diff --git a/crates/witness/src/lib.rs b/crates/witness/src/lib.rs
index f7a40d3..a7619c1 100644
--- a/crates/witness/src/lib.rs
+++ b/crates/witness/src/lib.rs
@@ -38,6 +38,7 @@ pub struct RowMajorMatrix<T: Sized + Sync + Clone + Send + Copy> {
     inner: p3::matrix::dense::RowMajorMatrix<T>,
     // num_row is the real instance BEFORE padding
     num_rows: usize,
+    log2_num_rotation: usize,
     is_padded: bool,
     padding_strategy: InstancePaddingStrategy,
 }
@@ -53,6 +54,7 @@ impl<T: Sized + Sync + Clone + Send + Copy + Default + FieldAlgebra> RowMajorMat
             inner: p3::matrix::dense::RowMajorMatrix::rand(rng, num_row_padded, cols),
             num_rows: rows,
             is_padded: true,
+            log2_num_rotation: 0,
             padding_strategy: InstancePaddingStrategy::Default,
         }
     }
@@ -60,6 +62,7 @@ impl<T: Sized + Sync + Clone + Send + Copy + Default + FieldAlgebra> RowMajorMat
         Self {
             inner: p3::matrix::dense::RowMajorMatrix::new(vec![], 0),
             num_rows: 0,
+            log2_num_rotation: 0,
             is_padded: true,
             padding_strategy: InstancePaddingStrategy::Default,
         }
@@ -72,7 +75,8 @@ impl<T: Sized + Sync + Clone + Send + Copy + Default + FieldAlgebra> RowMajorMat
         mut self,
         blowup_factor: Option<usize>,
     ) -> p3::matrix::dense::RowMajorMatrix<T> {
-        let padded_height = next_pow2_instance_padding(self.num_instances());
+        let padded_height = next_pow2_instance_padding(self.num_instances())
+            * Self::num_rotation(self.log2_num_rotation);
         if let Some(blowup_factor) = blowup_factor {
             if blowup_factor != CAPACITY_RESERVED_FACTOR {
                 tracing::warn!(
@@ -98,7 +102,21 @@ impl<T: Sized + Sync + Clone + Send + Copy + Default + FieldAlgebra> RowMajorMat
         num_cols: usize,
         padding_strategy: InstancePaddingStrategy,
     ) -> Self {
-        let num_row_padded = next_pow2_instance_padding(num_rows);
+        Self::new_by_rotation(num_rows, 0, num_cols, padding_strategy)
+    }
+
+    /// rotation controls how many physical rows each logical row spans.
+    ///
+    /// for example, if `log2_num_rotation = 2`, then each logical row
+    /// is expanded into `2^2 = 4` physical rows.
+    pub fn new_by_rotation(
+        num_rows: usize,
+        log2_num_rotation: usize,
+        num_cols: usize,
+        padding_strategy: InstancePaddingStrategy,
+    ) -> Self {
+        let num_row_padded =
+            next_pow2_instance_padding(num_rows) * Self::num_rotation(log2_num_rotation);
 
         let mut value = Vec::with_capacity(CAPACITY_RESERVED_FACTOR * num_row_padded * num_cols);
         value.par_extend(
@@ -109,6 +127,7 @@ impl<T: Sized + Sync + Clone + Send + Copy + Default + FieldAlgebra> RowMajorMat
         RowMajorMatrix {
             inner: p3::matrix::dense::RowMajorMatrix::new(value, num_cols),
             num_rows,
+            log2_num_rotation,
             is_padded: matches!(padding_strategy, InstancePaddingStrategy::Default),
             padding_strategy,
         }
@@ -126,6 +145,7 @@ impl<T: Sized + Sync + Clone + Send + Copy + Default + FieldAlgebra> RowMajorMat
         RowMajorMatrix {
             inner: m,
             num_rows,
+            log2_num_rotation: 0,
             is_padded: matches!(padding_strategy, InstancePaddingStrategy::Default),
             padding_strategy,
         }
@@ -146,32 +166,42 @@ impl<T: Sized + Sync + Clone + Send + Copy + Default + FieldAlgebra> RowMajorMat
         next_pow2_instance_padding(self.num_instances()) - self.num_instances()
     }
 
+    // return raw num_instances without rotation
     pub fn num_instances(&self) -> usize {
         self.num_rows
     }
 
+    fn num_rotation(log2_num_rotation: usize) -> usize {
+        1 << log2_num_rotation
+    }
+
     pub fn iter_rows(&self) -> Chunks<'_, T> {
-        self.inner.values[..self.num_instances() * self.n_col()].chunks(self.inner.width)
+        let num_rotation = Self::num_rotation(self.log2_num_rotation);
+        self.inner.values[..self.num_instances() * num_rotation * self.n_col()]
+            .chunks(num_rotation * self.inner.width)
     }
 
     pub fn iter_mut(&mut self) -> ChunksMut<'_, T> {
-        let max_range = self.num_instances() * self.n_col();
-        self.inner.values[..max_range].chunks_mut(self.inner.width)
+        let num_rotation = Self::num_rotation(self.log2_num_rotation);
+        let max_range = self.num_instances() * num_rotation * self.n_col();
+        self.inner.values[..max_range].chunks_mut(num_rotation * self.inner.width)
     }
 
     pub fn par_batch_iter_mut(&mut self, num_rows: usize) -> rayon::slice::ChunksMut<'_, T> {
-        let max_range = self.num_instances() * self.n_col();
-        self.inner.values[..max_range].par_chunks_mut(num_rows * self.inner.width)
+        let num_rotation = Self::num_rotation(self.log2_num_rotation);
+        let max_range = self.num_instances() * self.n_col() * num_rotation;
+        self.inner.values[..max_range].par_chunks_mut(num_rows * num_rotation * self.inner.width)
     }
 
     pub fn padding_by_strategy(&mut self) {
-        let start_index = self.num_instances() * self.n_col();
+        let num_rotation = Self::num_rotation(self.log2_num_rotation);
+        let start_index = self.num_instances() * num_rotation * self.n_col();
 
         match &self.padding_strategy {
             InstancePaddingStrategy::Default => (),
             InstancePaddingStrategy::Custom(fun) => {
                 self.inner.values[start_index..]
-                    .par_chunks_mut(self.inner.width)
+                    .par_chunks_mut(num_rotation * self.inner.width)
                     .enumerate()
                     .for_each(|(i, instance)| {
                         instance.iter_mut().enumerate().for_each(|(j, v)| {
@@ -277,8 +307,9 @@ impl<F: Sync + Send + Copy + FieldAlgebra> Index<usize> for RowMajorMatrix<F> {
     type Output = [F];
 
     fn index(&self, idx: usize) -> &Self::Output {
+        let num_rotation = Self::num_rotation(self.log2_num_rotation);
         let num_col = self.n_col();
-        &self.inner.values[num_col * idx..][..num_col]
+        &self.inner.values[num_rotation * num_col * idx..][..num_rotation * num_col]
     }
 }