diff --git a/Cargo.toml b/Cargo.toml
index c306f93..304c4ae 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -22,6 +22,7 @@ default-features = false
 [dependencies.rand]
 version = "0.5"
 default-features = false
+features = ["i128_support"]
 
 [dependencies.digest]
 version = "^0.7"
diff --git a/src/ed25519.rs b/src/ed25519.rs
index 8760a3f..9a2d2a9 100644
--- a/src/ed25519.rs
+++ b/src/ed25519.rs
@@ -935,13 +935,18 @@ where
     use std::vec::Vec;
 
     use core::iter::once;
+    use rand::thread_rng;
 
     use curve25519_dalek::traits::IsIdentity;
     use curve25519_dalek::traits::VartimeMultiscalarMul;
 
-    let zs: Vec<Scalar> = signatures.iter().map(|_| Scalar::random(csprng)).collect();
+    // Select a random 128-bit scalar for each signature.
+    let zs: Vec<Scalar> = signatures
+        .iter()
+        .map(|_| Scalar::from(thread_rng().gen::<u128>()))
+        .collect();
 
-    // Compute z $= ℤ/lℤ, (∑ s[i]z[i] (mod l))
+    // Compute the basepoint coefficient, ∑ s[i]z[i] (mod l)
     let B_coefficient: Scalar = signatures
         .iter()
         .map(|sig| sig.s)