diff --git a/circuits/lib/src/configs/insecure/threshold.nr b/circuits/lib/src/configs/insecure/threshold.nr
index f4b520f984..91bc812cdd 100644
--- a/circuits/lib/src/configs/insecure/threshold.nr
+++ b/circuits/lib/src/configs/insecure/threshold.nr
@@ -1167,7 +1167,7 @@ pub global THRESHOLD_SHARE_DECRYPTION_BIT_R1: u32 = 43;
 pub global THRESHOLD_SHARE_DECRYPTION_BIT_R2: u32 = 35;
 pub global THRESHOLD_SHARE_DECRYPTION_BIT_D: u32 = 35;
 
-pub global THRESHOLD_SHARE_DECRYPTION_R1_BOUNDS: [Field; L] = [8796083584897, 8796061564801];
+pub global THRESHOLD_SHARE_DECRYPTION_R1_BOUNDS: [Field; L] = [8796083584898, 8796061564802];
 pub global THRESHOLD_SHARE_DECRYPTION_R2_BOUNDS: [Field; L] = [34359701504, 34359615488];
 
 pub global THRESHOLD_SHARE_DECRYPTION_CONFIGS: ShareDecryptionConfigs<L> = ShareDecryptionConfigs::new(
diff --git a/circuits/lib/src/configs/secure/threshold.nr b/circuits/lib/src/configs/secure/threshold.nr
index d5dc2c4c52..40ec5fbc58 100644
--- a/circuits/lib/src/configs/secure/threshold.nr
+++ b/circuits/lib/src/configs/secure/threshold.nr
@@ -32916,7 +32916,7 @@ pub global THRESHOLD_SHARE_DECRYPTION_BIT_R2: u32 = 52;
 pub global THRESHOLD_SHARE_DECRYPTION_BIT_D: u32 = 52;
 
 pub global THRESHOLD_SHARE_DECRYPTION_R1_BOUNDS: [Field; L] =
-    [4611686035875690497, 9223372037660080129, 9223372045176272897, 9223372051618723841];
+    [4611686035875690498, 9223372037660080130, 9223372045176272898, 9223372051618723842];
 pub global THRESHOLD_SHARE_DECRYPTION_R2_BOUNDS: [Field; L] =
     [1125899911102464, 2251799813881856, 2251799815716864, 2251799817289728];
 
diff --git a/circuits/lib/src/core/threshold/pk_generation.nr b/circuits/lib/src/core/threshold/pk_generation.nr
index e4ccc80171..45b9320c14 100644
--- a/circuits/lib/src/core/threshold/pk_generation.nr
+++ b/circuits/lib/src/core/threshold/pk_generation.nr
@@ -100,12 +100,7 @@ impl<let N: u32, let L: u32, let BIT_EEK: u32, let BIT_SK: u32, let BIT_E_SM: u3
     }
 
     /// Flattens all witness data into a single array for Fiat-Shamir challenge generation
-    fn payload(
-        self,
-        sk_commitment: Field,
-        pk_commitment: Field,
-        e_sm_commitment: Field,
-    ) -> Vec<Field> {
+    fn payload(self, sk_commitment: Field, pk_commitment: Field) -> Vec<Field> {
         let mut inputs = Vec::new();
 
         // Flatten CRS polynomials a (L polynomials of degree N)
@@ -117,7 +112,6 @@ impl<let N: u32, let L: u32, let BIT_EEK: u32, let BIT_SK: u32, let BIT_E_SM: u3
         // Use commitments instead of full polynomials
         inputs.push(sk_commitment);
         inputs.push(pk_commitment);
-        inputs.push(e_sm_commitment);
 
         // Flatten quotient polynomials (L polynomials each)
         inputs = flatten::<_, _, BIT_R1>(inputs, self.r1);
@@ -129,38 +123,24 @@ impl<let N: u32, let L: u32, let BIT_EEK: u32, let BIT_SK: u32, let BIT_E_SM: u3
     /// Main execution function
     /// Returns (commit(threshold_sk), commit(threshold_pk), commit(e_sm))
     pub fn execute(self) -> (Field, Field, Field) {
-        // Step 1: Perform range checks on all secret witness values
         self.perform_range_checks();
 
-        // Step 2: Compute commitments
         let sk_commitment = compute_share_computation_sk_commitment::<N, BIT_SK>(self.sk);
         let e_sm_commitment =
             compute_share_computation_e_sm_commitment::<N, L, BIT_E_SM>(self.e_sm);
         let pk_commitment = compute_threshold_pk_commitment::<N, L, BIT_PK>(self.pk0, self.pk1);
 
-        // Step 3: Generate Fiat-Shamir challenges using commitments
-        let gammas = self.generate_challenge(sk_commitment, pk_commitment, e_sm_commitment);
+        let gamma = self.generate_challenge(sk_commitment, pk_commitment);
+        self.verify_evaluations(gamma);
 
-        // Step 4: Verify public key equations for each modulus
-        for i in 0..L {
-            let gamma = gammas.get(i);
-            self.verify_public_key_for_modulus(i, gamma);
-        }
-
-        // Step 5: Return all commitments
         (sk_commitment, pk_commitment, e_sm_commitment)
     }
 
     /// Generates Fiat-Shamir challenge values using the SAFE cryptographic sponge
-    fn generate_challenge(
-        self,
-        sk_commitment: Field,
-        pk_commitment: Field,
-        e_sm_commitment: Field,
-    ) -> Vec<Field> {
-        let inputs = self.payload(sk_commitment, pk_commitment, e_sm_commitment);
-
-        compute_threshold_pk_challenge::<L>(inputs)
+    fn generate_challenge(self, sk_commitment: Field, pk_commitment: Field) -> Field {
+        let inputs = self.payload(sk_commitment, pk_commitment);
+
+        compute_threshold_pk_challenge(inputs)
     }
 
     /// Performs range checks on all secret witness values
@@ -190,32 +170,22 @@ impl<let N: u32, let L: u32, let BIT_EEK: u32, let BIT_SK: u32, let BIT_E_SM: u3
         }
     }
 
-    /// Verifies the threshold public key generation equations for a specific CRT basis
-    fn verify_public_key_for_modulus(self, i: u32, gamma: Field) {
-        // Evaluate all polynomials at the random challenge point gamma
-        let a_at_gamma = self.a.map(|a_poly| a_poly.eval(gamma));
-
-        let eek_at_gamma = self.eek.eval(gamma);
-        let sk_at_gamma = self.sk.eval(gamma);
-
-        let r1_at_gamma = self.r1.map(|r1_poly| r1_poly.eval(gamma));
-        let r2_at_gamma = self.r2.map(|r2_poly| r2_poly.eval(gamma));
-
-        let pk0_at_gamma = self.pk0.map(|pk0_poly| pk0_poly.eval(gamma));
-        let pk1_at_gamma = self.pk1.map(|pk1_poly| pk1_poly.eval(gamma));
-
-        // Evaluate the cyclotomic polynomial X^N + 1 at gamma
+    fn verify_evaluations(self, gamma: Field) {
         let cyclo_at_gamma = gamma.pow_32(N as Field) + 1;
+        let sk_at_gamma = self.sk.eval(gamma);
+        let eek_at_gamma = self.eek.eval(gamma);
 
-        // pk0_i = -a_i * sk + eek + r2_i * (X^N + 1) + r1_i * q_i
-        let expected_pk0 = -a_at_gamma[i] * sk_at_gamma
-            + eek_at_gamma
-            + r2_at_gamma[i] * cyclo_at_gamma
-            + r1_at_gamma[i] * self.configs.qis[i];
-
-        assert(pk0_at_gamma[i] == expected_pk0, "Public key equation 1 failed");
-
-        // Equation 2: pk1_i = a_i
-        assert(pk1_at_gamma[i] == a_at_gamma[i], "Public key equation 2 failed");
+        for i in 0..L {
+            let expected_pk0 = -self.a[i].eval(gamma) * sk_at_gamma
+                + eek_at_gamma
+                + self.r2[i].eval(gamma) * cyclo_at_gamma
+                + self.r1[i].eval(gamma) * self.configs.qis[i];
+
+            assert(self.pk0[i].eval(gamma) == expected_pk0, "Public key equation 1 failed");
+            assert(
+                self.pk1[i].eval(gamma) == self.a[i].eval(gamma),
+                "Public key equation 2 failed",
+            );
+        }
     }
 }
diff --git a/circuits/lib/src/math/commitments.nr b/circuits/lib/src/math/commitments.nr
index 9f3d842b21..0da0568ecf 100644
--- a/circuits/lib/src/math/commitments.nr
+++ b/circuits/lib/src/math/commitments.nr
@@ -244,8 +244,8 @@ pub fn compute_ciphertext_commitment<let N: u32, let L: u32, let BIT_CT: u32>(
 
 /// COMMITMENTS FOR CHALLENGES
 
-pub fn compute_threshold_pk_challenge<let L: u32>(payload: Vec<Field>) -> Vec<Field> {
-    compute_challenge::<L>(payload, DS_CLG_PK_GENERATION)
+pub fn compute_threshold_pk_challenge(payload: Vec<Field>) -> Field {
+    compute_commitment(payload, DS_CLG_PK_GENERATION)
 }
 
 pub fn compute_share_encryption_challenge<let L: u32>(payload: Vec<Field>) -> Vec<Field> {
diff --git a/crates/zk-helpers/src/circuits/commitments.rs b/crates/zk-helpers/src/circuits/commitments.rs
index 1d7bd61d43..b145b1808d 100644
--- a/crates/zk-helpers/src/circuits/commitments.rs
+++ b/crates/zk-helpers/src/circuits/commitments.rs
@@ -424,21 +424,16 @@ pub fn compute_aggregated_shares_commitment(agg_shares: &CrtPolynomial, bit_msg:
 ///
 /// # Arguments
 /// * `payload` - Prepared payload as a vector of field elements
-/// * `l` - Number of moduli
 ///
 /// # Returns
-/// A vector of `BigInt` challenges (2*L elements)
-pub fn compute_threshold_pk_challenge(payload: Vec<Field>, l: usize) -> Vec<BigInt> {
+/// A `BigInt` representing the commitment hash value
+pub fn compute_threshold_pk_challenge(payload: Vec<Field>) -> BigInt {
     let input_size = payload.len() as u32;
-    let io_pattern = [0x80000000 | input_size, (2 * l as u32)];
+    let io_pattern = [0x80000000 | input_size, 1];
 
-    compute_commitments(payload, DS_CLG_PK_GENERATION, io_pattern)
-        .into_iter()
-        .map(|challenge_field| {
-            let challenge_bytes = challenge_field.into_bigint().to_bytes_le();
-            BigInt::from_bytes_le(num_bigint::Sign::Plus, &challenge_bytes)
-        })
-        .collect()
+    let challenge_field = compute_commitments(payload, DS_CLG_PK_GENERATION, io_pattern)[0];
+    let challenge_bytes = challenge_field.into_bigint().to_bytes_le();
+    BigInt::from_bytes_le(num_bigint::Sign::Plus, &challenge_bytes)
 }
 
 /// Compute share encryption challenge.
@@ -600,12 +595,16 @@ mod tests {
     }
 
     #[test]
-    fn compute_threshold_pk_challenge_returns_2l_elements() {
+    fn compute_threshold_pk_challenge_returns_single_bigint() {
         let payload = vec![Field::from(1u64), Field::from(2u64)];
-        let l = 3;
+        let input_size = payload.len() as u32;
+        let io_pattern = [0x80000000 | input_size, 1];
+        let expected_challenge = field_to_bigint(
+            compute_commitments(payload.clone(), DS_CLG_PK_GENERATION, io_pattern)[0],
+        );
 
-        let challenges = compute_threshold_pk_challenge(payload, l);
-        assert_eq!(challenges.len(), 2 * l);
+        let challenge = compute_threshold_pk_challenge(payload);
+        assert_eq!(challenge, expected_challenge);
     }
 
     #[test]
diff --git a/crates/zk-helpers/src/circuits/threshold/share_decryption/computation.rs b/crates/zk-helpers/src/circuits/threshold/share_decryption/computation.rs
index 1a999fe702..839e3dc631 100644
--- a/crates/zk-helpers/src/circuits/threshold/share_decryption/computation.rs
+++ b/crates/zk-helpers/src/circuits/threshold/share_decryption/computation.rs
@@ -177,11 +177,11 @@ impl Computation for Bounds {
             // r_2j bounds: [- (q_j-1)/2 , (q_j-1)/2] (cyclotomic quotients)
             r2_bounds.push(qi_bound.clone());
 
-            // r_1j upper bound: (qi_bound * (qi_bound * n + 3) - qi_bound) / qi_bigint
+            // r_1j upper bound: (n * ((q_j-1)/2)^2 + 4 * (q_j-1)/2) / q_j
             // Symmetric lower bound used by range_check_2bounds. Variables: qi_bound = (q_j-1)/2,
             // qi_bigint = q_j, n = degree.
             r1_bounds.push(
-                (&qi_bound * (&qi_bound.clone() * &n + BigInt::from(3)) - &qi_bound.clone())
+                (&qi_bound.clone() * &qi_bound.clone() * &n + BigInt::from(4) * &qi_bound.clone())
                     / &qi_bigint,
             );
         }