# UNDF: UNDF-2026-000000304
--- a/substrate/frame/aura/src/lib.rs
+++ b/substrate/frame/aura/src/lib.rs
@@ -441,6 +441,8 @@ impl<T: Config> IsMember<T::AuthorityId> for Pallet<T> {
 	fn is_member(authority_id: &T::AuthorityId) -> bool {
-		Authorities::<T>::get().iter().any(|id| id == authority_id)
+		// Authorities is stored sorted (invariant maintained by set_authorities).
+		// Binary search replaces O(A) linear scan with O(log A).
+		Authorities::<T>::get().binary_search(authority_id).is_ok()
 	}
 }

Note: Requires Authorities BoundedVec to be kept sorted. The set_authorities
call site must sort before storing. Aura already processes authorities in
session index order which is stable — sorting once on write is correct.

--- a/substrate/frame/babe/src/lib.rs
+++ b/substrate/frame/babe/src/lib.rs
@@ -508,5 +508,6 @@ impl<T: Config> IsMember<AuthorityId> for Pallet<T> {
 	fn is_member(authority_id: &AuthorityId) -> bool {
-		Authorities::<T>::get().iter().any(|id| &id.0 == authority_id)
+		Authorities::<T>::get()
+			.binary_search_by(|id| id.0.cmp(authority_id))
+			.is_ok()
 	}
 }

--- a/substrate/frame/beefy/src/lib.rs
+++ b/substrate/frame/beefy/src/lib.rs
@@ -737,5 +737,6 @@ impl<T: Config> IsMember<T::BeefyId> for Pallet<T> {
 	fn is_member(authority_id: &T::BeefyId) -> bool {
-		Authorities::<T>::get().iter().any(|id| id == authority_id)
+		Authorities::<T>::get().binary_search(authority_id).is_ok()
 	}
 }