diff --git a/src/protocol/oprf/shuffle/mod.rs b/src/protocol/oprf/shuffle/mod.rs
index 29faff337..536cb7d14 100644
--- a/src/protocol/oprf/shuffle/mod.rs
+++ b/src/protocol/oprf/shuffle/mod.rs
@@ -10,6 +10,10 @@ use super::super::{
 use crate::{
     error::Error,
     helpers::{Direction, Message, ReceivingEnd, Role},
+    secret_sharing::{
+        replicated::{semi_honest::AdditiveShare, ReplicatedSecretSharing},
+        SharedValue,
+    },
 };
 
 #[derive(Step)]
@@ -25,16 +29,11 @@ pub(crate) enum OPRFShuffleStep {
 
 /// # Errors
 /// Will propagate errors from transport and a few typecasts
-pub async fn shuffle<C, S, Sl, Sr>(
-    ctx: C,
-    batch_size: u32,
-    shares: (Sl, Sr),
-) -> Result<(Vec<S>, Vec<S>), Error>
+pub async fn shuffle<C, I, S>(ctx: C, batch_size: u32, shares: I) -> Result<(Vec<S>, Vec<S>), Error>
 where
     C: Context,
-    Sl: IntoIterator<Item = S>,
-    Sr: IntoIterator<Item = S>,
-    S: Clone + Add<Output = S> + Message,
+    I: IntoIterator<Item = AdditiveShare<S>>,
+    S: SharedValue + Add<Output = S> + Message,
     for<'b> &'b S: Add<S, Output = S>,
     for<'b> &'b S: Add<&'b S, Output = S>,
     Standard: Distribution<S>,
@@ -49,24 +48,23 @@ where
     match ctx.role() {
         Role::H1 => run_h1(&ctx, batch_size, shares, pis, zs).await,
         Role::H2 => run_h2(&ctx, batch_size, shares, pis, zs).await,
-        Role::H3 => run_h3(&ctx, batch_size, shares, pis, zs).await,
+        Role::H3 => run_h3(&ctx, batch_size, pis, zs).await,
     }
 }
 
-async fn run_h1<C, Sl, S, Sr, Zl, Zr>(
+async fn run_h1<C, I, S, Zl, Zr>(
     ctx: &C,
     batch_size: u32,
-    (a, b): (Sl, Sr),
+    shares: I,
     (pi_31, pi_12): (Vec<u32>, Vec<u32>),
     (z_31, z_12): (Zl, Zr),
 ) -> Result<(Vec<S>, Vec<S>), Error>
 where
     C: Context,
-    Sl: IntoIterator<Item = S>,
-    Sr: IntoIterator<Item = S>,
+    I: IntoIterator<Item = AdditiveShare<S>>,
+    S: SharedValue + Add<Output = S> + Message,
     Zl: IntoIterator<Item = S>,
     Zr: IntoIterator<Item = S>,
-    S: Clone + Add<Output = S> + Message,
     for<'a> &'a S: Add<Output = S>,
     Standard: Distribution<S>,
 {
@@ -80,7 +78,10 @@ where
         generate_random_table_solo(batch_size, &ctx_b_hat, Direction::Right).collect();
 
     // 2. Run computations
-    let mut x_1: Vec<S> = add_single_shares(add_single_shares(a, b), z_12).collect();
+    let a_add_b_iter = shares
+        .into_iter()
+        .map(|s: AdditiveShare<S>| s.left().add(s.right()));
+    let mut x_1: Vec<S> = add_single_shares(a_add_b_iter, z_12).collect();
     apply_permutation(&pi_12, &mut x_1);
 
     let mut x_2: Vec<S> = add_single_shares(x_1, z_31).collect();
@@ -91,20 +92,19 @@ where
     Ok((a_hat, b_hat))
 }
 
-async fn run_h2<C, S, Sl, Sr, Zl, Zr>(
+async fn run_h2<C, I, S, Zl, Zr>(
     ctx: &C,
     batch_size: u32,
-    (_b, c): (Sl, Sr),
+    shares: I,
     (pi_12, pi_23): (Vec<u32>, Vec<u32>),
     (z_12, z_23): (Zl, Zr),
 ) -> Result<(Vec<S>, Vec<S>), Error>
 where
     C: Context,
-    Sl: IntoIterator<Item = S>,
-    Sr: IntoIterator<Item = S>,
+    I: IntoIterator<Item = AdditiveShare<S>>,
+    S: SharedValue + Add<Output = S> + Message,
     Zl: IntoIterator<Item = S>,
     Zr: IntoIterator<Item = S>,
-    S: Clone + Add<Output = S> + Message,
     for<'a> &'a S: Add<S, Output = S>,
     for<'a> &'a S: Add<&'a S, Output = S>,
     Standard: Distribution<S>,
@@ -115,6 +115,7 @@ where
         generate_random_table_solo(batch_size, &ctx_b_hat, Direction::Left).collect();
 
     // 2. Run computations
+    let c = shares.into_iter().map(|s| s.right());
     let mut y_1: Vec<S> = add_single_shares(c, z_12).collect();
     apply_permutation(&pi_12, &mut y_1);
 
@@ -153,17 +154,15 @@ where
     Ok((b_hat, c_hat))
 }
 
-async fn run_h3<C, S, Sl, Sr, Zl, Zr>(
+async fn run_h3<C, S, Zl, Zr>(
     ctx: &C,
     batch_size: u32,
-    (_c, _a): (Sl, Sr),
     (pi_23, pi_31): (Vec<u32>, Vec<u32>),
     (z_23, z_31): (Zl, Zr),
 ) -> Result<(Vec<S>, Vec<S>), Error>
 where
     C: Context,
-    Sl: IntoIterator<Item = S>,
-    Sr: IntoIterator<Item = S>,
+    S: SharedValue + Add<Output = S> + Message,
     Zl: IntoIterator<Item = S>,
     Zr: IntoIterator<Item = S>,
     S: Clone + Add<Output = S> + Message,
diff --git a/src/query/runner/oprf_shuffle/query.rs b/src/query/runner/oprf_shuffle/query.rs
index cdcac3a31..21365fc0b 100644
--- a/src/query/runner/oprf_shuffle/query.rs
+++ b/src/query/runner/oprf_shuffle/query.rs
@@ -9,6 +9,7 @@ use crate::{
     },
     one_off_fns::assert_stream_send,
     protocol::{context::Context, oprf::shuffle::shuffle},
+    secret_sharing::replicated::{semi_honest::AdditiveShare, ReplicatedSecretSharing},
 };
 
 pub struct OPRFShuffleQuery {
@@ -39,11 +40,7 @@ impl OPRFShuffleQuery {
             ))
         })?;
 
-        let shares = (
-            split_shares(input.as_slice(), Direction::Left),
-            split_shares(input.as_slice(), Direction::Right),
-        );
-
+        let shares = split_shares(&input);
         let (res_l, res_r) = shuffle(ctx, batch_size, shares).await?;
         Ok(combine_shares(res_l, res_r))
     }
@@ -51,9 +48,13 @@ impl OPRFShuffleQuery {
 
 fn split_shares(
     input_rows: &[ShuffleInputRow],
-    direction: Direction,
-) -> impl Iterator<Item = ShuffleShare> + '_ {
-    let f = move |input_row| ShuffleShare::from_input_row(input_row, direction);
+) -> impl Iterator<Item = AdditiveShare<ShuffleShare>> + '_ {
+    let f = move |input_row| {
+        let l = ShuffleShare::from_input_row(input_row, Direction::Left);
+        let r = ShuffleShare::from_input_row(input_row, Direction::Right);
+        ReplicatedSecretSharing::new(l, r)
+    };
+
     input_rows.iter().map(f)
 }
 
diff --git a/src/query/runner/oprf_shuffle/share.rs b/src/query/runner/oprf_shuffle/share.rs
index 168691a40..8d1edac2b 100644
--- a/src/query/runner/oprf_shuffle/share.rs
+++ b/src/query/runner/oprf_shuffle/share.rs
@@ -1,4 +1,4 @@
-use std::ops::Add;
+use std::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign};
 
 use generic_array::GenericArray;
 use rand::{distributions::Standard, Rng};
@@ -7,13 +7,14 @@ use typenum::Unsigned;
 use super::ShuffleInputRow;
 use crate::{
     ff::{Field, Gf32Bit, Gf40Bit, Gf8Bit, Serializable},
-    helpers::{Direction, Message},
+    helpers::Direction,
+    secret_sharing::SharedValue,
 };
 pub type ShuffleShareMK = Gf40Bit;
 pub type ShuffleShareBK = Gf8Bit;
 pub type ShuffleShareF = Gf32Bit;
 
-#[derive(Debug, Clone, Copy)]
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
 pub struct ShuffleShare {
     pub timestamp: ShuffleShareF,
     pub mk: ShuffleShareMK,
@@ -22,6 +23,91 @@ pub struct ShuffleShare {
     pub trigger_value: ShuffleShareF,
 }
 
+impl AddAssign for ShuffleShare {
+    fn add_assign(&mut self, rhs: Self) {
+        self.timestamp += rhs.timestamp;
+        self.mk += rhs.mk;
+        self.is_trigger_bit += rhs.is_trigger_bit;
+        self.breakdown_key += rhs.breakdown_key;
+        self.trigger_value += rhs.trigger_value;
+    }
+}
+impl Sub for ShuffleShare {
+    type Output = Self;
+
+    fn sub(self, rhs: Self) -> Self::Output {
+        Self::Output {
+            timestamp: self.timestamp - rhs.timestamp,
+            mk: self.mk - rhs.mk,
+            is_trigger_bit: self.is_trigger_bit - rhs.is_trigger_bit,
+            breakdown_key: self.breakdown_key - rhs.breakdown_key,
+            trigger_value: self.trigger_value - rhs.trigger_value,
+        }
+    }
+}
+impl SubAssign for ShuffleShare {
+    fn sub_assign(&mut self, rhs: Self) {
+        self.timestamp -= rhs.timestamp;
+        self.mk -= rhs.mk;
+        self.is_trigger_bit -= rhs.is_trigger_bit;
+        self.breakdown_key -= rhs.breakdown_key;
+        self.trigger_value -= rhs.trigger_value;
+    }
+}
+impl Neg for ShuffleShare {
+    type Output = Self;
+
+    fn neg(self) -> Self::Output {
+        Self::Output {
+            timestamp: self.timestamp.neg(),
+            mk: self.mk.neg(),
+            is_trigger_bit: self.is_trigger_bit.neg(),
+            breakdown_key: self.breakdown_key.neg(),
+            trigger_value: self.trigger_value.neg(),
+        }
+    }
+}
+impl Mul for ShuffleShare {
+    type Output = Self;
+
+    fn mul(self, rhs: Self) -> Self::Output {
+        Self::Output {
+            timestamp: self.timestamp * rhs.timestamp,
+            mk: self.mk * rhs.mk,
+            is_trigger_bit: self.is_trigger_bit * rhs.is_trigger_bit,
+            breakdown_key: self.breakdown_key * rhs.breakdown_key,
+            trigger_value: self.trigger_value * rhs.trigger_value,
+        }
+    }
+}
+impl MulAssign for ShuffleShare {
+    fn mul_assign(&mut self, rhs: Self) {
+        self.timestamp *= rhs.timestamp;
+        self.mk *= rhs.mk;
+        self.is_trigger_bit *= rhs.is_trigger_bit;
+        self.breakdown_key *= rhs.breakdown_key;
+        self.trigger_value *= rhs.trigger_value;
+    }
+}
+
+impl SharedValue for ShuffleShare {
+    type Storage = <ShuffleShareF as SharedValue>::Storage;
+
+    const BITS: u32 = ShuffleShareF::BITS
+        + ShuffleShareMK::BITS
+        + ShuffleShareF::BITS
+        + ShuffleShareBK::BITS
+        + ShuffleShareF::BITS;
+
+    const ZERO: Self = Self {
+        timestamp: ShuffleShareF::ZERO,
+        mk: ShuffleShareMK::ZERO,
+        is_trigger_bit: ShuffleShareF::ZERO,
+        breakdown_key: ShuffleShareBK::ZERO,
+        trigger_value: ShuffleShareF::ZERO,
+    };
+}
+
 impl ShuffleShare {
     #[must_use]
     pub fn from_input_row(input_row: &ShuffleInputRow, shared_with: Direction) -> Self {
@@ -153,5 +239,3 @@ impl Serializable for ShuffleShare {
         }
     }
 }
-
-impl Message for ShuffleShare {}
diff --git a/src/secret_sharing/replicated/semi_honest/additive_share.rs b/src/secret_sharing/replicated/semi_honest/additive_share.rs
index 10b8b2b39..b1eb2a850 100644
--- a/src/secret_sharing/replicated/semi_honest/additive_share.rs
+++ b/src/secret_sharing/replicated/semi_honest/additive_share.rs
@@ -20,7 +20,6 @@ pub struct AdditiveShare<V: SharedValue>(V, V);
 impl<V: SharedValue> SecretSharing<V> for AdditiveShare<V> {
     const ZERO: Self = AdditiveShare::ZERO;
 }
-
 impl<V: SharedValue> LinearSecretSharing<V> for AdditiveShare<V> {}
 
 impl<V: SharedValue + Debug> Debug for AdditiveShare<V> {