diff --git a/ferveo-wasm/tests/node.rs b/ferveo-wasm/tests/node.rs
index b4234d07..25f24d9f 100644
--- a/ferveo-wasm/tests/node.rs
+++ b/ferveo-wasm/tests/node.rs
@@ -8,8 +8,9 @@ use wasm_bindgen_test::*;
 
 type TestSetup = (
     u32,
-    usize,
-    usize,
+    u32,
+    u32,
+    u32,
     Vec<Keypair>,
     Vec<Validator>,
     ValidatorArray,
@@ -21,11 +22,13 @@ type TestSetup = (
 
 fn setup_dkg() -> TestSetup {
     let tau = 1;
-    let shares_num = 16;
+    let shares_num: u32 = 16;
     let security_threshold = shares_num * 2 / 3;
+    let min_shares_num = shares_num;
 
-    let validator_keypairs =
-        (0..shares_num).map(gen_keypair).collect::<Vec<Keypair>>();
+    let validator_keypairs = (0..shares_num as usize)
+        .map(gen_keypair)
+        .collect::<Vec<Keypair>>();
     let validators = validator_keypairs
         .iter()
         .enumerate()
@@ -38,8 +41,9 @@ fn setup_dkg() -> TestSetup {
     let messages = validators.iter().map(|sender| {
         let dkg = Dkg::new(
             tau,
-            shares_num as u32,
-            security_threshold as u32,
+            shares_num,
+            min_shares_num,
+            security_threshold,
             &validators_js,
             sender,
         )
@@ -54,8 +58,9 @@ fn setup_dkg() -> TestSetup {
 
     let mut dkg = Dkg::new(
         tau,
-        shares_num as u32,
-        security_threshold as u32,
+        shares_num,
+        min_shares_num,
+        security_threshold,
         &validators_js,
         &validators[0],
     )
@@ -81,6 +86,7 @@ fn setup_dkg() -> TestSetup {
     (
         tau,
         shares_num,
+        min_shares_num,
         security_threshold,
         validator_keypairs,
         validators,
@@ -97,6 +103,7 @@ fn tdec_simple() {
     let (
         tau,
         shares_num,
+        min_shares_num,
         security_threshold,
         validator_keypairs,
         validators,
@@ -112,8 +119,9 @@ fn tdec_simple() {
         .map(|(validator, keypair)| {
             let mut dkg = Dkg::new(
                 tau,
-                shares_num as u32,
-                security_threshold as u32,
+                shares_num,
+                min_shares_num,
+                security_threshold,
                 &validators_js,
                 &validator,
             )
@@ -151,6 +159,7 @@ fn tdec_precomputed() {
     let (
         tau,
         shares_num,
+        min_shares_num,
         security_threshold,
         validator_keypairs,
         validators,
@@ -166,8 +175,9 @@ fn tdec_precomputed() {
         .map(|(validator, keypair)| {
             let mut dkg = Dkg::new(
                 tau,
-                shares_num as u32,
-                security_threshold as u32,
+                shares_num,
+                min_shares_num,
+                security_threshold,
                 &validators_js,
                 &validator,
             )
diff --git a/ferveo/benches/benchmarks/validity_checks.rs b/ferveo/benches/benchmarks/validity_checks.rs
index a6dd9f48..381f1070 100644
--- a/ferveo/benches/benchmarks/validity_checks.rs
+++ b/ferveo/benches/benchmarks/validity_checks.rs
@@ -45,11 +45,7 @@ fn setup_dkg(
     let me = validators[validator].clone();
     PubliclyVerifiableDkg::new(
         &validators,
-        &DkgParams {
-            tau: 0,
-            security_threshold: shares_num / 3,
-            shares_num,
-        },
+        &DkgParams::new(0, shares_num / 3, shares_num, shares_num).unwrap(),
         &me,
     )
     .expect("Setup failed")
diff --git a/ferveo/examples/bench_primitives_size.rs b/ferveo/examples/bench_primitives_size.rs
index 18adf673..8f133200 100644
--- a/ferveo/examples/bench_primitives_size.rs
+++ b/ferveo/examples/bench_primitives_size.rs
@@ -80,11 +80,7 @@ fn setup_dkg(
     let me = validators[validator].clone();
     PubliclyVerifiableDkg::new(
         &validators,
-        &DkgParams {
-            tau: 0,
-            security_threshold,
-            shares_num,
-        },
+        &DkgParams::new(0, security_threshold, shares_num, shares_num).unwrap(),
         &me,
     )
     .expect("Setup failed")
diff --git a/ferveo/src/api.rs b/ferveo/src/api.rs
index af3edcd4..e62a718a 100644
--- a/ferveo/src/api.rs
+++ b/ferveo/src/api.rs
@@ -199,15 +199,17 @@ impl Dkg {
     pub fn new(
         tau: u32,
         shares_num: u32,
+        min_shares_num: u32,
         security_threshold: u32,
         validators: &[Validator],
         me: &Validator,
     ) -> Result<Self> {
-        let dkg_params = crate::DkgParams {
+        let dkg_params = crate::DkgParams::new(
             tau,
             security_threshold,
+            min_shares_num,
             shares_num,
-        };
+        )?;
         let dkg = crate::PubliclyVerifiableDkg::<E>::new(
             validators,
             &dkg_params,
@@ -312,7 +314,7 @@ impl AggregatedTranscript {
             .0
             .domain
             .elements()
-            .take(dkg.0.dkg_params.shares_num as usize)
+            .take(dkg.0.dkg_params.shares_num() as usize)
             .collect();
         self.0.make_decryption_share_simple_precomputed(
             &ciphertext_header.0,
@@ -406,6 +408,7 @@ mod test_ferveo_api {
         rng: &mut StdRng,
         tau: u32,
         security_threshold: u32,
+        min_shares_num: u32,
         shares_num: u32,
     ) -> TestInputs {
         let validator_keypairs = gen_keypairs(shares_num);
@@ -426,6 +429,7 @@ mod test_ferveo_api {
                 let dkg = Dkg::new(
                     tau,
                     shares_num,
+                    min_shares_num,
                     security_threshold,
                     &validators,
                     sender,
@@ -456,16 +460,28 @@ mod test_ferveo_api {
             // TODO: Refactor DKG constructor to not require security threshold or this case.
             //  Or figure out a different way to simplify the precomputed variant API.
             let security_threshold = shares_num;
+            let min_shares_num = shares_num;
 
-            let (messages, validators, validator_keypairs) =
-                make_test_inputs(rng, tau, security_threshold, shares_num);
+            let (messages, validators, validator_keypairs) = make_test_inputs(
+                rng,
+                tau,
+                security_threshold,
+                min_shares_num,
+                shares_num,
+            );
 
             // Now that every validator holds a dkg instance and a transcript for every other validator,
             // every validator can aggregate the transcripts
             let me = validators[0].clone();
-            let mut dkg =
-                Dkg::new(tau, shares_num, security_threshold, &validators, &me)
-                    .unwrap();
+            let mut dkg = Dkg::new(
+                tau,
+                shares_num,
+                min_shares_num,
+                security_threshold,
+                &validators,
+                &me,
+            )
+            .unwrap();
 
             let pvss_aggregated = dkg.aggregate_transcripts(&messages).unwrap();
             assert!(pvss_aggregated.verify(shares_num, &messages).unwrap());
@@ -489,6 +505,7 @@ mod test_ferveo_api {
                             tau,
                             shares_num,
                             security_threshold,
+                            min_shares_num,
                             &validators,
                             validator,
                         )
@@ -546,15 +563,22 @@ mod test_ferveo_api {
         for shares_num in [4, 7] {
             let tau = 1;
             let security_threshold = shares_num / 2 + 1;
+            let min_shares_num = shares_num;
 
-            let (messages, validators, validator_keypairs) =
-                make_test_inputs(rng, tau, security_threshold, shares_num);
+            let (messages, validators, validator_keypairs) = make_test_inputs(
+                rng,
+                tau,
+                security_threshold,
+                min_shares_num,
+                shares_num,
+            );
 
             // Now that every validator holds a dkg instance and a transcript for every other validator,
             // every validator can aggregate the transcripts
             let mut dkg = Dkg::new(
                 tau,
                 shares_num,
+                min_shares_num,
                 security_threshold,
                 &validators,
                 &validators[0],
@@ -581,6 +605,7 @@ mod test_ferveo_api {
                         let mut dkg = Dkg::new(
                             tau,
                             shares_num,
+                            min_shares_num,
                             security_threshold,
                             &validators,
                             validator,
@@ -632,22 +657,34 @@ mod test_ferveo_api {
         let rng = &mut StdRng::seed_from_u64(0);
 
         let tau = 1;
-        let security_threshold = 3;
         let shares_num = 4;
+        let min_shares_num = shares_num;
+        let security_threshold = shares_num - 1;
 
-        let (messages, validators, _) =
-            make_test_inputs(rng, tau, security_threshold, shares_num);
+        let (messages, validators, _) = make_test_inputs(
+            rng,
+            tau,
+            security_threshold,
+            min_shares_num,
+            shares_num,
+        );
 
         // Now that every validator holds a dkg instance and a transcript for every other validator,
         // every validator can aggregate the transcripts
         let me = validators[0].clone();
-        let mut dkg =
-            Dkg::new(tau, shares_num, security_threshold, &validators, &me)
-                .unwrap();
+        let mut dkg = Dkg::new(
+            tau,
+            shares_num,
+            min_shares_num,
+            security_threshold,
+            &validators,
+            &me,
+        )
+        .unwrap();
 
         let local_aggregate = dkg.aggregate_transcripts(&messages).unwrap();
         assert!(local_aggregate
-            .verify(dkg.0.dkg_params.shares_num, &messages)
+            .verify(dkg.0.dkg_params.shares_num(), &messages)
             .is_ok());
     }
 
@@ -656,11 +693,17 @@ mod test_ferveo_api {
         let rng = &mut StdRng::seed_from_u64(0);
 
         let tau = 1;
-        let security_threshold = 3;
         let shares_num = 4;
+        let security_threshold = shares_num - 1;
+        let min_shares_num = shares_num;
 
-        let (messages, _, _) =
-            make_test_inputs(rng, tau, security_threshold, shares_num);
+        let (messages, _, _) = make_test_inputs(
+            rng,
+            tau,
+            security_threshold,
+            min_shares_num,
+            shares_num,
+        );
 
         // We only need `security_threshold` transcripts to aggregate
         let messages = &messages[..security_threshold as usize];
@@ -688,8 +731,13 @@ mod test_ferveo_api {
 
         // Unexpected transcripts in the aggregate or transcripts from a different ritual
         // Using same DKG parameters, but different DKG instances and validators
-        let (bad_messages, _, _) =
-            make_test_inputs(rng, tau, security_threshold, shares_num);
+        let (bad_messages, _, _) = make_test_inputs(
+            rng,
+            tau,
+            security_threshold,
+            min_shares_num,
+            shares_num,
+        );
         let mixed_messages = [&messages[..2], &bad_messages[..1]].concat();
         let bad_aggregate = AggregatedTranscript::new(&mixed_messages);
         let result = bad_aggregate.verify(shares_num, messages);
diff --git a/ferveo/src/bindings_python.rs b/ferveo/src/bindings_python.rs
index ed965f3e..09fa0753 100644
--- a/ferveo/src/bindings_python.rs
+++ b/ferveo/src/bindings_python.rs
@@ -93,6 +93,11 @@ impl From<FerveoPythonError> for PyErr {
                 }
                 Error::InvalidVariant(variant) => {
                     InvalidVariant::new_err(variant.to_string())
+                },
+                Error::InvalidDkgParameters(num_shares, security_threshold, min_shares_num) => {
+                    InvalidDkgParameters::new_err(format!(
+                        "num_shares: {num_shares}, security_threshold: {security_threshold}, min_shares_num: {min_shares_num}"
+                    ))
                 }
             },
             _ => default(),
@@ -128,6 +133,7 @@ create_exception!(exceptions, ValidatorPublicKeyMismatch, PyValueError);
 create_exception!(exceptions, SerializationError, PyValueError);
 create_exception!(exceptions, InvalidByteLength, PyValueError);
 create_exception!(exceptions, InvalidVariant, PyValueError);
+create_exception!(exceptions, InvalidDkgParameters, PyValueError);
 
 fn from_py_bytes<T: FromBytes>(bytes: &[u8]) -> PyResult<T> {
     T::from_bytes(bytes)
@@ -452,6 +458,7 @@ impl Dkg {
     pub fn new(
         tau: u32,
         shares_num: u32,
+        min_shares_num: u32,
         security_threshold: u32,
         validators: Vec<Validator>,
         me: &Validator,
@@ -460,6 +467,7 @@ impl Dkg {
         let dkg = api::Dkg::new(
             tau,
             shares_num,
+            min_shares_num,
             security_threshold,
             &validators,
             &me.0,
@@ -734,6 +742,7 @@ mod test_ferveo_python {
     fn make_test_inputs(
         tau: u32,
         security_threshold: u32,
+        min_shares_num: u32,
         shares_num: u32,
     ) -> TestInputs {
         let validator_keypairs = (0..shares_num)
@@ -757,6 +766,7 @@ mod test_ferveo_python {
                 let dkg = Dkg::new(
                     tau,
                     shares_num,
+                    min_shares_num,
                     security_threshold,
                     validators.clone(),
                     &sender,
@@ -777,9 +787,14 @@ mod test_ferveo_python {
         let shares_num = 4;
         // In precomputed variant, the security threshold is equal to the number of shares
         let security_threshold = shares_num;
+        let min_shares_num = shares_num;
 
-        let (messages, validators, validator_keypairs) =
-            make_test_inputs(tau, security_threshold, shares_num);
+        let (messages, validators, validator_keypairs) = make_test_inputs(
+            tau,
+            security_threshold,
+            min_shares_num,
+            shares_num,
+        );
 
         // Now that every validator holds a dkg instance and a transcript for every other validator,
         // every validator can aggregate the transcripts
@@ -788,6 +803,7 @@ mod test_ferveo_python {
         let mut dkg = Dkg::new(
             tau,
             shares_num,
+            min_shares_num,
             security_threshold,
             validators.clone(),
             &me,
@@ -817,6 +833,7 @@ mod test_ferveo_python {
                 let mut dkg = Dkg::new(
                     tau,
                     shares_num,
+                    min_shares_num,
                     security_threshold,
                     validators.clone(),
                     validator,
@@ -854,10 +871,15 @@ mod test_ferveo_python {
     fn test_server_api_tdec_simple() {
         let tau = 1;
         let shares_num = 4;
-        let security_threshold = 3;
+        let security_threshold = shares_num - 1;
+        let min_shares_num = shares_num;
 
-        let (messages, validators, validator_keypairs) =
-            make_test_inputs(tau, security_threshold, shares_num);
+        let (messages, validators, validator_keypairs) = make_test_inputs(
+            tau,
+            security_threshold,
+            min_shares_num,
+            shares_num,
+        );
 
         // Now that every validator holds a dkg instance and a transcript for every other validator,
         // every validator can aggregate the transcripts
@@ -865,6 +887,7 @@ mod test_ferveo_python {
         let mut dkg = Dkg::new(
             tau,
             shares_num,
+            min_shares_num,
             security_threshold,
             validators.clone(),
             &me,
@@ -894,6 +917,7 @@ mod test_ferveo_python {
                 let mut dkg = Dkg::new(
                     tau,
                     shares_num,
+                    min_shares_num,
                     security_threshold,
                     validators.clone(),
                     validator,
diff --git a/ferveo/src/bindings_wasm.rs b/ferveo/src/bindings_wasm.rs
index e412b6e0..5daae742 100644
--- a/ferveo/src/bindings_wasm.rs
+++ b/ferveo/src/bindings_wasm.rs
@@ -340,6 +340,7 @@ impl Dkg {
     pub fn new(
         tau: u32,
         shares_num: u32,
+        min_shares_num: u32,
         security_threshold: u32,
         validators_js: &ValidatorArray,
         me: &Validator,
@@ -352,6 +353,7 @@ impl Dkg {
         let dkg = api::Dkg::new(
             tau,
             shares_num,
+            min_shares_num,
             security_threshold,
             &validators,
             &me.to_inner()?,
@@ -510,15 +512,13 @@ impl AggregatedTranscript {
     #[wasm_bindgen]
     pub fn verify(
         &self,
-        shares_num: usize,
+        shares_num: u32,
         messages: &ValidatorMessageArray,
     ) -> JsResult<bool> {
         set_panic_hook();
         let messages = unwrap_messages_js(messages)?;
-        let is_valid = self
-            .0
-            .verify(shares_num as u32, &messages)
-            .map_err(map_js_err)?;
+        let is_valid =
+            self.0.verify(shares_num, &messages).map_err(map_js_err)?;
         Ok(is_valid)
     }
 
diff --git a/ferveo/src/dkg.rs b/ferveo/src/dkg.rs
index 3f7fc09d..cf11acf8 100644
--- a/ferveo/src/dkg.rs
+++ b/ferveo/src/dkg.rs
@@ -15,9 +15,63 @@ use crate::{
 
 #[derive(Copy, Clone, Debug, Serialize, Deserialize)]
 pub struct DkgParams {
-    pub tau: u32,
-    pub security_threshold: u32,
-    pub shares_num: u32,
+    tau: u32,
+    security_threshold: u32,
+    min_shares_num: u32,
+    shares_num: u32,
+}
+
+impl DkgParams {
+    pub fn new(
+        tau: u32,
+        security_threshold: u32,
+        min_shares_num: u32,
+        shares_num: u32,
+    ) -> Result<Self> {
+        if min_shares_num > shares_num {
+            return Err(Error::InvalidDkgParameters(
+                shares_num,
+                security_threshold,
+                min_shares_num,
+            ));
+        }
+        if shares_num < security_threshold {
+            return Err(Error::InvalidDkgParameters(
+                shares_num,
+                security_threshold,
+                min_shares_num,
+            ));
+        }
+        if min_shares_num < security_threshold {
+            return Err(Error::InvalidDkgParameters(
+                shares_num,
+                security_threshold,
+                min_shares_num,
+            ));
+        }
+        Ok(Self {
+            tau,
+            security_threshold,
+            min_shares_num,
+            shares_num,
+        })
+    }
+
+    pub fn tau(&self) -> u32 {
+        self.tau
+    }
+
+    pub fn security_threshold(&self) -> u32 {
+        self.security_threshold
+    }
+
+    pub fn min_shares_num(&self) -> u32 {
+        self.min_shares_num
+    }
+
+    pub fn shares_num(&self) -> u32 {
+        self.shares_num
+    }
 }
 
 #[derive(Clone, Debug, Serialize, Deserialize, Eq, PartialEq)]
@@ -350,6 +404,7 @@ pub(crate) mod test_common {
 
     pub fn setup_dkg_for_n_validators(
         security_threshold: u32,
+        min_shares_num: u32,
         shares_num: u32,
         my_index: usize,
     ) -> TestSetup {
@@ -359,11 +414,8 @@ pub(crate) mod test_common {
         let me = validators[my_index].clone();
         let dkg = PubliclyVerifiableDkg::new(
             &validators,
-            &DkgParams {
-                tau: 0,
-                security_threshold,
-                shares_num,
-            },
+            &DkgParams::new(0, security_threshold, min_shares_num, shares_num)
+                .unwrap(),
             &me,
         )
         .expect("Setup failed");
@@ -374,18 +426,19 @@ pub(crate) mod test_common {
     ///
     /// The [`test_dkg_init`] module checks correctness of this setup
     pub fn setup_dkg(validator: usize) -> TestSetup {
-        setup_dkg_for_n_validators(2, 4, validator)
+        setup_dkg_for_n_validators(2, 4, 4, validator)
     }
 
     /// Set up a dkg with enough pvss transcripts to meet the threshold
     ///
     /// The correctness of this function is tested in the module [`test_dealing`]
     pub fn setup_dealt_dkg() -> TestSetup {
-        setup_dealt_dkg_with_n_validators(2, 4)
+        setup_dealt_dkg_with_n_validators(2, 4, 4)
     }
 
     pub fn setup_dealt_dkg_with_n_validators(
         security_threshold: u32,
+        min_shares_num: u32,
         shares_num: u32,
     ) -> TestSetup {
         let rng = &mut ark_std::test_rng();
@@ -395,6 +448,7 @@ pub(crate) mod test_common {
             .map(|my_index| {
                 let (mut dkg, _) = setup_dkg_for_n_validators(
                     security_threshold,
+                    min_shares_num,
                     shares_num,
                     my_index as usize,
                 );
@@ -405,8 +459,12 @@ pub(crate) mod test_common {
             .collect();
 
         // Create a test DKG instance
-        let (mut dkg, keypairs) =
-            setup_dkg_for_n_validators(security_threshold, shares_num, 0);
+        let (mut dkg, keypairs) = setup_dkg_for_n_validators(
+            security_threshold,
+            min_shares_num,
+            shares_num,
+            0,
+        );
         messages.iter().for_each(|(sender, message)| {
             dkg.apply_message(sender, message).expect("Setup failed");
         });
@@ -436,6 +494,7 @@ mod test_dkg_init {
             &DkgParams {
                 tau: 0,
                 security_threshold: shares_num / 2,
+                min_shares_num: shares_num - 1,
                 shares_num,
             },
             &unknown_validator,
diff --git a/ferveo/src/lib.rs b/ferveo/src/lib.rs
index 59a44024..22f10f65 100644
--- a/ferveo/src/lib.rs
+++ b/ferveo/src/lib.rs
@@ -101,6 +101,9 @@ pub enum Error {
 
     #[error("Invalid variant: {0}")]
     InvalidVariant(String),
+
+    #[error("Invalid DKG parameters: number of shares {0}, threshold {1}, minimum number of shares {2}")]
+    InvalidDkgParameters(u32, u32, u32),
 }
 
 pub type Result<T> = std::result::Result<T, Error>;
@@ -196,8 +199,12 @@ mod test_dkg_full {
         // Works for both power of 2 and non-power of 2
         for shares_num in [4, 7] {
             let threshold = shares_num / 2 + 1;
-            let (dkg, validator_keypairs) =
-                setup_dealt_dkg_with_n_validators(threshold, shares_num);
+            let min_shares_num = shares_num - 1;
+            let (dkg, validator_keypairs) = setup_dealt_dkg_with_n_validators(
+                threshold,
+                min_shares_num,
+                shares_num,
+            );
             let msg = "my-msg".as_bytes().to_vec();
             let aad: &[u8] = "my-aad".as_bytes();
             let public_key = dkg.public_key();
@@ -235,8 +242,12 @@ mod test_dkg_full {
         for shares_num in [4, 7] {
             // In precomputed variant, threshold must be equal to shares_num
             let threshold = shares_num;
-            let (dkg, validator_keypairs) =
-                setup_dealt_dkg_with_n_validators(threshold, shares_num);
+            let min_shares_num = shares_num;
+            let (dkg, validator_keypairs) = setup_dealt_dkg_with_n_validators(
+                threshold,
+                min_shares_num,
+                shares_num,
+            );
             let msg = "my-msg".as_bytes().to_vec();
             let aad: &[u8] = "my-aad".as_bytes();
             let public_key = dkg.public_key();
@@ -295,8 +306,15 @@ mod test_dkg_full {
     #[test]
     fn test_dkg_simple_tdec_share_verification() {
         let rng = &mut test_rng();
+        let shares_num = 4;
+        let security_threshold = shares_num - 1;
+        let min_shares_num = shares_num - 1;
 
-        let (dkg, validator_keypairs) = setup_dealt_dkg_with_n_validators(3, 4);
+        let (dkg, validator_keypairs) = setup_dealt_dkg_with_n_validators(
+            security_threshold,
+            min_shares_num,
+            shares_num,
+        );
         let msg = "my-msg".as_bytes().to_vec();
         let aad: &[u8] = "my-aad".as_bytes();
         let public_key = dkg.public_key();
@@ -360,10 +378,14 @@ mod test_dkg_full {
     fn test_dkg_simple_tdec_share_recovery() {
         let rng = &mut test_rng();
 
-        let security_threshold = 3;
         let shares_num = 4;
-        let (dkg, validator_keypairs) =
-            setup_dealt_dkg_with_n_validators(security_threshold, shares_num);
+        let security_threshold = shares_num - 1;
+        let min_shares_num = shares_num - 1;
+        let (dkg, validator_keypairs) = setup_dealt_dkg_with_n_validators(
+            security_threshold,
+            min_shares_num,
+            shares_num,
+        );
         let msg = "my-msg".as_bytes().to_vec();
         let aad: &[u8] = "my-aad".as_bytes();
         let public_key = &dkg.public_key();
@@ -410,7 +432,7 @@ mod test_dkg_full {
                     &domain_points,
                     &dkg.pvss_params.h.into_affine(),
                     &x_r,
-                    dkg.dkg_params.security_threshold as usize,
+                    dkg.dkg_params.security_threshold() as usize,
                     rng,
                 );
                 (v_addr.clone(), deltas_i)
@@ -519,10 +541,14 @@ mod test_dkg_full {
     fn test_dkg_simple_tdec_share_refreshing() {
         let rng = &mut test_rng();
 
-        let security_threshold = 3;
         let shares_num = 4;
-        let (dkg, validator_keypairs) =
-            setup_dealt_dkg_with_n_validators(security_threshold, shares_num);
+        let min_shares_num = shares_num - 1;
+        let security_threshold = shares_num - 1;
+        let (dkg, validator_keypairs) = setup_dealt_dkg_with_n_validators(
+            security_threshold,
+            min_shares_num,
+            shares_num,
+        );
         let msg = "my-msg".as_bytes().to_vec();
         let aad: &[u8] = "my-aad".as_bytes();
         let public_key = &dkg.public_key();
@@ -552,7 +578,7 @@ mod test_dkg_full {
                 let deltas_i = prepare_share_updates_for_refresh::<E>(
                     &domain_points,
                     &dkg.pvss_params.h.into_affine(),
-                    dkg.dkg_params.security_threshold as usize,
+                    dkg.dkg_params.security_threshold() as usize,
                     rng,
                 );
                 (v_addr.clone(), deltas_i)
diff --git a/ferveo/src/pvss.rs b/ferveo/src/pvss.rs
index 4f63da82..db91f9d2 100644
--- a/ferveo/src/pvss.rs
+++ b/ferveo/src/pvss.rs
@@ -138,7 +138,7 @@ impl<E: Pairing, T> PubliclyVerifiableSS<E, T> {
     ) -> Result<Self> {
         let phi = SecretPolynomial::<E>::new(
             s,
-            (dkg.dkg_params.security_threshold - 1) as usize,
+            (dkg.dkg_params.security_threshold() - 1) as usize,
             rng,
         );
 
@@ -482,7 +482,7 @@ mod test_pvss {
         // Check that a polynomial of the correct degree was created
         assert_eq!(
             pvss.coeffs.len(),
-            dkg.dkg_params.security_threshold as usize
+            dkg.dkg_params.security_threshold() as usize
         );
         // Check that the correct number of shares were created
         assert_eq!(pvss.shares.len(), dkg.validators.len());
@@ -544,6 +544,7 @@ mod test_pvss {
 
         let shares_num = 4;
         let security_threshold = shares_num - 1;
+        let min_shares_num = shares_num - 1;
         let keypairs = gen_keypairs(shares_num);
         let mut validators = gen_validators(&keypairs);
         let me = validators[0].clone();
@@ -555,11 +556,8 @@ mod test_pvss {
         // And because of that the DKG should fail
         let result = PubliclyVerifiableDkg::new(
             &validators,
-            &DkgParams {
-                tau: 0,
-                security_threshold,
-                shares_num,
-            },
+            &DkgParams::new(0, security_threshold, min_shares_num, shares_num)
+                .unwrap(),
             &me,
         );
         assert!(result.is_err());
@@ -578,7 +576,7 @@ mod test_pvss {
         // Check that a polynomial of the correct degree was created
         assert_eq!(
             aggregate.coeffs.len(),
-            dkg.dkg_params.security_threshold as usize
+            dkg.dkg_params.security_threshold() as usize
         );
         // Check that the correct number of shares were created
         assert_eq!(aggregate.shares.len(), dkg.validators.len());