word, rc) in state.iter_mut().zip(rcs.iter()) {
+                    *word = pow_5::value(*word + rc);
+                }
+                let key = state.map(KeyConstant);
+                *state = matmul::value(mds, *state);
+                ret.insert(key, *state);
+            };
+
+            let part_round = |ret: &mut MulAddCacheMap, state: &mut [F; 3], rcs: &[F; 3]| {
+                // In a partial round, the S-box is only applied to the first state word.
+                // and the compact constants has only first rc is not zero
+                state[0] = pow_5::value(state[0]+rcs[0]);
+                let key = state.map(KeyConstant);
+                *state = matmul::value(mds, *state);
+                ret.insert(key, *state);
+            };
+
+            let (ret, _) = iter::empty()
+            .chain(iter::repeat(&full_round as &dyn Fn(&mut MulAddCacheMap, &mut [F; 3], &[F; 3])).take(r_f))
+            .chain(iter::repeat(&part_round as &dyn Fn(&mut MulAddCacheMap, &mut [F; 3], &[F; 3])).take(r_p))
+            .chain(iter::repeat(&full_round as &dyn Fn(&mut MulAddCacheMap, &mut [F; 3], &[F; 3])).take(r_f))
+            .zip(CONSTANTS.0.iter())
+            .fold((MulAddCacheMap::new(), [F::zero();3]), |(mut ret, mut state), (round, rcs)| {
+                round(&mut ret, &mut state, rcs);
+                (ret, state)
+            });
+
+            ret
+        };
+
     }
 
     impl CachedConstants for F {
@@ -50,6 +167,18 @@ mod bn254 {
         fn cached_mds_inv() -> &'static Mds<Self> {
             &CONSTANTS.2
         }
+        #[cfg(feature = "cached")]
+        fn cached_pow5(self) -> (Self, Option<Self>) {
+            let key = KeyConstant(self);
+            let ret = POW5_CONSTANTS.get(&key).copied();
+            (key.0, ret)
+        }
+        #[cfg(feature = "cached")]
+        fn cached_muladd(vector: [Self; 3]) -> ([Self; 3], Option<[Self; 3]>) {
+            let key = vector.map(KeyConstant);
+            let ret = MULADD_CONSTANTS.get(&key).copied();
+            (key.map(|k| k.0), ret)
+        }
     }
 }
 
@@ -60,3 +189,17 @@ pub fn round_constant<F: CachedConstants>(index: usize) -> [F; 3] {
 pub fn mds<F: CachedConstants>() -> &'static Mds<F> {
     F::cached_mds()
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_constants() {
+        println!(
+            "{:?},{:?}",
+            bn254::POW5_CONSTANTS.keys(),
+            bn254::POW5_CONSTANTS.values()
+        );
+    }
+}
diff --git a/src/poseidon/septidon/septuple_round.rs b/src/poseidon/septidon/septuple_round.rs
index 95e36f5..d1443a7 100644
--- a/src/poseidon/septidon/septuple_round.rs
+++ b/src/poseidon/septidon/septuple_round.rs
@@ -1,7 +1,7 @@
 use super::loop_chip::LoopBody;
-use super::params::{mds, CachedConstants};
+use super::params::{calc::matmul, CachedConstants};
 use super::state::{Cell, SBox};
-use super::util::{join_values, matmul, query, split_values};
+use super::util::{join_values, query, split_values};
 use halo2_proofs::circuit::{Region, Value};
 //use halo2_proofs::halo2curves::bn256::Fr as F;
 use halo2_proofs::plonk::{ConstraintSystem, Constraints, Error, Expression, VirtualCells};
@@ -82,7 +82,7 @@ impl SeptupleRoundChip {
         input: &[Expression<F>; 3],
     ) -> [Expression<F>; 3] {
         let sbox_out = [sbox.output_expr(meta), input[1].clone(), input[2].clone()];
-        matmul::expr(mds(), sbox_out)
+        matmul::expr(sbox_out)
     }
 
     pub fn input(&self) -> [Cell; 3] {
@@ -111,7 +111,7 @@ impl SeptupleRoundChip {
             // Assign the following S-Boxes.
             state[0] = sbox.assign(region, offset, round_constants[i], state[0])?;
             // Apply the matrix.
-            state = split_values(join_values(state).map(|s| matmul::value(mds(), s)));
+            state = split_values(join_values(state).map(|s| matmul::value(s)));
             Ok(())
         };
 
diff --git a/src/poseidon/septidon/state.rs b/src/poseidon/septidon/state.rs
index b0faee7..d12ef21 100644
--- a/src/poseidon/septidon/state.rs
+++ b/src/poseidon/septidon/state.rs
@@ -1,4 +1,4 @@
-use super::params;
+use super::params::{self, CachedConstants};
 use halo2_proofs::circuit::{Region, Value};
 //use halo2_proofs::halo2curves::bn256::Fr as F;
 use halo2_proofs::arithmetic::FieldExt;
@@ -72,7 +72,7 @@ impl SBox {
     }
 
     /// Assign the witness of the input.
-    pub fn assign<F: FieldExt>(
+    pub fn assign<F: CachedConstants>(
         &self,
         region: &mut Region<'_, F>,
         offset: usize,
@@ -91,7 +91,7 @@ impl SBox {
             offset + self.input.region_offset(),
             || input,
         )?;
-        let output = input.map(|i| params::sbox::value(i, round_constant));
+        let output = input.map(|i| params::calc::sbox::value(i, round_constant));
         Ok(output)
     }
 
@@ -103,10 +103,10 @@ impl SBox {
         meta.query_fixed(self.round_constant, Rotation(self.input.offset))
     }
 
-    pub fn output_expr<F: FieldExt>(&self, meta: &mut VirtualCells<'_, F>) -> Expression<F> {
+    pub fn output_expr<F: CachedConstants>(&self, meta: &mut VirtualCells<'_, F>) -> Expression<F> {
         let input = self.input_expr(meta);
         let round_constant = self.rc_expr(meta);
-        params::sbox::expr(input, round_constant)
+        params::calc::sbox::expr(input, round_constant)
     }
 }
 
diff --git a/src/poseidon/septidon/transition_round.rs b/src/poseidon/septidon/transition_round.rs
index ab55e7f..4b9a7c6 100644
--- a/src/poseidon/septidon/transition_round.rs
+++ b/src/poseidon/septidon/transition_round.rs
@@ -1,7 +1,7 @@
 use super::params;
-use super::params::{mds, round_constant, CachedConstants};
+use super::params::{calc::matmul, round_constant, CachedConstants};
 use super::state::Cell;
-use super::util::{join_values, matmul, split_values};
+use super::util::{join_values, split_values};
 use halo2_proofs::circuit::{Region, Value};
 //use halo2_proofs::halo2curves::bn256::Fr as F;
 use halo2_proofs::plonk::{Advice, Column, ConstraintSystem, Constraints, Error, Expression};
@@ -58,11 +58,11 @@ impl TransitionRoundChip {
     ) -> [Expression<F>; 3] {
         let rc = Expression::Constant(Self::round_constant());
         let sbox_out = [
-            params::sbox::expr(input[0].clone(), rc),
+            params::calc::sbox::expr(input[0].clone(), rc),
             input[1].clone(),
             input[2].clone(),
         ];
-        matmul::expr(mds(), sbox_out)
+        matmul::expr(sbox_out)
     }
 
     fn round_constant<F: CachedConstants>() -> F {
@@ -102,11 +102,11 @@ impl TransitionRoundChip {
 
     fn first_partial_round<F: CachedConstants>(input: &[Value<F>; 3]) -> [Value<F>; 3] {
         let sbox_out = [
-            input[0].map(|f| params::sbox::value(f, Self::round_constant())),
+            input[0].map(|f| params::calc::sbox::value(f, Self::round_constant())),
             input[1],
             input[2],
         ];
-        let output = join_values(sbox_out).map(|s| matmul::value(mds(), s));
+        let output = join_values(sbox_out).map(|s| matmul::value(s));
         split_values(output)
     }
 
diff --git a/src/poseidon/septidon/util.rs b/src/poseidon/septidon/util.rs
index 142afe9..f51f0df 100644
--- a/src/poseidon/septidon/util.rs
+++ b/src/poseidon/septidon/util.rs
@@ -41,7 +41,7 @@ pub fn split_values<F: FieldExt>(values: Value<[F; 3]>) -> [Value<F>; 3] {
     ]
 }
 
-pub mod pow_5 {
+pub(crate) mod pow_5 {
     use super::FieldExt;
     use halo2_proofs::plonk::Expression;
 
@@ -57,7 +57,7 @@ pub mod pow_5 {
 }
 
 /// Matrix multiplication expressions and values.
-pub mod matmul {
+pub(crate) mod matmul {
     use super::super::params::Mds;
     use super::FieldExt;
     use halo2_proofs::plonk::Expression;
diff --git a/tests/hash_proving.rs b/tests/hash_proving.rs
index daefbea..20affea 100644
--- a/tests/hash_proving.rs
+++ b/tests/hash_proving.rs
@@ -17,7 +17,7 @@ use halo2_proofs::{
     circuit::{Layouter, SimpleFloorPlanner},
     plonk::{Circuit, ConstraintSystem, Error},
 };
-use poseidon_circuit::poseidon::Pow5Chip;
+//use poseidon_circuit::poseidon::Pow5Chip;
 use poseidon_circuit::{hash::*, DEFAULT_STEP};
 use rand::SeedableRng;
 use rand_chacha::ChaCha8Rng;
@@ -26,7 +26,7 @@ struct TestCircuit(PoseidonHashTable<Fp>, usize);
 
 // test circuit derived from table data
 impl Circuit<Fp> for TestCircuit {
-    type Config = SpongeConfig<Fp, Pow5Chip<Fp, 3, 2>>;
+    type Config = PoseidonHashConfig<Fp>;
     type FloorPlanner = SimpleFloorPlanner;
 
     fn without_witnesses(&self) -> Self {
@@ -44,8 +44,7 @@ impl Circuit<Fp> for TestCircuit {
         config: Self::Config,
         mut layouter: impl Layouter<Fp>,
     ) -> Result<(), Error> {
-        let chip =
-            SpongeChip::<Fp, DEFAULT_STEP, Pow5Chip<Fp, 3, 2>>::construct(config, &self.0, self.1);
+        let chip = PoseidonHashChip::<Fp, DEFAULT_STEP>::construct(config, &self.0, self.1);
         chip.load(&mut layouter)
     }
 }