diff --git a/coins/monero/src/frost.rs b/coins/monero/src/frost.rs
index e0cef7c4..0a276288 100644
--- a/coins/monero/src/frost.rs
+++ b/coins/monero/src/frost.rs
@@ -11,7 +11,7 @@ use curve25519_dalek::{
   edwards::EdwardsPoint as DPoint
 };
 
-use ff::PrimeField;
+use ff::{Field, PrimeField};
 use group::Group;
 
 use transcript::{Transcript as TranscriptTrait, DigestTranscript};
@@ -59,6 +59,10 @@ impl Curve for Ed25519 {
     true
   }
 
+  fn random_nonce<R: RngCore + CryptoRng>(_secret: Self::F, rng: &mut R) -> Self::F {
+    dfg::Scalar::random(rng)
+  }
+
   // This will already be a keccak256 hash in the case of CLSAG signing, making it fine to simply
   // return as-is, yet this ensures it's fixed size (a security requirement) and unique regardless
   // of how it's called/what it's called with
diff --git a/crypto/frost/src/lib.rs b/crypto/frost/src/lib.rs
index a600466a..54abee1d 100644
--- a/crypto/frost/src/lib.rs
+++ b/crypto/frost/src/lib.rs
@@ -3,6 +3,8 @@ use std::collections::HashMap;
 
 use thiserror::Error;
 
+use rand_core::{RngCore, CryptoRng};
+
 use ff::{Field, PrimeField};
 use group::{Group, GroupOps};
 
@@ -32,7 +34,7 @@ pub enum CurveError {
 // It uses GenericArray which will hopefully be deprecated as Rust evolves and doesn't offer enough
 // advantages in the modern day to be worth the hassle -- Kayaba
 pub trait Curve: Clone + Copy + PartialEq + Eq + Debug {
-  /// Field element type
+  /// Scalar field element type
   // This is available via G::Scalar yet `C::G::Scalar` is ambiguous, forcing horrific accesses
   type F: PrimeField;
   /// Group element type
@@ -57,6 +59,9 @@ pub trait Curve: Clone + Copy + PartialEq + Eq + Debug {
   /// If little endian is used for the scalar field's Repr
   fn little_endian() -> bool;
 
+  /// Securely generate a random nonce. H4 from the IETF draft
+  fn random_nonce<R: RngCore + CryptoRng>(secret: Self::F, rng: &mut R) -> Self::F;
+
   /// Hash the message for the binding factor. H3 from the IETF draft
   // This doesn't actually need to be part of Curve as it does nothing with the curve
   // This also solely relates to FROST and with a proper Algorithm/HRAM, all projects using
@@ -80,7 +85,7 @@ pub trait Curve: Clone + Copy + PartialEq + Eq + Debug {
   #[allow(non_snake_case)]
   fn hash_to_F(dst: &[u8], msg: &[u8]) -> Self::F;
 
-  /// Constant size of a serialized field element
+  /// Constant size of a serialized scalar field element
   // The alternative way to grab this would be either serializing a junk element and getting its
   // length or doing a naive division of its BITS property by 8 and assuming a lack of padding
   #[allow(non_snake_case)]
diff --git a/crypto/frost/src/sign.rs b/crypto/frost/src/sign.rs
index ae33735b..5ccb139c 100644
--- a/crypto/frost/src/sign.rs
+++ b/crypto/frost/src/sign.rs
@@ -80,7 +80,10 @@ fn preprocess<R: RngCore + CryptoRng, C: Curve, A: Algorithm<C>>(
   rng: &mut R,
   params: &mut Params<C, A>,
 ) -> PreprocessPackage<C> {
-  let nonces = [C::F::random(&mut *rng), C::F::random(&mut *rng)];
+  let nonces = [
+    C::random_nonce(params.view().secret_share(), &mut *rng),
+    C::random_nonce(params.view().secret_share(), &mut *rng)
+  ];
   let commitments = [C::generator_table() * nonces[0], C::generator_table() * nonces[1]];
   let mut serialized = C::G_to_bytes(&commitments[0]);
   serialized.extend(&C::G_to_bytes(&commitments[1]));
diff --git a/crypto/frost/src/tests/literal/p256.rs b/crypto/frost/src/tests/literal/p256.rs
index 75aa07bb..c36a046d 100644
--- a/crypto/frost/src/tests/literal/p256.rs
+++ b/crypto/frost/src/tests/literal/p256.rs
@@ -1,9 +1,9 @@
 use core::convert::TryInto;
 
-use rand::rngs::OsRng;
+use rand::{RngCore, CryptoRng, rngs::OsRng};
 
 use ff::{Field, PrimeField};
-use group::GroupEncoding;
+use group::{Group, GroupEncoding};
 
 use sha2::{digest::Update, Digest, Sha256};
 
@@ -102,6 +102,13 @@ impl Curve for P256 {
     false
   }
 
+  fn random_nonce<R: RngCore + CryptoRng>(secret: Self::F, rng: &mut R) -> Self::F {
+    let mut seed = vec![0; 32];
+    rng.fill_bytes(&mut seed);
+    seed.extend(&secret.to_repr());
+    Self::hash_to_F(&[CONTEXT_STRING, b"nonce"].concat(), &seed)
+  }
+
   fn hash_msg(msg: &[u8]) -> Vec<u8> {
     (&Sha256::new()
       .chain(CONTEXT_STRING)
@@ -151,7 +158,7 @@ impl Curve for P256 {
       .map_err(|_| CurveError::InvalidLength(33, slice.len()))?;
 
     let point = ProjectivePoint::from_bytes(&bytes.into());
-    if point.is_none().into() {
+    if point.is_none().into() || point.unwrap().is_identity().into() {
       Err(CurveError::InvalidPoint)?;
     }